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ig^ In the Press, 

I.— A SCHOOL HISTORY OF ENGLAND. 

II.— AN ARITHMETIC FOR BEGINNERS. 



LONDON : 

•IMPKIN, MARSHALL. & CO., STATIONERS' HALL COUBI 

HAMILTON, ADAMS, & CO., PATERNOSTER ROW; 

WHITTAKER & CO,, AVE MARIA LANE. 

EDINBURGH: OLIVBB & BOYD. 



DR. CORNWELL'S EDTJCATIQML WOEKS. 

ARITHMETIC FOR BEGINNERS. 

BEING AN 

ELEMEKTAKY INTRODUCTION TO 

COENWELL AND FITCH'S 
SCHOOL AEITHMETIC. 




SAME AUTHOES. 



LONDON: 
SIMPKIN, MARSHALL & CO., STATIONERS' HALL COURT j 

HAMILTON, ADAMS AND CO., PATERNOSTER ROW ; 

WHITTAKER AND CO., AVE MARIA LANE, 

EDINBURGH : OLIVER AND BOYD. 

1872. 



''Ifir 

LONDON : 



PBINTBD BY J. AND W. BIDEB, 
BAKIHOLOMEW CLOSE. 




PREFACE. 



In preparing tliis "Arithmetic for Beginners" an en- 
deavour has been made to keep in view two or tliree 
simple principles which are suggested by familiar expe- 
rience in teaching, but which are often overlooked : — 

(1) That yount? children learn the processes and mean- 
ing of arithmetic more readily by the help of short, easy 
jDroblems, than by dealing at first with numbers too large 
for their imagination to grasp: 

(2) That the diflficulties of this study should be pre- 
sented to the understanding of a learner one at a time. 

(3) That as soon as each principle or rule has been 
learned and illustrated, exercises are needed, calling on 
the scholar to put the rule or principle into practice. 

Accordingly, it will be found that the sums and examples 
in this little book are very simple, dealing for the most 
part with the familiar computations in use in ordinary 
life. They are so grouped and graduated that each step 
is seen to be a very natural sequel to the former. The 
tables of notation, addition, and multiplication are so 
divided, that as soon as each small portion of them 
is learned, a few exercises are given in the use of that 
portion before the next portion is attempted. 

The range of the book includes all the most important 
applications of the simple and compound rules, and a 
brief introduction to Fractions, but does not extend to' 
Proportion and Decimals. 



CONTENTS. 



TAQM 
SIMPLE NUMBERS AND THEIR NAMES . . . . .6 

COUNTING . 6 

NUMBERS COMPOSED OF TENS ....... 6 

COUNTING 8 

ADDING AND SUBTRACTING . . . . . . .12 

HUNDREDS .......... 15 

THOUSANDS 19 

THE MULTIPLICATION TABLE AND ITS USES . . . .21 

MILLIONS 28 

LONG MULTIPLICATION 30 

DIVISION .......... 34 

SIGNS AND THEIR USES 40 

EXERCISES IN SIGNS . . . . . . . .41 

MISCELLANEOUS EXAMPLES IN SIMPLE RULES . . . .42 

MONEY 44 

MONEY TABLES 46 

ADDITION AND SUBTRACTION OF MONEY 47 

MULTIPLICATION OF MONEY 64 

HOUSEHOLD ACCOUNTS AND SIMPLE BILLS . . . .68 

SIMPLE REDUCTION AND OTHER USES OF MULTIPLICATION . . 60 

DIVISION OF MONEY 62 

REDUCTION AND OTHER USES OF DIVISION . . . .66 

MISCELLANEOUS EXERCISES . . . . . , . 68 ' 

WEIGHT 69 

LENGTH 72 

SURFACE 76 

CAPACITY OR BULK 79 

TIME 81 

INTRODUCTION TO FRACTIONS 85 

MULTIPLICATION AND DIVISION BY FRACTIONAL NUMBERS . . 87 
ANSWERS TO EXERCISES 90 






AElTHilETIC FOR BEGINNERS. 



SIMPLE NUMBERS AND THEIR NAMES. 

NAME OF THE OBJECTS. NUMBER OF THE SPOTS SHOWN. 

SPOTS. IN WORDS. IN FIGURES. 

• One I 

• • Two 2 

• • • Three 3 

• • • • Four 4 

• • • • • Eive 5 

• ••••• Six 6 

• •••••• Seven 7 

• ••••••• Eight 8 

• •••••••• Nine 9 

Exercise I. 

^» (i) Say what is tJie name of each figure : — 
4, 7, 3» 2> 6, 5, 7, I, 9i 8. 
(2) Write the figure for each mimher : — 
Nine, three, four, seven, five, six, three, eight, two. 



6 ahithmetic for beginners. 

Counting. 

[Nine counters, marbles or pebbles, should be used, 
and the learner may be allowed to use the fingers for 
finding each result.] 

1. Count how many fingers you have on your hand. 

2. Take two away, and how many remain ? 

3. How many letters are there in the word " JSTumber " 1 

4. If I have five shillings in my purse, and put three 
more in, how many have I 1 

5. There are eight children in a class, and four go aAvay; 
how many are left 1 

6. Begin with the number nine, and say the numbers 
backwards, taldng away one each time. 

(7) Place under each of the following pairs of figures the 
sum to which they amount : — 

46525746 
32173123 



(8) Place under each of the following pairs of figures 
the difference between them : — 

87645987 
24333453 



NUMBERS COMPOSED OF TENS. 

!• "When a figure stands in the second place to 
the left, it means ten times more than if it stands in 
the first. Thus,— 



II 


Ten and one 


eleven 


12 


Ten and two 


twelve 


n 


Ten and three 


thirteen 


16 


Ten and six 


sixteen 


10 


Ten and nine 


nineteen 


24 


Two tens and four 


twenty-four 



NUMBEES AND THEIR NAMES. 7 

57 Five tens and seven fifty-seven 

63 Six tens and three sixty-three 

88 Eight tens and eight eighty-eight 

14 Ten and four fourteen 

47 Four tens and seven forty-seven 

93 Nine tens and three ninety-three 

65 Six tens and five sixty-five 

72 Seven tens and two seventy-two 

99 Nine tens and nine ninety-nine 

Exercise II. 
1^ (i) Give the figures for these numhers : — 
Thirty-four, seventeen, sixty-five, forty-three. 
Eighty-seven, twenty-five, seventy-six, fifty-two. 
Ninety-six, eighty-four, twenty-six, thirty-nine. . 

(2) Give the mimhers for these figures : — 
12, 34, 29, 64, 83. 
25, 52, • 95, 72, 81. 
i3> 62, 94, 31. 24. 

^* A cipher or is used to show that there is 
no number to fill a vacant place. Thus, — 

lo means ten. 

20 „ two tens, or twenty. 

30 ,, three tens, or thirty. 

50 „ five tens, or fifty. 

70 „ seven tens, or seventy. 

Exercise III. 
1^ (i) Put into figures these numhers : — 

Seventy, ninety, twenty, eighty, forty, ten. 

(2) Fut into words the figures — 

20, 50, 80, 30, 70, 90, 10. 

(3) Write out in order the tohole of the figures from one 
to ninety-nine. 



8 arithmetic fou beginnees. 

Counting. 

[A box of marbles or pebbles, a bag of nuts or some 
counters, should be used; the abacus or ball-frame will 
also be useful. At first no greater number than twelve 
should be placed before the learner.] 



The following should be learned by heart 



Two and one are three 



two 

three 

four 

five 

six 

seven 

eight 

nine 

ten 

eleven 

twelve 



four 

five 

six 

seven 

eight 

nine 

ten 

eleven 

twelve 

thirteen 

fourteen 



3 
4 

5 
6 

7 
8 

9 

lO 

II 

12 
13 
14 



Three and one are four 



eight 

nine 

ten 



two „ five 

three „ six 

four „ seven 

five „ eight 8 

six „ nine 9 

seven „ ten 10 

„ eleven 1 1 
„ twelve 1 2 
„ thirteen 13 

eleven „ fourteen 14 

5 



twelve „ fifteen i 



Exercise IV. 

1. Count the fingers of both hands; the panes of glass 
in the window ; the books on the table ; the scholars in 
the class. 

2. If I have three nuts in one pocket, and four in the 
other, how many have I ? 

3. Place two pebbles in one hand and five in the 
other, and say how many they make. 

4. Add five farthings to three. 

5. How many legs are there on two chairs? 

6. Count out as many pebbles as you have fingers on 
your hand. 

7. Arrange on the floor as many stones as there are 
panes in the window, or children in the class. 

8. Make four marks on a slate ; add three more ; count 
them all together. 



SIMPLE COUNTING. 9 

9. If there are ten scholars in the class, and four go 
away, how many are left 1 

10. Out of six pence I spend four pence ; how many 
pence are left ? 

11. How many more are eight nuts than three ? 

12. One child has .ten apples, and the other seven; 
how many more has the first ? 

13. Make twelve strokes on the slate ; rub out three, 
and see how many remain. 

14. Place eleven marbles on the floor; take two away, 
and say how many remain. 

15. Begin with the number twelve, and repeat back- 
wards to one. 

16. Say how many letters are in each word of the first 
line on this page. 

17. What is the difference between the number of 
letters in " Caroline " and in " Jane " 1 



Exercise Y. 

1. Two and four, seven and three, eight and two, nine 
and one, four and three, two and six, eight and three, 
three and five. 

2. Take two from eight, from seven, from nine, from 
six, from five. 

3. Take three from twelve, from seven, from eleven, 
from ten, from nine, from eight. 

4. Add 6 to 3, 2 to 7, 5 to 3, 3 to 7, 8 to 2. 

5. Add 7 to 2, 3 to 8, 6 to 3, 9 to 2. 

6. What is the difference between 10 and 12, between 
II and I, between 4 and 6, between 9 and 3 '? 

7. Take 2 from 11, from 9, from 7, from 6, from 3. 

8. Take 3 from 12, from 4, from 9, from 5, from 8. 

9. Take 7 from 9, from 10, from 8, from 12. 

10. Take 5 from 10, from 12, from 9, from 7. 

1 1. How many more are 1 2 than 8, than 6, than eleven, 
than four ? 

12. How many should be added to twelve to make 
fifteen ? 

B 2 



10 



AEITHMETIC FOB- BEGINXEBS. 



Exercise YI. 

1^ (i) Place underneath each of the follotoing pairs 
of figures the sum to which they amount: — 

754756989 
232323233 



(2) Place underneath each of the following x>ciirs of 
figures the difference hetween them : — 

5 7 8 9 12 8 7 6 9 10 II 
23263513638 













The folloicing shoidd he learned 


hy heart : — 




Four and four are eight 


8 


Five and five are ten 


10 


„ five „ nine 


9 


5) 


six „ eleven 


II 


„ six „ ten 


10 


)j 


seven „ twelve 


12 


„ seven „ eleven 


TI 


)> 


eight „ thirteen 


13 


„ eight „ twelve 


12 


» 


nine „ fourteen 


J4 


„ nine „ thirteen 


13 


)) 


ten „ fifteen. 


15 


„ ten „ fourteen 


U 


JJ 


eleven „ sixteen 


16 


„ eleven „ fifteen 


15 


)} 


twelve „ seventeen 


17 


„ twelve „ sixteen 


16 








Six and six are twelve 


12 


Seven and seven are — 




„ seven „ thirteen 


13 




fourteen 


14 


„ eight „ fourteen 


14 


» 


eight are fifteen 


15 


„ nine „ fifteen 


15 


» . 


nine „ sixteen 


16 


„ ten „ sixteen 


16 


j> 


ten „ seventeen 


17 


„ eleven „ seventeen 


17 


J) 


eleven „ eighteen 


18 


„ twelve „ eighteen 


18 


j> 


twelve „ nineteen 


19 



Eight and eight are sixteen 16 
,, nine are seventeen 17 
„ ten ,, eighteen 18 
„ eleven „ nineteen 19 
„ twelve „ twenty 20 



Nine and nine are — 

eighteen 18 
„ ten are nineteen 19 
„ eleven „ twenty 20 
„ twelve „ twenty-one 2 1 



COUNTING. 11 

Exercise VJX 

1. There are two piles of books, seven in one and five 
in the other ; how many are there in all ? 

2. Find the difference between 15 and 7. 

3. Eight cows are in one field, and nine in the other; 
how many are there in all ] 

4. There are nine lamps in one street, and five in the 
other ; how many are there in both ? How many more 
are there in one street than in the other 1 

5. Take the number eighteen, and repeat the ^numbers 
backwards to one. 

6. Suppose there were seventeen sticks in a row, and 
yon took away two, and then two, and then two, &c., how 
many would be left each time i 

7. Add four apples to seven, and take away three. 

8. If out of seventeen nuts I give away four, how many 
remain? 

9. How many more are eighteen than three I 

10. Of twelve eggs four were broken; how many 
remained ? 

11. Take seven shillings out of a purse containing 
fifteen ; five out of twelve ; eight out of sixteen. 

12. How many days are in two weeks? 

13. How many hours is it from four o'clock to eleven ? 

Exercise Vill. 

I^° (i) Place underneath each of the following pairs 
of figures the sum to which they amxmnt : — 

79864698 
43859435 



(2) Flace underneath each of the following pairs of 
figures the difference between them : — 

12 16 14 8 10 15 18 II 13 
579357946 



12 ARITHMETIC FOR BEGINNERS. 

ADDING AND SUBTRACTING HIGHER 
NU^IBERS. 

3. AVhen numbers are "written with, two or more 
figures, and have to be added or subtracted, the sum must 
be worked by steps. 

Example I. Add eighteen to twenty-four. 

2 I 4 24 Eight and four are twelve. 

I I 8 18 One ten and two tens are three tens. 
— So 24 and 18 amount to 3 tens and 12. 

3 I 1 2 42 But twelve consists of one ten and two. 

Therefore there are in all four tens and 
two. 

The one ten is " carried " from the right column to the 
left, and the answer is forty-two. 

Whenever the figures in a column amount to more 
than ten, the ten or tens are carried to the next. 

Example II. Take twenty-three from fifty-seven. 

57 Three from seven leaves four. 

23 Two tens from five tens leaveg three tens. 

— So twenty-three taken from fifty-seven leaves 

34 thirty-four. 

Exercise IX. 

(i) Work these additions : — 
24 39 68 59 38 54 63 36 
13 42 24 32 16 21 12 14 



(2) Place underneath each pair of numbers the differ- 
ence between them : — 

47 84 65 69 85 48 6z 35 28 
23 51 14 10 31 24 30 14 12 



SUBTRACTION. 13 

4. Sometimes one figure of the number to be taken 
away is greater than the figure above it. Thus, — 

73 Twenty-eight can be taken from seventy-three, 

28 but eight cannot be taken from three. 

— In such cases we add ten to both lines. 
Add ten to the three ^ \ 7 I 

Eight from thirteen leaves five 8 ( 18 

Add ten to the two tens - ^ ' 



I 



Three tens from seven tens leaves 

four tens. ^ ^ 

Adding ten to both does not alter the difference.* 

So the difference between 73 and 28 is 45. 

o. In subtracting it is better to set down the greater 
number above the less. 

Exercise X. 

1^^ Place underneath each pair of numbers the differ- 
ence bettceen them : — 

17 20 35 71 93 85 50 33 12 
9 16 16 24 26 17 16 28 7 



1. Take sixteen from twenty, twenty-nine from sixty- 
five, forty-three from eighty-one. 

2. !N'inety hurdles are wanted to make a fence, and the 
owner has only forty-seven; how many more must he buy ? 

3. How much are twenty-four pence more than nine 
pence ] 

4. If I have fifty books, and give away eighteen, how 
-many remain ] 

5. How many shillings are in two purses, of which the 
one contains twenty-nine, and the other forty-seven ] 

6. How many must be added to seventeen marbles to 
make forty ] 

7. Take from eighty, the two numbers, forty-two and 
seventeen, and say what remains. 

* See "School Arithmetic," p. 12, and "Science of Arithmetie," 
Axiom YI. 



14 ARITHMETIC TOR BEGIITNERS. 

8. Count the letters in eacli of the two lines of this 
question, and find the difference. 

9. If a man owes me ;£'75, and pays me only ;£'48, 
how much is he still in my debt ? 

10. Of thirty-five children in a school eighteen go home ; 
how many remain 1 

11. Take thirty-six pence from seventy. 







Exercise XT. 






}^ Work the following 


addition 


sz^ms : — 




(I.) 8 

10 






(2-) 9 

2 




36 


7 
26 


29 
12 


6 


35 
8 


53 
17 


12 
5 


19 


20 


12 


10 


6 


20 


4 


18 


20 


17 


20 


7 


20 


7 


15 


6 


3 


15 



3. Add together 14, 7, 30, and 6. 

4. Find the sum of 28, 16, and 54. 

5. How much do twenty-seven, twenty-eight, and 
twenty-nine make ? 

6. A man has to pay four bills, of ^26, ^g, £zi9 
and ;£'2o each ; to what sum do they amount ? 

7. There are four paths in a garden, measuring 29 yards, 
31 yards, 27 yards, and 18 yards respectively; what is 
their total length ? 

8. Add together 46 and 36, and take 26 from the 
amount. 

9. Out of -QS'^i I first pay a bill of ;^i7 and then 
another of ;£2 2 ; how much have I left ? 

10. Add together 10, 11, 12, and 13, and take the 
amount from seventy-five. 

11. Take forty-six from the sum of 22, 23, and 24. 

12. How many times can eight be taken from 90 ? 



HinfDEEDS. 15 

G. When a fignre stands in the third place from the 

right it. means hundreds. 

Thus, 731 seven HUNDRED and thirty-one. 

800 eight HTINDRED. 

210 two HUNDRED and ten. 
305 three hundred and five. 

Exercise XII. 
^^ (i) Read in vjords the following figures : — 
902, 516, 201, 824, 753, 961. 
587, 911, 340, 921, 812. 
Explanation. — ^The first numher is made np of nine 
hundred, no tens and two, and is read nine hundred and 
two. The second is made up of five hundred, one ten 
and six, and is read five hundred and sixteen. 

(2) Give the figures for the follomng numbers : — 
Seven hundred and eleven. Three hundred and six. 
Four hundred and fourteen. Eive hundred and nine. 
Eight hundred and twelve. Three hundred and seventy-four. 
Six hundred and nineteen. !Xine hundred and twelve. 
Five hundred and ten. Four hundred and fifty. 

Examjple of Addition of Hundreds. 



3 


6 


5 


= Three hundred and sixty-five 


5 


I 



8 
4 


= Eighteen. 

= Five hundred and four. 




3 

I 


9 

2 


= Thirty-nine. 
=: Twelve. 



9 I 3 I 8 = iS^ine hundred and thirty-eight. 

Two and nine, and four, and eight, and five, make 
twenty-eight. Set down eight and carry two tens. 

Two tens, and one, and three, and one, and six, make 
thirteen tens, or one hundred, and three tens. Set down 
three tens and carry one hundred. 

One hundred, and five, and three, make nine hundred. 
Set down nine hundred. 

The whole sum is nine hundred and thirty-eight. 



16 ARITmiETIC TOR BEGINNERS. 

7. Caution. — Always put figures of the same meaning 
in the same column, — tens under tens, hundreds under 
hundreds, &c. 

Exercise XIII. 
Work the follmcing additions : — 

(•■) 







(2 


.) 268 


321 


185 


) 231 


212 


610 


15 


250 


27 


28 


83 


19 


305 


18 


3 


540 


124 


124 


219 


302 


19 


79 


71 


63 


6 


65 


204 


6 


60 


115 


54 


4 


12 















3. There are in a library forty-two books in one row, 
twenty-eight in another, eighty in another, and sixteen in 
the last ; how many are there in all ? 

4. A man owes ^£719 to Jones, ^£28 to Smith, ;£ioo 
to Brown, and ;3ji7 to Johnson; what does he owe 
altogether 1 

5. Count the panes in four windows, having twenty-four 
panes in each. 

6. On a farm are 14 oxen, 208 sheep, 17 horses, and 
3 1 pigs ; how many animals in all 1 

7. In the five classes of a school there are nineteen, 
twenty-seven, thirty, fifteen, and twenty four ; how many 
are there in all ? 

8. Add together a dozen, a score, six, and eleven. 

9. In four bags of marbles there are 27, 16, 39, and 20 
respectively ; how many marbles are there in all 1 

10. If I change half a sovereign into twenty sixpences, 
half a crown into five, and a florin into four, and if I 
have seventeen sixpences besides, how many sixpences 
have I in all '? 

1 1. There were three candidates at an election, of whom 
the first had 159 votes, the second 216, and the third 
four hundred ; how many people voted 1 



SUBTRACTION. 17 

8. In subtracting, add ten to the npper line whenever 
the figure beneath cannot be taken from it. But when- 
ever ten is added to the npper line it mnst also be added 
as one, to the figore next to the left on the lower line. 

Example of working Subtraction with Hundreds. 

What is the difTerence between 385 and 731 1 
Set down the crreater number above the other. 



o 



731) 7 I 13 

385 ', _ 4 1 9 



II Since 5 cannot be taken 

5 from I, add ten to the one (4). 

— Five from eleven leaves six. 



346 ) 3 I 4 I 6 Set down six- 

Add one ten to eight tens in the lower line. 
9 tens cannot be taken from 3 tens, so add ten ten* to 

the upper line. 

Nine from thirteen leaves four. Set down 4 tens. 
Add ten tens, which are one hundred, to the 3 hundred. 
Four hundreds from seven hundreds leaves three 

^hundreds. Set down 3 hundreds. 

The difference is three hundred and forty-six. 

EXERCISB XIY. 

1. Add together three hundred and four, five hundred 
and seventeen, and one hundred and thirty-eight. 

2. Take sixty-five from one hundred j and three hun- 
dred and fourteen from six hundred. 

3. How many more books has one gentleman who has 
856 in his library than another who has 695 ? 

4. What sum given to a person who has 28 pounds 
would make up his money to 50 pounds ? 

5. How many must be put in a bag containing 163 
nuts to make up the number to 350 1 

6. Out of a set of 150 prints, 26 are lost : how many 
remain ? 

7. Of two windows, containing twenty-four panes 
each, seventeen panes are broken : how many remain 
whole 1 



18 ARITHMETIC TO*. BEGINNERS. 

8. A person lias saved jQi^"] : how mucli more must 
lie save to make up ;^5oo 1 

g. '\'\niat is the difference between the incomes of two 
persons, of whom one has ^6y^, and the other ;^85o a 
year ? 

lo. At an election one candidate has 847 votes, and the 
other 691 : what is the majority'^ 

T 1. A man owes two sums of money, ;£6^ and jQi^'y 
he has only £^^0 to pay : hoAV much does he still owe % 

12. Out of a debt of ;£'ioo a man pays first ^^25 and 
afterwards jQ2)^ : how much remains unpaid ] 

13. Add together three hundred and fourteen and tAvo 
hundred and seventy six, and take four hundred and six- 
teen from the result. 



Work the following siibtractions : — 

(14.) 729 512 840 (15.) 368 500 

434 326 127 29 124 



(16.) 287 206 597 (17.) 500 240 629 
153 9 329 18 73 142 



18. Take 187 and 456 from 900. 

19. From 314 and 625 take 274. 

20. A man drives 32 miles on Monday, 25 on Tuesday, 
24 on Wednesday, rests on Thursday, drives again 20 
miles on Friday, and 18 on Saturday: how far has he 
travelled in the week % 

21. In two villages, containing 136 and 348 people 
respectively : what is the total population % 

22. At the census of 1861 a parish had 343 inhabi- 
tants, and in 187 1 there were 512 ; what was the in- 
crease ? 

23. Take the sum of 243 and 356 from nine hundred 
and fifty. 



THOUSANDS. 19 

0. When a figure, stands in the fourth place from the 
right it means thousands. Thus, — 

1340 One THOUSAND three hundred and forty. 

7298 Seven thousand two hundred and ninety-eight. 

2000 Two THOUSAND. 

3040 Three thousand and forty. 
5012 Five THOUSAND and twelve. 

Exercise XY. 
^p° (i) Read in wfyrds these figures : — 

7342, 1085, 71 12, 9026, 3720, 5102. 
8721, 1963, 2018, 1702, 3960, 8541. 
2165, 3094, 2708, 6130, 5291, 5012. 

(2) Express in figures these numbers : — 

Three thousand nine hundred and twelve. Two 
thousand and seventeen. Five thousand and nine. Six 
thousand eight hundred and twelve. Four thousand and 
fourteen. Five thousand six hundred and four. ^Nine 
thousand eight hundred and eighty-eight. Four thousand 
and fifty. Six hundred and forty-one. One thousand 
two hundred and eleven. 

Exercise XYI. 

1. How many miles would a man travel in a week who 
went 58 miles on Monday, 126 on Tuesday, 70 on 
Wednesday, 119 on Thursday, 310 on Friday, and 67 on 
Saturday ? 

2. If there are five hundred and forty-six people living 
in one street, two thousand seven hundred and four 
in another, and three hundred and eleven in the next, 
how many are there in all 1 

3. An irregularly shaped field has four sides, of which 
the first is 1204 feet long, the second 395, the third 2038, 
and the fourth 685 ; how many feet are there in the 
fence surrounding the field ] 



20 ARITHMETIC FOB, BEGINNERS. 

4. If a man has five debtors who owe him ;^57, 
;£io38, ^19, ;^2i2, and ;£"66 respectively, how mnch 
is owing to him 1 and if he owes ;£"2 95, what is he worth ? 

5. How much longer is a road a thousand miles long 
than one measuring 674 miles ? 

6. To what sum must I add ^£'453 to make up ;!^84o 1 

7. Three boys have respectively 79 nuts, 83 nuts, and 
220 nuts; how many has the last more than the two 
others put together 1 

8. If at an election 794 voted for A, 1628 for B, and 
1577 for C, what was the majority of B over C, of B over 
A, and of C over A "? 

9. Take 372 twice from a thousand, and say what 
remains. 

1^ In the folloiclng sums, lilace iDords by the side of 
each line, thus : — 

17 1 2 One thousand seven hundred and twelve. 

29 Twenty-nine. 

4804 Eour thousand eight hundred and four. 

712 Seven hundred and twelve. 

16 Sixteen. 

7273 Seven thousand two hundred and seventy-three. 



(12.) 







Addition. 






3162 


2984 


1061 (11.) 


127 


219 


845 


127 


2138 


3069 


62 


17 


3206 


547 


218 


1357 


209 


518 


1019 


57 


287 


1630 


79 


67 


135 


4096 


7 


3120 


125 


2634 


23 






Suhtradion. 






1270 


2160 


7140 (13) 


51^30 


2070 


184 


1329 


2765 


2271 


614 







_, 







MULTIPLICATION. 



21 



THE MLLTIPLICATIOX TABLE AIS^D ITS USES. 
10« The following shoidd he learned hy heart: — 



Two twos are four . . 4 


Three threes are nine . 9 


„ threes „ six . . 6 


„ fours are twelve . .12 


„ fours „ eight . . 8 


„ fives „ fifteen . .15 


„ fives „ ten . . 10 


„ sixes „ eighteen . 18 


„ sixes „ twelve . 12 


„ sevens „ twenty-one 21 


„ sevens „ fourteen . 14 


„ eights „ twenty-four 2 4 


„ eights „ sixteen . 16 


„ nines „ twenty- 


„ nines „ eighteen . 18 


seven 27 


„ tens „ twenty . 20 


„ tens „ thirty . .30 


„ elevens „ twenty-two 2 2 


„ elevens „ thirty- three 33 


„ twelves „ twenty-four 2 4 


„ twelves,, thirty six . 36 



These numbers are found by adding two and three 
at each step. 

Exercise XVIL 

1. How many legs have three chairs ? 

2. How many fingers are there on three hands ? 

3. If there are eight panes of glass in each window, 
how many in two windows ? In three ? 

4. In three purses containing eight shillings each, how 
many shillings are there ? 

5. What is the half of 12 ? of 16 ? of 1 8 ? of 20 ? 

6. What is the third part of 12 ] of 15 ? of 9 ? of 6 ? 

7. Divide twelve pence among two persons. Among 
three. 

8. Give fifteen nuts among three persons ; how many 
has each? 

9. "What is the third part of twenty-one ? 

10. How many threes are there in twelve % how many 
twos] 

1 1. What number multiplied by five gives fifteen % 

12. How many rows of twelve each could be made of 
twenty-four soldiers ? of eight each ? 



22 ABITHMETIC FOE EEGINXEBS. 

11. "When sums are worked in multiplication, a part 
of each answer is set doTni, and the rest carried, as in 
addition. See 3. 

Example I. 

Multiply 1762 by two. 



I 


7 


6 


2 
2 


1762 
2 


^ 


14 


12 


4 


3524 



Twice 2 are 4. Set down 4. 

Twice 6 teus are 12 tens. Set down 2 tens and remove 
10 tens, that is i hundred, to the hundreds. 

Twice 7 hundreds are 14 hundreds, and i hundred 
brought from the tens makes 15 hundreds. Set down 5 
hundreds and remove 10 hundreds, that is, i thousand, to 
the thousands. 

Twice I thousand is 2 thousand, and i brought from 
the hundreds makes 3 thousand. 

The result is 3,524. 



Example II. 

8 5718 

3 3 



'!■ 



15 I 21 I 3 I 24 17154 



Note. — The same should be set down as on the right. 

Exercise XVni. 

1. Find twice eighteen ; Three times twenty-five. 

2. Multiply forty-six by two; Thirty-eight by three. 

3. In three fields containing 106 sheep each, how many 
sheep % 

4. On two pages containing 453 words each, how many 
words? 

5. How many letters are there in 245 words of three 
letters each ? 



MUXTIPLICATIOX. 23 

6. In 3 rows of 169 trees each, how many trees ? 

7. Find the difference between twice forty-six and 
three times fifty-seven. 

8. In five columns of names, two contain thirty-eight 
each, and three contain thirty-seven each ; how many are 
there in all ? 

1^ Wo rTc the folloioing questions : — 
(9.) 17 529 123 1406 (10.) 718 627 526 
2323 223 



sixes „ thirty . 


•30 


sevens „ thirty-five 


•35 


eights „ forty . 


. 40 


nines „ forty-five 


•45 


tens „ fifty . . 


•50 


elevens „ fifty-five 


.55 


twelves „ sixty . 


.60 



Multiplication Table {continued). 

The following should he learned hy heaH : — 

Four fours are sixteen . 16 . Five fives are twenty-five 25 

„ fives „ twenty . . 20 

„ sixes „ twenty-four 24 

„ sevens „ twenty-eight 28 

„ eights „ thirty-two .32 

„ nines „ thirty-six .36 

„ tens „ forty . . 40 

„ elevens,, forty-four .44 

„ twelves,, forty-eight . 48 
12. It is not necessary that all these tables shall be of 
the same length, and shall begin with the number two. 
For five times three is the same as three times five, 
which has been already learned. The diagram will show 
this : — 

3 
3 
3 
3 
3 



5 = 



In the same manner it might be shoiaiftitji^ scseendODrors 
are the same as four sevens, or that fif ^^IJdWrte^sft T « 




to eight fives. 



V. 



-■«\' 



24) AKITHMETIC FOK BEGIXNEKS. 



Exercise XIX. 



1. What are seven fours? five sixes ? four sevens? 

2. Three fives 1 eight fours? five twos? four threes ? 

3. How many lingers are there on four hands ? on 
seven ? on nine ? 

4. How many pence in nine fourpenny-pieces ? in 
seven? in three? in six? 

5. There are four farthings in a penny. Change into 
farthings — five pence, nine pence, fourpence. 

6. Change into pence — three sixpences, four, five, two. 

7. What is the eighth part of 32 ? the seventh of 28I 
the third of 2 1 ? the ninth of 18 ? 

8. How many sixes are^ there in 30 ? how many fives 
in twenty ? 

9. Find how many marbles are possessed by four 
children who have eight each. 

10. How many legs have twelve chairs ? 

11. If there are twelve pence in a shilling, how many 
are there in five shillings ? 

12. Multiply eleven by five, by three, by four. 



(13.) 1712 5098 7121 (14.) 5060 

3 24 4 



(15.) 8121 1563 7096 (16.) 6127 8193 

425 43 



(17.) 202 1027 3162 (18.) 1964 719 

354 54 



MULTIPLICITIOX. 



The Multiplication Table Continued). 
The following should he learned hy heart : — 
Six sixes are thirty-six . 36 Seven sevens are forty- 



„ sevens „ forty-two . 42 

„ eights ,_, forty-eight . 48 

„ nines „ fifty-four . 54 

„ tens „ sixty . .60 

„ elevens „ sixty-six . 66 

„ twelves „ seventy-two 7 2 

Eight eights are sixty-four 64 

„ nines „ seventy- two 72 

„ tens „ eighty . . 80 

„ elevens „ eighty-eight 88 

„ twelves „ ninety-six , 96 



nine 49 
„ eights are fifty-six . .56 
„ nines „ sixty-three . 6^ 
„ tens „ seventy . .70 
„ elevens „ seventy-seven 77 
„ twelves „ eighty-four . 84 

Xine nines are eighty-one 8 1 
„ tens „ ninety . . 90 
„ elevens „ ninety -nine. 99 
„ twelves „ one hundred 

and eiofht 108 



Exercise XX. 

1. What are seven eights ? three sixes 1 four nines 1 

2. How many shillings must I give for five articles at 
seven shillings each ] For seven at nine shillings each ] 

3. How many marbles are there in eight bags contain- 
ing nine each ? In seven containing five each ? 

4. AVhat is the seventh part of forty-two 1 the ninth of 
seventy-two ? The third of twent^^-seven ? 

5. Eind the fifth of thii-ty, the third, the sixth, the 
tenth. 

6. Divide twenty-four cakes among four children, 
among six, among eight, among twelve, among two. 

7. How many squares are on the carpet in four rows 
seven each ? in five rows of eight each 1 

8. If seven boxes containing nine pence each were 
emptied, how many pence would there be in all ] 

9. In how many rows could you arrange forty-eight 
soldiers, and how many would there be in each 1 

10. Write out the whole of the tables, from twice two 
to nine times twelve, working them by addition. 



26 ARITHMETIC FOR BEGINNERS. 

Example of Working Multiplication. 
13. Ill nine villages, each containing two thousand 
four hundred and seventeen persons, how many persons 
live] 

2417 Two thousand four hundred and seventeen. 
9 



21,753 Twenty-one thousand seven hundred and fifty- 
three. 

Nine times seven are 63. Set down 3 and carry the 
6 tens. 

Nine times i ten are 9 tens, and 6 tens make fifteen 
tens. Set down 5 tens and carry i hundred. 

Nine times 4 hundreds are 36, and i make 37 hundreds. 
•Set down 7 hundreds and carry the 3 thousands. 

Nine times 2 thousand are 18, and 3 make 21 thousand. 
Set down 21. 

The result is. Twenty-one thousand seven hundred 
and fifty-three. 



Exercise XXI. 

1. Multiply four hundred and thirteen by five and by 
six. 

2. In a regiment of 950 men, each has eleven rounds of 
cartridge ; how many rounds are there in all ? 

3. There are twelve pence in a shilling; how many 
pence are there in 1 3 shillings 1 in 2 7 shillings ? in 48 
shillings 1 in 173 shillings? 

4. There are 8 bushels in a quarter of corn; how 
many bushels are there in 17 quarters? in 39 quarters? 
in 217 quarters ? 

5. If a town contains 16,382 houses, and on an average 
7 persons in each house, what is its population ? 

6. There are twelve inches in a foot ; how many inches 
are there in 14 feet ? In 59 feet ? In 625 feet? , 



MULTIPtilCA.lIOK. 27 

7. What is the weight in pounds of seventy-nine 
parcels weighing nine pounds each 2 

8. What is the di erence in number between 213 rows 
of trees containing 5 each, and 326 rows containing 
4 each? 

9. How many words are there in seven columns of a 
spelling-book containing eighty-nine words each 1 

10. There are four quarts in a gallon ; how many 
quarts are there in 29 gallons 1 In 538 gallons 1 In 714 
gallons 1 

11. Add together the values of six houses worth £'J2^ 
each, and of nine houses worth ;^ii32 each. 

1 2. Which is greater, and by how much 1 — seven times 
twenty-nine, or six times thu'ty-nine ? 

13. Add together 357 and 619, and multiply the 
result by 8. 

14. On unpacking 6 parcels containing 234 biscuits 
each, how many do I find in all ? 

Work the following sums : — 

(15.) 728 6139 278 (16.) 1472 963 8714 
5 II 12 567 



(17.) 3194 8625 2169 (18.) 8271 3192 2028 
3 12 7 696 



(19.) 4163 2196 5127 (20.) 1815 4137 2017 
857 968 



C21.) T379 51S0 6178 (22.) 5163 8041 5172 
6 II 12 7 9 12 



28 ARITHMETIC FOR BEGINNERS. 

MILLIONS. 

14. Any number written mth six figures to its right 
means millions. 

A million is equal to one thousand thousands. 

Thus 2,000,000 means two millions, 

5> Ij563;Ooo „ one million five hundred and 
sixty-three thousand. 

„ 8,045,195 „ eight millions forty-five thou- 
sand one hundred and ninety- 
five. 

„ 14,628,014 „ fourteen millions six hundred 
and twenty-eight thousand and 
fourteen. 

15, XoTE. — It is always useful, in reading numbers 
consisting of many figures, to divide them into threes from 
the right. The group of figures mth six to the right 
means millions ; that with only three figures to the right 
means thousands. Thus, 27,416,845, is to be read 
twenty-seven million, four hundred and sixteen thousand, 
eight hundred and forty -five, and 217,013,302, is to be 
read 217 million, 13 thousand, 302. 

Exercise XXII. 
(a) Express in words these figures : — 

(i.) 171,028 6,510 17,216,370 

(2.) 6,380,521 10,714,816 9,500^00 - 

(3.) 318,721,625 219,346,285 10,716,800 

(4.) 192,005 31^060 18,851,000 

(5.) 7,120,008 3,197,620 85,070,110 

(6) Express in figures these numbers:- — 

* I. Two miUious. Eight millions five hundred thousand. 

2. Three hundred and forty-two thousand five hundred 

and nineteen. 

3. Six millions ten thousand and nineteen. Fourteen 

millions and eleven. 



MILLIONS. ' 29 

4. Fourteen millions, tliree hundred and fifteen thou- 

sand, six hundred and nine. 

5. Eleven millions and fifteen. Seven millions, tliree 

hundred and twelve thousand. 

6. Fjorty-six millions, three hundred and nineteen 

thousand, six hundred and fifty-four. 

7 . Three hundred and t\Yenty-two millions, seven hun- 

dred and twelve thousand, nine hundred and 
eleven. 

8. Fifty- one millions, six thousand and three. Three 

millions and twelve. 

10. We multiply a number by 10 Avhen we place a 
(jipher after it, or remove it one place to the left. We 
aiultiply by 100 when we place two ciphers; and by 1,000 
when we place three ciphers, or remove it three places to 
the leit. Thus : — ^, 

728,niultipliedby 10 is 7,280 =: seven thousand two 

hundred and eighty. 
„ „ 100 „ 72,800 = seventy- two thousand 

eight hundred. 
„ „ 1,000 „ 728,000 = seven hundred and 

twenty-eight thousand. 
„ „ 10,000 „ 7,280,000 = seven millions two 

hundred and eighty 
thousand. 

Exercise XXIII. 

1. Multiply 17 by ten ; 28 by ten ; Three hundred and 
ten by ten. 

2. Multiply 216 by 10; by a hundred, by a thousand. 

3. How many men are their in 200 regiments contain- 
ing 976 men each 1 

4. Take a hundred times 1384 from a thousand times 
the same number. 

5. Add together a hundred times 117 and a thousand 
times 65. 

6. Multiply 738 by 10 ; 21 by 100 ; and 317 by i,oooj 
and add the results together. 

7. What are five hundred times sixty-five ? 



30 ARITHMETIC FOR BEGIlfNERS. 

17. 'When a multiplier consists of two or more figures, 
the multiplication is to be worked in two or more lines, 
thus : — 

Exam]jle (a). Multij^ly 3172 by 18; that is, by eight 
and by ten. 

3172 
18 



25376 Eight times 3172 (see 13). 
31720 Ten times 3172 (see lO). 

57,096 Eighteen times 3172. 



18. Note. — The result of multiplying numbers is 
called their Product. Thus 63 is the product of 7 and 9 ; 
TOO is the product of 10 and 10; and 57,096 is the 
product of 3172 and 18. 

Example (b). How many biscuits are there in 327 cases 
containing 4638 each 1 

4638 
327 

32466 Seven times 4638 (see 13). 
92760 Twenty (or ten times two) times 4638 (see\^). 
139 1400 Three hundred (or 100 times 3) times 4638. 



1,516,626 Three hundred and twenty-seven times 4638. 



Note. — The cipher (0) at the end of the second line, and the two 
ciphers (00) at the end of the third line are not necessary in the 
■working of the snm, and are usually omitted. 

Exercise XXIV. 

1. Find the number of houses in eighteen streets 
containing sixty-seven houses each. 

2. Multiply four hundred and thirty-five by twenty-six. 

3. How many nuts will be required for seventy-four 
children that they may have twenty-five apiece ? 



LONG 5I[JL*riPLICATI0X. 31 

4. In forty-seven regiments, comprising one thousand 
three hundred and seventy-five men each, how many 
soldiers are there ? 

5. What number would be produced by multiplying 
6283 by 147 1 

6. In twenty-eight chests of tea weighing 315 lbs. each, 
how many lbs. are there ? 

7. There are 112 lbs. in a cwt. ; how many lbs. are 
there in 1 7 cwt. 1 How many in 3 1 5 cwt. ? 

8. There are 28 lbs. in a quarter; how many lbs. are 
there in 11 quarters'? How many in 29 quarters? 

9. Find the difference between twenty-seven times three 
hundred and sixteen, and thirty-nine times one hundred 
and twenty-eight. 

10. There are 20 shillings in ^^i ; how many shillings 
are there in ;£"i2 8 "? How many in ^2163 1 

11. Add together the product of 763 and 29, and the 
product of 2138 and 17. 

12. In a church there are 85 pews, of which 47 hold 
seven persons each, and the rest six each. How many 
persons can be seated in it 1 

13. There are 16 ounces in i lb.; how many ounces 
are there in 827 lbs. ? How many in 1236 lbs. ? 



14. 


21036 

26 


5172 
19 


15- 
17. 

19. 


31062 
29 


17831 
35 












16. 


813 
813 


215 
106 


37205 
59 


11825 
37 












18. 


17386 

37 


5068 
162 


41380 
370 


21639 
306 













32 ARITHMETIC POR BEGINKEBS. 

10« When one number is the product of two others, 
we may multiply by it by multiplying by those two 
others in succession. 

Examjjle (a). ^Multiply 3 1 7 2 by eighteen. !N'ow eighteen 
equals twice nine. There are therefore two methods of 
doiijg this ; first, that which is shown in 17, and second, 
as follows : — 



3172 
9 



28548 nine times 3172. 
2 



57096 twice nine times 3172, 
or eighteen times 3172. 



(h) Multiply 7298 by 42. 'Now 42 equals 6 times 7. 
This sum may therefore be worked in either of these 
two ways : — 

I. 7298 

42 



14596 twice 7298. 
291,920 forty times 7298. 



306,516 forty-two times 7298, 



2. 7298 

7 



51086 seven times 7298. 
6 



306,516 six times seven times 7298, or forty-two 
— — ■ — times 7298. 



LONG MrLTIPLICATIOir. \ /> 0:#^ 

Exercise XXV. ^^'^^gli 

Wo?'7c each of the foUovnng sums in ttQO ways as in the 
exami')lp.s just given : — 

1. Multiply 729 by 24. 8643 ^J 3^- 

2. Find the number of windows in 39 houses containing 
twenty-one 'windows each. 

3. What is the product of 623 and 108? of 5163 
and 96 ? 

4. There are 24 grains in a pennyweight of gold ; how 
many grains are there in 47 dwts. ? in 318 dwts. ? 

5. There are 36 inches in a yard ; how many inches 
are there in 17 yards? in 108 yards? in 94 yards ? 

6. 2372 50861 7. 3198 21945 

35 27 . 120 72 









8. 


51738 
49 


2136 
44 








10. 


17293 
45 


3187 
50 








12. 


31920 
96 


41785 
80 













9- 


3702 
15 


81369 
63 








II. 


71938 
32 


21964 
56 








13- 


3621 
108 


413298 
81 









14. Subtract 236 from 500, and multiply the result 
^756. 

15. Add together sixty-three times 251, and fifty-four 
times 835. 

16. Find the product of 28, and 56, and 40. 

c 2 



34 ARITHitETIC FOR BEGIXNEBS. 

DIVISION. 

20. To divide a number is to separate it into 
equal parts. There are ten parts in the line in 
the margin. When divided by five there are 
two parts. When divided by two there are five. 
Division is the reverse of multiplication. Thus, 
if we divide twelve shillings among six persons, 
each of those persons has two shillings, because 
six times two makes twelve. So on dividing 
the number 35 into seven parts, we find the 
— number five. 

Example of Division. — /. 
Divide 864 by 2. 
2)864 The half of eight hundred is 4 hundred ; set 

down 4 under the hundreds. 

43 2 The half of six tens is 3 tens ; set down 3 

— under the tens. 

The half of four is 2 ; set down 2. 
Therefore the half of 864 is 432. 

Example of Division. — II. 
Divide 7625 by 7. 
7)7625 The seventh part of 7 thousands is one 

thousand ; set down i in the thousands 

1089-2 place. 

The seventh part of 6 hundreds cannot 

be taken. 

There is therefore no figure in the hundreds place in 
the answer. 

The nearest seventh part of 62 tens is 8 tens, or the 
seventh of 56 tens; this leaves 6 tens or 60 units un- 
divided ; set down 8 under the 2, and carry the 6 tens to 
the 5 units. 

Sixty-five divided by 7 give 9, and leave 2 undivided; 
set down 9, and place 2 as the remainder to the right. 

The answer to the, question is 1089, and 2 remaining. 



DIVISION. 35 

21, The answer to a question in Division is called the 
QUOTIENT. The dividing number or divisor should be set 
down on the left side, and each figure of the quotient 
should be set down as it is found, and the remainder 
carried to the next figure to the right. 

Exercise XXYI. 

1. What is the fourth part of 84728 ^ Of 212 ? 

2. Divide ;^2oo among five persons. Among ten. 

3. What number multiplied by 3 will produce 1236 1 

4. There are 1 2 pence in a shilling ; how many 
shillings are there in 504 pence? in 1584 pence? in 
3192 pence? 

5. If 1000 nuts are distributed among children who 
are to have 8 apiece, how many children receive them ? 

6. On a page of 5 columns there are 1525 words; how 
many are there in each column ? 

7. In a regiment of 1200 men how many rows could 
be formed of eight each ? Of six each ? Of ten each ? Of 
four each ? 

8. If a sum of ;£" 17,038 were left equally between 
seven persons, how much would each receive ? 

9. In a street there are in all 1672 windows, each house 
having 8 ; how many houses are there ? 

10. What is the diiference between the ninth part and 
the third part of 95,086 ? 

II. 2)42846 12. 3)3579 



13. 8)672091 5)49028 14. 7)31685 10)71986 



15- 1.1)43972 3)2176381 16. 4)359851 12)63987 



17. 8)31698 12)57629 18. 7)56941 6)410847 



36 



AUITHlifETIC FOR BEGIN^'EBS. 



22, When the divisor is greater than 12, the process 
is called long division. The following example shows 
the method of working each step in such a process : — 



Example of Long Division 
Divide 73476 Ijy 26. 
{a) 26)73476(2000 



(*) 



Divide 73 thousands by twenty- 
six, and the nearest answer is 
proved by trial to be 2, or 2 thou- 
sands. 

Take 26 times 2 thousands from 
the dividend. 

This leaves 21476 undivided. 

Divide 214 hundreds by 26, 
and the nearest answer is 8, or 8 
hundreds. 

Take 26 times 800 from the 
remainder. 

This leaves 676 undivided. 

In 67 tens 26 is contained 2 
times, or 2 tens. 

Take 26 times 2 tens from 676. 

This leaves 156 undivided. 

Divide 156 by 26, and the 
answer is 6. 

There is no remainder. 

The answer is 2826. 



!N'oTB. It is usual to omit the ciphers shown in («), and 
to set down the figures as in {h), bringing down each new 
figure of the dividend as it is required. 



52000 


800 


21476 
20800 


6 


676 
520 




156 
156 


26)73476(2826 

52 


214 
208 


67 

52 


156 





DIVISION. 



Exercise XXYII. 



37 



1. What is the fifteenth part of six hundred'? 

2 . D ivide twelve hundred and sixty-eight by twenty-four. 

3. How many packets, containing 14 lbs. each, can be 
made up out of a chest containing 11 34 lbs. 1 

4. T^ind the forty-seventh part of two millions. 

5. What number multiplied by 17 will make 5712 ? 

6. Add together the fifteenth and the sixteenth part of 
two hundred and forty. 

7. A mile contaius 63,360 inches. If a number of 
flagstones measuring 32 inches are laid end to end, how 
many will be required to extend so far as a mile 1 

8. There are twenty shillings in ;,^i ; how many pounds 
are there in 3560 shillings? 

9. How many times can I take the number 6^ out of a 
thousand 1 

10. Two hundred and fifty-nine bushels of corn were 
eaten in a certain time by 37 horses : how many bushels 
on an average were eaten by each ? 

11. What is the difference between the twenty-fourth 
and the twenty-fifth part of twelve thousand 1 

12. Divide seventeen thousand six hundred and ninety- 
two by one hundred and twelve. 

1^ Work the folloicing sums in division : — 

13. 16)7263 31)107,821 25)31,690 

14. 711)350,006 82)51,472 33)98,217 

15. 3024)863,197,281 357)862,319 13)62,501 

16. 713)627,812 305)1,796,831 314)816,291 
17- 351)472,098 713)542,618 18)72,196 

18. Take 72,638 from a million, and divide the result 
by 27. 

19. Add together 2,163 ^^^ 5i,02 7,anddi^^dethesum 
of those numbers by 135. 



38 ARITHMETIC FOR BEGINNERS. 

!S3» We divide a number by lo, by loo, by i,ooo, by 
10,000, or by 100,000, when we cut off as many figures as 
there are ciphers in the divisor. Thus : — 

We divide 100 by 10 by cutting off one nought, which 
leaves 10 : 500 divided by to becomes 50, one nought 
having been removed; divided by 100 it becomes 5> 
two noughts having been removed. 

750,000 divided by 100 gives 7,500 
,» » 1,000 „ 750 

4,693,825 divided by 10,000 „ 469 and 3,825 rem'* 
„ „ 100,000 „ 46 „ 93,825 „ 

24. Hence, when there are ciphers at the end of a 
divisor, we cut off as many figures from the dividend, and 
divide by the rest of the figures of the divisor. 

Example (a) Divide 726,837 by 5000. 
5,000) 726,837 

145-1837 remainder. 
We divide by 1000 by cutting off 3 figures (23). 
Eut 726 divided by 5 gives 145 and leaves i thousand 
remaining. 

The quotient, therefore, is 145 and 1837 remainder. 

Example (b) Divide 835,426 by 3700. 

37,00)8354,26(225 A- 'A ^. X. 

^. Here we divide by 100 by 

cutting off the two figures to the 

95 right. 

74- • We then divide the 8354 by 

37 ill the usual way. 
jgr The answer is 225, with a re- 

mainder 29. 



29 
The quotient, therefore, is 225, with a remainder 2926. 



Divisioy. 39 

Exercise XXVm. 

1. Find the hundredth part of 3279. 

2. TThat is the thousandth part of 392,185 ? 

3. Divide 1,769,382 by ten, by a hundred. By a 
thousand. By ten thousand. 

4. Find the hundredth part of 1,769; Of 38,351 ; Of 
52,684; Of 479,382. 

5. How many times greater are 3 2 70 than 32 7] 826,000 
than 826 ? 479,300 than 4793 1 

6. Divide 479 by sixty. 

7. From a total of 47,963 men how many regiments 
could be told off containing 800 each ? 

8. How many times are 170 contained in 34,823 ? 

9. Divide 387,256 by 280 and by 28,000. 

10. Divide 1,723.865 by 4500. 

11. There are 20 shillings in a pound, how many 
pounds are there in 1080 shillings 1 In 2370 shillings 1 

12. There are 60 fourpenny pieces in a pound, how 
many pounds are there in 7360 fourpenny pieces ? In 
40,960 fourpenny pieces ] 

13. Add together 496 and 5080, and divide the result 
by 320. 

14. Multiply 76 by 15, and 238 by 30, and divide the 
sum of the two products by 30. 

15. There are 1760 yards in a mile, how many miles 
are there in a million yards ] 

16. 23o)i86752( i240o)798265( 

17. 528o)32695o( 3i8oo)2763975( 

18. i56oo)279638( 32o)567928( 
19- 3oo)379687( i24oo)7i9876( 

20. A^Tiat number multiplied by 300 would give 
52,797,000? 

21. Take 5,286 from two millions, and divide the 
result by seventeen hundred. 



40 ARITHMETIC FOR BEGINNERS. 



SIGNS AND THEIR USES. 

25. The four principal processes in arithmetic are 
often expressed, for convenience and shortness, by signs, 
as follow : — 

+ is the sign of addition, and is called 2)^us 

Thus 7 + 9 is read 7 plus 9, and means 9 added 
to ). 
— is the sign of subtraction, and is called minus. 

Thus 9 — 7 is read 9 minus 7, and means 7 taken 
from 9. 
X is the sign of multiplication. 

Thus 9 X 7 is read 9 into 7, and means 9 multiplied 

-1- is the sign of division. 

Thus 20 -1- 5 is read 20 hy 5, and means 20 divided 
by 5 . This is sometimes expressed by placing the 
divisor underneath the dividend. "-^ means 20 
divided by 5. 

zr is the sign of equality. 

Thus 5 + 3 = 8 means 5 with 3 added to it equals 
8, or is equal to 8. 
( ) means that the whole quantity within the bracket 
is affected by the sign before it. Thus, 18- — (6 + 3) 
means that the sum of 6 and 3 or 9 must be subtracted 
from 18. And (12 — 7) x (3 + 4) means that 12 — 7 
or 5 must be multiplied by 3 + 4 or 7. 

Hence, — 

7 + 9 = 16. Seven ^jZz^s 9 equals 16. 

9 — 7 = 2. Nine minus 7 equals 2. 

9 X 7 = 63. Nine multiplied by 7 equals 63. 

20 -i- 5 — 4. Twenty divided by 5 equals 4. 

2S. = 24d. Two shillings equals 24 pence. 

;^3 = 60s. Three pounds equals 60 shillings. 

Expressions of this kind, showing equality between 
two different expressions for the same number, are called 

EQUATIONS. 



41 



EXERCISES IX SIGXS. 
ExsBCiaE XXIX. 

fg^ (a) BeadaefoUommg exprtssi&mg: — 

8 + 4 12-15 <> + 7 

3X6 20 + 8 l8-^2 

Four nods = cne acre; Two pints = one qoait. 
xbree fininMBnT Mecca = two 



{b) Pbee tlie true lesnll afier Oie ii%n of eqmlitf in 
eadi of tiwee cases: — 

I. 20 + 16 + 3 = . 2. 18 + 17 — 5 = 
3.8x2x5== . 10 — 5—3 = 
4. 16 -£- 9 28 X 4 

5~ — ' 4 + 3 = 

5.15 + 16 + 17—28= . 6.5x8x4 = 

156 + 230 + 49 + 7 = 
8. (15 4^ 8 X 2) + {12 X 6 X 3) = 
9l 27 — 16 + 187 — (23 + 15) = 
ID. (24 + 17 + 26 + 33) -^ (30— 5) = 

262 -i- 18 — 7 

II. = 

12. 236 X 15 X 9 = . 418 + 275 — 63 =. 

13- 540 + 127 + 165 - (783 - 219) = 

14. (3401 X 16) + (542 X 28) =z 

15- (i74<> + 5«4 - 1926) X (2347 - 1978) = . 

^^4i3;x 51 

4278 - 1396 
(e) Make up six equations amikr to tiiose in tibe 



42 ARITHMETIC FOR BEGNNERS. 

Exercise XXX. 

Miscellaneous Examples of the Simple Rules. 

1. An empty jar weiglis 308 grains ; when full of water 
it weighs 4372 grains, what is the weight of the water ] 

2. A person born in 1792 lived 75 years, in what 
year did he die ? 

3. Milton, who was born in 1608, died in the year 1 674, 
how old was he when he died ] 

4. A labourer earns 17 shillings a week, how many 
shillings does he receive in the whole year of 5 2 weeks 1 

5. From a fountain 15 pints of water flow per minute, 
how many flow in an hour (60 minutes), and in a day (24 
hours) 1 

6. A man buys cloth for 585 shillings, at 13 shHlings 
per yard, how many yards does he buy 1 

7. Add fifteen to twenty, take away five, divide the 
remainder by six, and multiply the result by seven. 

8. There are seven days in a week, how many days are 
there in 176 weeks ] 

9. If a railway train travels 38 miles an hour, how far 
will it go in 1 6 hours 1 

10. In fifteen bags, containing equal numbers, there 
are 1980 nuts, how many are in each ? 

11. A landowner sold 327 acres of land at £,1^ per 
acre, and 278 acres at ;£^23 per acre, what was the total 
purchase-money 1 

12. If a person owed ^^1200, and paid back at different 
times ;£'298, ;£"i54, £^(>Zi ^^^ £^Si ^^^^^ P^^ of his 
debt remained unpaid ? 

13. Multiply 628 by 156, and divide the product by 
700. 

14. What is the difference between 168 + 95 -f 64 
and i6 X 8 x 5 2 

15. If I take i860 steps in walking a mile, how many 
shall I take in walking 1 5 miles and a half ? 



MISCELLAXBOrS EXAMPLES OF THE SIMPLE RULES. 43 

1 6. To what number can I add 768 to make up 1,100 1 

17. How many pounds vreight are there in 7 bags of 
sugar containing 224 lbs. each; and in eleven bags con- 
taining 168 lbs. each] 

18. What is the forty-fifth part of a million ? 

19. A mile is equal to 1,760 yards ; how many yards 
are there in 2 7 miles ? How many in 1 8 miles ? 

20. Take 238 from a thousand; and multiply the re- 
mainder by thirty-four. 

21. Take the number 6, double it, double the result, 
and again until the sixth time ; to what will it amount ? 

22. AVhat number is that which, multiplied by 64, will 
give 81,856 as product? 

23. Multiply 154 by itself; and the result by the same 
number. 

24- (365 + 18 + 279) - (274 + 115). 

25. There are four to^vns with an average population 
of 11,476 persons each; how many people are there in 
them all ] 

26. Find the difference between the twenty-fifth part 
and the twentieth part of one million. 

27. London contained 2,680,735 persons at the census 
of 185 1, 3,222,720 at the census of 1861, and 3,883,092 
in 187 1 ; iind the increase at each period. 

28. (623 + 35 + 108) X (723^- 518). 

29. Subtract 374 from 8,000, three times in succession, 
and find the result. 

30. In a spelling-book there are 56 pages, each con- 
taining 2 columns of words, and in each column 64 words ; 
how many words are there in all 1 

31. What is the difference between the sum of 1,684 
and 2,132, and the product of 185 and 247 ] 

32. The population of the United Kingdom in 1871 
was 31,465,480 ; of these, 3,358,613 were inhabitants of 
Scotland, and 5,402,759 of Ireland ; how many remained 
in England and Wales ] 

33. Find the number of soldiers in an army consisting 
of five divisions, each division containing eight regiments 
composed of 1,250 men each. 



44 ABITHMETIC FOB, BEGDJlfEBS. 

MOXEY. 

SO* The coins in use in England are — 
Gold. The Sovereign. 

„ Half-sovereign. 
Silver. The Crown, or Five Shilling piece. 

„ Half-crown. 

„ Florin, or Two Shilling piece. 

„ SJiilliug. 

„ Sixpence. 

„ Fourpenny piece. 

„ Threepenny piece. 
Copper. The Penny. 

„ Halfpenny. 

„ FaHhing. 
But of the names of these coins only four are used in 

keeping accounts. 
» 
The following table must be learned by heart : — 

Four Farthings make One Pexny. 

Twelve Pence „ One Shilling. 

Twenty Shillings „ Oxe Sovereign, or Pound. 

The letters £ s. d. are commonly used to show Pounds, 
Shillings, and Pence.* 

Thus ;£i 6s. yd. is read one pound six shillings and 
seven pence. 

£1^6 I2S, 8d. is read one hundred and thirty-six 
pounds twelve shillings and eight pence. 

Farthings are not separately enumerated, but are always 
written as parts or fractions of pence. Thus, — 

\ means a fourth of a penny, or a Farthing. 

I means a half of a penny, or a Halfpenny. 

f means three-fourths of a penny, or Three Farthings. 

Thus 17s. 6^d. is read seventeen shillings and sixpence 
ferthing. 

£1 I2S. 3M. is read one pound twelve shillings 
and threepence halfpenny. 

* These letters are the initials of the names of Roman coins — 
Libri, Solidi, Denarii, — -"which were not of exactly the same value as 
pounds, shillings, and pence, although the names are still used. 



MONEY KULES. 4$ 

Exercise XXXI. 
Read the following expressions : — 

1. i6s. 2d., £i I2S. 3d., £45 7s. lod. 

2. ;£io 19s. 3id., £27 15s. 6id., ^239 5s. lid. 

3. ;^4028 OS. 6|d., ;^3i92 12s. o|d.,;^i5oo 6s. ii^d. 

Write in figures the following sums of money : — 

1. Eightpence, fourpence halfpenny, elevenpence three 
farthings. 

2. One pound twelve and ninepence ; Three pounds five 
and sixpence halfpenny. 

3. ^Nineteen pounds four and sixpence farthing ; Twenty- 
four pounds eleven and ninepence haKpenny. 

4. Twenty-five pounds and sixpence ; Twelve pounds five 
shillings and three farthings. 

Exercise XXXII. 
Simple Calculations in Money. 

1. How many farthings are there in twopence ? How 
many pence in three sixpences 1 

2. Add together fourpence, fivepence, and sixpence. 

3. Add together three farthings and seven farthings. 

4. What change will he left on paying yd. out of is. ? 

5. What is a quarter of a shilling ? A half of half-a- 
crown 1 

6. If I buy five articles at 2d. each, and seven at 3d. 
each, how much will they cost 1 

7. Out of a two shilling piece I spend 6d., 4d., and 
5jd., how much change shall I receive 1 

8. Divide sixpence among four children. 

9. To how many people can I give twopence each out 
of half-a-crown 1 

10. What is the difference between seven fourpenny 
pieces and five sixpences 1 

11. Add together eight farthings and eight halfpence. 

12. How many fourpenny pieces are worth the same as 
five shillings 1 



46 



ARITHMETIC FOR BEGINNERS. 



Five farthings 
Eight farthings 
Twelve farthings 
Sixteen farthings 
Twenty farthings 
Twenty-four farthings 
Forty-eight farthings 



MOJS^EY TABLES. 
To he learned by heart 
Farthings. 
make one penny farthing ... o 

two pence o 

three pence o 

four pence o 

five pence o 

six pence o 

one shilling i 



Twelve pence 
Twenty pence 
Twenty-four pence 
Thirty pence 
Thirty- six pence 
Forty pence 

Forty-eight pence 
Fifty pence 
Sixty pence 
Seventy pence 
Eighty pence 
Ninety pence 
A hundred pence 



Twenty shillings 
Twenty-one shillings 
Thirty shillings 
Forty shillings 
Fifty shillings 
Sixty shillings 
Seventy shillings 
Eighty shillings 
Ninety shillings 
One hundred shillinf^rs 



Pence. 
make one shilling 



one shilling and eight pence i 

two shillings 2 

two shillings and six pence 2 

three shillings 3 

three shillings and four 

pence 3 

four shillings 4 

four shillings and two pence 4 

five shillings 5 

five shillings and ten pence 5 
six shillings and eight pence 6 
sevenshillings and six pence 7 
eight shillings and four pence 8 
Shillings. 

make one pound ^i o 

„ one guinea * i i 

., one pound ten 1 10 

two pounds 2 o 

two pounds ten ...... 2 10 

three pounds 3 o 

three pounds ten ... 3 10 

four pounds 4 o 

four pounds ten ... 4 
five pounds 5 



10 



* Though guineas are no longer coined, this name for twenty-one 
shillings is frequently used. 



Example 


I. 


£Z 6s. 


5d 




£ 


s. 


d. 


I 


7 


6 


o 


i8 


9 


3 


6 


5 


5 


12 


8 



MONEY RULES. 47 



ADDITIO:tT A^T) SUBTRACTION OF MOXEY. 

27. When sums of money have to be added or sub- 
tracted, the pounds, shillings, pence, and farthings should 
be arranged in columns and dealt with separately. 

Add together jQi 7s. 6d., i8s. pd., 

"We first add the pence. 5 and 9 and 
6 make 20. But as 12 pence make one 
shilling, 20 pence make i shilling and 
8 pence. 

Set down 8 under the pence, and 
carry i to the shillings, i and 6 and 
18 and 7 make 32 shillings. 

But as 20 shillings make i pound, 
32 shillings make j£\ and 12 shillings. 

Set down 12 shillings and carry ^1 
to the pounds, i, 3 and i make ^5. 

Set down 5 under the pounds. 

The answer is jQ^ 12 s. 8d. 

Example II. Take ;^i6 3s. 4|d. from ;;^2 7 i8s. 6Jd. 

Take a halfpenny from three far- 
things, one farthing remains. Set it 
jQ s. d. doAvn in the farthings place. 
27 18 6 1 Take fourpence from sixpence. Two 

^6 3 4-2 pence remain, and must be set down 

under the pence. 

II 15 2 J Take three shillings from eighteen, 

fifteen remain, and must be set down 

under the shillings. 

Sixteen pounds from twenty-seven 
leave eleven. 

The answer is eleven pounds fifteen shillings and two- 
pence farthing. 



48 AllITUilETlC POR BEGINNERS. 

Exercise XXXIII. 

1. Add together 2S. 6d., i8s. 4d., and ^i 13s. 9d. 

2. Find the amount of ;^2 14s. yd., j£i i6s. 3d., 
;z^i2 6s. 8d., and ^ij 2s. 4d. 

3. Subtract ^^ los. from ^^ i8s. yd. 

4. What is the difference between ;£'i23 12s. 9d. and 
£71 5s. 4d.? 

£ s. d. 

27 15 8 

19 6 7 

324 12 4 

9 5 8 



^ s. 


d. 


18 7 


10 


6 12 





15 


9 


24 13 


6 





TFori: the foUoicing subtractions : — 

6. ^ s. d. £ s. d. 

24 12 8 319 6 5 

12 7 5 28 3 2 



£ 


s. 


d. 


234 


2 


9 


19 


18 


4 


123 


6 


7 


5 


10 





£ i 


3. 


d. 


200 ] 


[8 


7i 


172 ] 


[2 


6d 





7. If I buy coffee for 3s. 8d., tea for 5s. 4d., sugar for 
I lid., and soap for is. 4d., how much shall I spend ? 

8. Add together a sovereign, a half-crown, three six- 
pences, four shillings, and sevenpence halfpenny. 

9. At a stationer's I bought 3 quires of paper for lod., 
some envelopes for 6d., two books, of which one cost 3s. 6d. 
and the other 4s. 8d., and some newspapers for pd. ; so how 
much did my bill amount to ? 

10. To what sum will the following coins amount : — 
five sovereigns, six half sovereigns, three crowns, eight 
florins, and sixteen pence ? 

11. Add together fifty guineas and seventeen pounds, 
and subtract forty-seven pounds five shillings from the 
rasult. 



COMPOUND ADDITTCN. 49 

ADDITIOX OF 'MO:SEY—co7.lmu€d. 

28, It iB roquirt-d to add together the following sums 
of money: — ^£1314 i6s. yd., /^zo^S 12s. g^A, ^i los., 
^316 5.S. 4|d., ;£"409i6 I2S. 8^d., and ;£'ioo8 16s. 5d. 

Add up three farthings, one farthing, 
and one halfpenny. Tliey make six 
fartliing"s, or one penny halfpenny'. 
Set down a halfpenny and carry one 
penny. 

One and 5 and 8 and 4 and 9 and 7 

make 34 pence. Thirty-four pence are 

^ s. d. 2 shillings and 10 pence. Set down 

131416 7 10 pence and carry 2 shillings. 

2038 12 9.^ Two and 16 and 12 and 5 and 10 

I 10 o and 12 and 16 make 73. Seventy- 

316 5 4^ three shillings, 3 pounds 13 shillings, 

40916 12 8J Set down 13 shillings and cariy 3 

1008 16 5 pounds. 

Three and 8 and 6 and 6 and i and 

44596 13 io| 8 and 4 make 36 pounds. Set down 

6 and carry 3 to the tens. 

Three and i and i and 3 and i 
make 9 tens. Set down 9. 

Isine aud 3 and 3 make 15 hundreds. 
Set down 5 hundreds and carry i to 
the thousands. 

One and 2 and i make 4 thousands. 
Also set down 4 tens of thousands. 

The answer is 44 thousand five hundred and ninety-six 
Pounds thirteen Shillings and ten Pence halfpenny. 

Exercise XXXIV. 

1. Add together £^15 12s. 3d., ;£'2096 15s. 4id., 
^18 17s. 9id., and ;£4036 12s. 8|d. 

2. ;^i79 14s. 9H + £206 IIS. 5d. -f £iB 3S.7id., 
+ ;£3207 IIS. 7id. 

D 



50 ARITUMETIC FOR BEGnc^'ERS. 

3- £n^1 13s- 9i<i- + ^^6235 17s. 2d. + ^^480 I2S. 

A^' + ^3196 los. + £^(i 15s 3d. 

4. ;£75 15s. 8H + ;Jii25 i6s. 8d + ^726 13s. 
9i^- + ^£^3271 los. 6^d. 

5- ;^854 7s. 2d. + ;^io6 iis. 5jd. + ^1032 15s. 
8|d. + ;£6i95 14s. 7id. 

6. ;^2i36 13s. 6d. + ;£732 los. 8id. + ;^3i 19s. 
9|d. + ;£62 15s. 8d. + ;£3053 15s. 6d. 

7. If I have in my purse three ;^5 notes, four sove- 
reigns, and five half-sovereigns, three half-crowns, a florin, 
seven shillings, five sixpences, two fourpenny pieces, and 
five threepenny pieces, what sum have I in all ? 

8. A debtor owes to five creditors ^^189 15s., ;£"235 
16s. 3d., ;^io8 17s. 4d., ^50, and;^97 los. : how much 
does he owe altogether % 

9. Add together fifty pounds, fifty shillings, and fifty 
pence. 

£ s. 

1796 3 

28 17 

354 12 

9 10 

2038 12 

139 5 



10. £ 


s. 


d. 


J 083 


17 


3 


156 


4 


9^ 


I 


10 





28 


12 


6i 


375 


4 


8 


19 


2 


6 



d. 


£ s. 


d. 


54 


19 7 


6- 


9 


234 15 


8 


4 


18 


7f 


6 


65 12 


4-i 


2\ 


5098 4 


7 


7i 


325 16 


8 



II. ;£" S. d. ;^ S. d. j;^ S. d 

1275 6 7 30528 II 2^ 3271 14 7 



5196 14 


8| 


1976 6 


5J 


596 19 9j 


20127 8 


6 


287 14 


n 


1827 15 7| 


37 15 


5l 


4096 2 


8 


74 9 4* 


549 7 


H 


17278 15 


6 


20756 II 2| 


1726 12 


2 


3197 12 


8 


1982 7 9 


9 15 


8i 


150 10 





638 17 4 



12. Add together aU the English coins in present use. 
(See page 44 ) 



I ', 









MONEY KrUES. 






SI 


■ £ 


s. 


d 


£ s. d. 


£ 


8. 


d. 


28671 


14 


10 


3165 2 Si 


2167 


4 


9 


598 


7 


4^ 


I 19 2i 


31287 


5 


6i 


1365 


12 


6 


472 16 7 


2172 


19 


2 


209 


18 


2i 


1096 18 6| 


(>^ 


5 


6i 


4718 


6 


3 


12718 5 7 


1096 


12 


4l 


17 


12 


10 


3127 II II 


723 


8 


5 





SUBTEACTIOX OF SL^mYX—coittinued. 

S9* When, in any subtraction of money sum, the 
number in the upper line is less than that below it, the 
method of equal additions described in 4 must be used. 
It was there necessary to add ten to each line, because 
hundreds, thousands, <fcc., differ from each other by tens. 
But here it wOl be necessary to add a penny, a shilling, or 
a pound to each line, in order to work the subtraction. 

Example I. Subtract £^ 12s. 7d. from £1^ 16s. 3d. 

We can take the less sum 
from the greater ; but we 
cannot take 7 pence from 3 
pence. 

Add a shilling or 1 2 pence 
to the 3 pence in the upper 
line. Take 7 from 15 pence; 
there remain 8d. Set it down. 
Add a shilling to the lower 
line. Twelve and i are 13. 
Take 13 from 16. Set down 
the 3 shillings which remain. 
Take 9 from 15. Set down 
the £6 which remain. 
The answer is £6 3 s. 8d. 
One shilling has been added to both lines ; to the upper 
in the form of 1 2 pence, to the lower in the form of one 
shilling. 



£ 


s. 


d. 


15 


16 


3 


9 


12 


7 



6 


3 


8 


£ 
9 


s. 

16 

13 


d. 
7 


6 


3 


8 



o2 ARITHMETIC FOR MGUfNERS. 

Examplell. Find the difference between ;^i 250 los. 6|d. 
and ;^768 12s. 9|d. 

We cannot take a half- 
penny from a farthing. 

Add a penny (four far- 
things) to the upper line. 

Two farthings from 5 
leave three farthings to he 
set down. 

Add a penny to the 9 
pence of the lower line. Ten 
pence from 6 pence cannot 
be taken. Add 12 pence 
to the upper line. 

Ten pence from 18 pence 
leave 8 pence, to be set 
down. 

Add a shilling to the 

lower line. Thirteen shil- 

)t be taken. So add 20 

shillings to the upper line. 

Thirteen shillings from 30 shillings leaves 17 to be set 
down. 

Add ;!^i to the lower line. Xine pounds from o cannot 
be taken. Add ;£"io to the upper line. 

Kine pounds from 10 leaves jQi to be set down. 
Add ^10 to the lower line. Seven tens from 5 tens 
cannot be taken, so add 10 tens to the upper line. There 
remain 8 tens to be set down. 

Add 100 to the lower line. Eight hundred from 12 
hundred leaves 4 hundred to be set down. 
The difference is ^£'481 17s. 8|d. 

Note. — On comparing (a), which is the sum as ordi- 
narily set down, with (6), the sum as actually worked, it 
will be seen that a penny, a shilling, a pound, ;£io, and 
;^ioo have been successively added to both the upper 
and lower lines. 



(a) 


£ s. d. 

[250 10 6| 
768 12 pi 

481 17 8f 


£ 
(I) 12 1 15 

81 7 


s. d. f. 

io„3o„i8„5 

9„i3„io„2 


4l 8 


I »i7»8„3 


lings from 


10 shillings cam 



COMPOinfi) ADDITION AND SrBTKACTION. 63 

Exercise XXXV. 

1. Add together four shillings, four half-cro"WTis, four 
sixpences, and four pence, and take the sum from j£i. 

2. Take ^^-j^ 14s. 6d. three times from ^£^350 ios.,and 
say how much remains at last. 

3. What profit does a tradesman gain who buys goods 
for ^45 I OS., and sells part of them for j^^ij 9s. 6d., and 
the rest for ^^33 16s. lod. ? 

4. On offering to pay my tailor ;£'i9 4s. 6d. he allows 
me 19s. 3d. discount : what sum do I actually pay 1 

5. A gentleman leaves at death ;£" 1,256 to be divided 
among four daughters, of whom the first is to have 200 
guineas, the second 250 guineas, and the third three hun- 
dred : what sum remains for the fourth ] 

;^ s. d. £ s. d. £ s. d. 

6. 2582 15 4.^ 3287 II 5 2056 13 6 

196 8 6' 1965 4 8.1 1978 12 8 



£ s. d. 
7. 3069 10 o 
274 5 7i 





£ 


s. 


d. 


17862 


11 


3^ 


2974 


5 


6 











£ 


s. 


d. 


3000 








287 


13 


6* 





8. £1792 13s- 8d. -f- ;^236 14s. 7|d. — ;^io5o 
1 8s. lod. 

9- ;^2387 15s. 6d. + £35 MS. 2d. + ;^928 12s. 6d. 
— ^315475. 6d. 

10. Add together ^y^ 13s. 6Jd., ^219 los. iid., 
and £s^^ 4s. 6d., and subtract the result from ;^iooo. 

11. Add together fifty-four farthings, fifty-four shil- 
lings, and fifty-four pence. 

12. Find the difference between forty-nine fourpenny 
pieces and thirty-nine sixpences. 

13. "What sum of money is that which must be added 
to £2^ 15s. 6jd. to make ;£^ioo ] Prove the answer by 
adding it. 

14. How much is left after taking ;£^35 7s. 6d. twice 
over from £120 ics. ] 



t-* ahithmetic ron beolkkers. 

MULTIPLICATION OF MOXEY. 
SO* When any sum of money is to be multiplied, the 
farthings, pence, shillings, and pounds must be separately 
multipHed in order, and the results set down and carried 
as in addition. 

Example 7. Multiply £26 los. 4|d. by 4. 
£ s. d. Four times a halfpenny are 8 farthings, 

26 10 4^ or 2 pence. 

4 Carry 2 to the pence. 

Four times four are 16 pence, and 2 make 

106 I 6 18 pence, or i shilling and 6 pence, 

Set down 6 pence and carry i to the 

shillings. 
Four times 10 are 40 shillings, and i make 41 ; 41 shil- 
lings are 2 pounds i shilling. 

Set do^Tn i shilling and carry 2 to the pounds. 

Four times 6 are 24, and 2 make 26. 

Set down 6 pounds and carry 2 to the tens. 

Four times 2 tens are 8 tens, and 2 make 10 tens. 

Set doAyn 10. 

The answer is ;£^io6 is. 6d. 

Exercise XXXVI. 

1. Multiply 2S. 6d. by 5 ; £1 12s. 4d. by 6. 

2. Multiply £2 3s. Sjd. by 7 ; ^£6 2s. yd. by 3. 

3. Five pairs of gloves cost is. yjd. each : what is tha 
price of all 1 

4. Add together the cost of six books at 3s. 6d., and 
four at 5 s. 6d. each. 

5. What sum is that which, given among eight person.% 
allows them to receive ;£i2 17 s. 6d. each 1 

6. Find the price of 3 lbs. of sugar at 4.2d., 2 lbs. i\i 
coffee at is. 8d., and 4 lbs. of tea at 3s. 4d. per lb. 

£ s. ± £ s. d. £ s. d. 

7. 10 II 8J 267 13 17 9j 

452 



8. 







C031P0UND MULTIPLICATION. 






55 


£ 

21 


S. 

6 


d. ;^ s. d. £ 
2j i8 7 4 19 
6 7 


3 


d. 







;^ s. d. 
3 18 10 
4 




£ s. d. 
123 6 4I 
9 


^ s. d. 
24 12 3'J 
8 





10. £2 4s. 6d. X 12 ; 19s. 6|d. x 8. 
IT. £i^ 6s. 3d. X 9; ^2 Ss.'sld. X 6. 

12. ;!^IO JOS. lod. X 10. 

13. £2> i8s. 7id. X 8; ;£'i 9s. yjd. x 12. 

14. ;^43 2s. 6d. X II ; jQi los. 4d. x 6. 

15. A man bequeaths to seven institutions nineteen 
guineas each : how much is that in all ? 

16. In each of nine hags of money there are twenty- 
four sovereigns, fifteen half-sovereigns, twenty-one half- 
crowns, and eighteen shillings : what sum is contained in 
them all % 

17. What sum must he divided in order to give to 
eleven persons a legacy of £^() 12s. 6d. each? 

18. If I pay five hills averaging £i2> 17s. 8d. each, 
what change will remain from ;2^ioo ? 

19. What is the difference between seven times 
jQi 1 6s. 3d. and nine times £1 4s. 7d. ? 

20. {£2 i6s. 7d. + £s i8s. 8d.) x (12 - 3). 

21. (;£256 i2s. 6d. + £i2() los. - ;^i83 3s. 4d.) 

X (7 4- 4). ' . . 

22. Add ten times £2()^ 5s. lod. to eight times £1$^ 
13s. 4|d. 

23. Multiply ;£'78 6s. 5|d. by seven, and the result by 
five. 

24. What does an employer pay to 12 workmen, each 
of whom receives £^^ 12 s. 8d. yearly 1 

25. If eight persons receive nine half-crc 
sum is received by them iii aU ? J^^^^oe'^^ 




Sj'j 



ARITDMETIC FOR BEGIXXEBS. 



LONG MULTIPLICATION. 

31. When the multiplier is more than 1 2, it is 'neces- 
sary to proceed Ly steps, as in lO, Example \6). 

Example I. Multiply ^17 3 s. 6d. by 35 

Here, because 35 = 5 x 7,"we multiply by 7 and by 5 
in succession, and the second product is the answer 
req^uired. 

£ s. d. 

17 3 6 

7 



120 4 6 z= £i-j 3s. 6d. X 7. 
5 



601 2 6 = £l^ 3s. 6d. X 7 X 5. 



Example II. Multiply £2^4 13s. S^d. by 58. 

Here the multiplier 58 is not a product of any two 
numbers in the tables. AYe therefore take the nearest. 
56 equals 7x8; and after multiplying the number by 
56, we add twice tlie upper line to make up 58. 

£ s. d. 

254 13 Si 
7 

1782 15 11^ = 7 times the upper line. 
8 



14262 7 8 = 56 or 7 X 8 times the upper lifjt 
509 7 5 — twice the upper line. 



1477 1 15 I = 58 times the upper line. 



The nuswor is ^14771 15s. id. 



LONG MULTIPLICATION. n? 



Exercise XXXYIL 

1. Multiply jQt, I OS. 4d. by thirteen. 

2. Multiply ^26 15s. 3|d. by seventeen. 

3. Multiply ;^54 15s. 8|d. by nineteen. 

4. Add together five times £2 3s. 6d., and twenty- 
three times 17 s. 9d. 

5. What vrill 47 pairs of boots cost at £1 is. 6d. per 
pair? 

6. Find the price of three dozen articles at jQz 15s. pd. 
each. 

7. What will 59 acres of land cost at ;£^2 2 los. per 
acre? 

8. Multiply ;^37 15s. 6d. by 73, and subtract 
^£"1250 63. 4d. from the product. 

9. ^28 13s. 6d. X 19; ^12 14s. 7^d. X 23. 

10. ;^22o los. 4|d. X 41 ; ^£^153 i6s. 8id. X 26. 

11. ;^'274 los. 2d. X 30; £S^2 15s. 2id. X 23. 

12. £1 i6s. 5jd. X 37; ^'1862 I2S. 4id. X 53. 

13- ;£2i6 los. loid. X 17; £10 I2S. 3id. x 29. 

14- £^o^ 3S. iiid. X 53; ^617 2s. 9d. x 46. 



£ s. d. 


£ s. d. 


683 5 2 


7294 10 4^ 


31 


19 





16. Find the total cost of twenty- three articles at 
£1 9s. 6d. each, and of thirty-five articles at 17s. 8|d. 
each. 

17. What is the value of 24 casks of wine, each worth 

^i5 4s. 7d.? 

18. Deduct fifteen times ;^23 4s. 6d. from ;£^iooo. 

19. If a draper buys seventy-hve shawls at;^3 17 s. 6d. 
each, and sells them at four guineas and a half each, what 
proht does he gain ? 

20. AVhat is the cost of 19 tons of iron at £<) 9s. 6d. 
per ton ? 

J' 2 



58 



AKITHiLETIC FOR BEGIXKERS. 



HOUSEHOLD ACCOUNTS AKD SIMPLE BILLS. 

S2» The most frequent use to ^liicli easy Multiplica- 
tion and Addition of money are put is the calculation of 
small accounts after making purchases at shops. 

Example I. If I buy at a stationer's six quires of note- 
paper at 4jd., three packets of envelopes at 8d. each, some 
drawing-paper for is. 3d., five black-lead pencils at 3id., 
two boxes of steel pens at is. 6d. each, and an inkstand 
for 4s. 6d., how much do I spend 1 

It is usual to arrange such an account thus : — 





s. 


d. 


6 quires of note-paper at 4 Jd. 


... 2 


3 


3 packets, of envelopes at 8d. 


... 2 





Drawing-paper 


I 


3 


5 pencils at 3|d. ... 


... I 


S\ 


2 boxes steel pens at is. 6d. 


••• 3 





Inkstand 


... 4 


6 



14 52 



Exercise XXXYIII. 



Compute and finish the following accounts: — 



5 lbs. of rice at 3|d. per lb. 

6 lbs. of soap at 5d. 

8 lbs. of Valencia raisins at 6^d. 

3 packets of starch at 5|d. . . . 

6 tablets of soap at 3d. 
5 quires of paper at 7d. 

2 quires of foolscap at 9 id. 
S packets of envelopes at 4d. 

4 magazines at pd. . . . 

7 prayer-books at 2s. 3d. ... 



BILLS AND ACCOUNTS. 5*) 

S. d. 

4 lbs. of tea at 3s. 6d. 

5 lbs. of coffee at is. Sd. 

7 lbs. of loaf sugar at 6^,d. ... 

6 lbs. of moist sugar at 4.UI. ... 

3 pairs of gloves at 3s. 9d. 

2 neckties at is. 6d. ... 

4 pairs of stockings at 2s. 2d. . . . 

3 silk handkerchiefs at 3s. 6d. . , . 



3. i3.yardslongclothat 3Jd., 25 yards shirting at 8.^d., 
2 dozen napkins at is. 4d. each, 3 tablecovers at 8s. od. 
each, 

4. 19 yards black silk at 5s. 2d. per yard, 5 yards crape 
at 6s. 6d., 12 yards black alpaca at is. yd., and 3 pairs kid 
gloves at 2s. 8d. 

5. 2 bottles of pickle at lojd., 3 of fruit at gd., i bottle 
of blackini^ at is. 2d., 9 lbs. of candles at 6|d. per lb. 

6. 5 pairs cotton hose at is. gd., 6 pairs worsted at 
2S. 3jd., 4 pairs merino at 3s. 2d. per i^air, and 2 dozen 
children's socks at yld. per pair. 

7. 27 1 yards of carpet at 4s. 9d. per yard, 27!- of felt 
at 9|d., making the same 27^ yards at 4d. per yard ; stair 
carpet, 27 yards at 3s. 9d. ; two dozen stair rods at 2hd. 
each. 

8. Two dozen port at 48s. per dozen, 2 dozen pale 
sherry at 46s., 3 dozen Sauterne at 24s., 4 dozen pints of 
claret at 13s. 

9. 3 pairs lace curtains at 23s. 9d. per pair; tapes, 
rings, &c., for the same, 6s. 6d. ; making up and fixing 
same, i8s. 6d. 18 yards grey silk at 6s. gd.; 14 yards of 
muslin at 8Jd. 

10. Making and fixing 3 window-blinds for drawing- 
room (2 at i8s. 4d. each, i at 12s. rod.); 7 blinds for 
bedrooms (viz., 2 at iis. 8d. each, i at 7s. 6d., and 4 at 
6s. 2d. each) ; rods, screws, lines, &c., for fixing, 6s. 6d. 
Altering spring rollers, 4s. 6d., cleaning and repairing 
outside blinds, ;!^i 3 s. 



GO ARITHMETIC FOR BEGIXXERS. 

SIMPLE REDUCTION, AXD OTHER USES OF 

MULTIPLICATION. 
Jl»$, Example I, How many pence are tlieire in £2^ ? 
;^23 Because there are 20 shil- 

20 - liners in jQi : 

There are in ^£^23 20 times 

460 = shillings in ;^ 2 3. 23 shillings, or ^60 shillings. 

12 And because there are 12 

pence in a shilling, there are 

5520 = pence in £27,. in 460 shillings 12 times 460, 

or 5520 pence. 

Hence there are 5520 pence in ^£^23. 

Example II. Reduce ^59 i6s. 2|d. to farthings. 
;^59 i6s. 2\^. AVe multiply ^59 

20 by 20, and add in 

the 16 sliillings. 

1196 zz shillings in ^59 i6s. There are thus 

12 .1196 shillings in 



£S9 i6s. 

14354 = pence in ;^59 i6s. 2d. We multiply 11 96 
4 I>y 12, and add in 



the 2 pence. 



57417 farthings in ;£"59 i6s. 2|d. There are thus 
14354 pence in ;^59 



1 6s. 2d. 

We multiply 14354 by 4, and add in the i farthing. 
There are thus 57417 farthings in ^£"59 i6s. 2jd. 

ExamjjU III. How many fourpenny pieces are there in 

'139 15s- ^ 

jQ s. d. We multiply ;£"i39 by 20, and add 

^39 150 ^^ ^^^^ 15 shillings. There are 2795 

20 shillings in ;^i 39 15s. 

But there are three fourpenny pieces 

2795 in a shilling. Therefore we multiply 

3 2795 shillings by 3. 

There are thus 8385 fourpenny pieces 



S385 in ^139 15s- 



SIMPLE KEDTTCTIOy. 61 



Exercise XXXTX. 

1. Eednce ;£i769 to sMUmgs; jCiS los. to pence. 

2. How many sixpences are there in ^1385 5s. ? 

3. If there were a coin worth two pence, how many 
could I have in change for two guineas ] 

4. Eeduce £^ 19s. 6jd. to farthings. 

5. Find the price of 17 articles at 2|d. each. 

6. How many things worth three halfpence each can I 
buy for 5 s. ? 

7. Find the difference between the number of four- 
penny pieces and the number of threepenny pieces in 
£2 15s. 

8. In seventeen half-crowns how many pence f 

9. If I changed a five-pound note into threepenny 
pieces, how many should I have ? 

10. How many more shillings are there than half- 
crowns in twenty guineas ] 

11. Reduce the two sums ^12 i6s 3 id. and ^£^24 7s. 9d. 
to farthings. 

12. Find the difference in pence between ^£36 14s. 8d. 
and^5o. 

13. Divide ^£^175 i6s. 9d. by 3, and give the answer in 
farthings. 

14. How many halfpence are equal in value to twelve 
bags of money containing j£i i6s. 3d. each ? 

15. Multiply ^£"763 i8s. 4d. by 15, and reduce the 
'answer to pence. 

16. How many halfpence are there in seventeen guineas ? 

17. How many farthings are there in seven times 
^i8 6s. 4d? 

18. Find the total number of farthings in nine guineas, 
three half-sovereigns, and fifteen half-crowns and seven 
sixpences. 

19. How many articles worth three halfpence each 
coidd I buy for j^^y los. ? 

20. Add the number of farthings in seven hundred and 
fifty founds to the number of shillings in the same sum. 



62 AETTHMETIC FOR BEGDTNEES. 

Divisio:Nr OF money. 

34, In dividing a sum of money, pounds, shillings, 
pence, and fartliings must be separately divided in succes- 
sion, and when there is any remainder, it must be reduced 
to the term next below it. 

Example I. Divide £^^ 6s. 3d. by three. 

£ s. d. We find one-third of £2^'^ by the 
2,)^T, 6 3 method of sunple division, lO. 

■ The answer is ;j^i i. 

1 1 2 I A third of 6s. is 2s. 

The third of 3d. is i penny. 

The answer is jQii 2s. 3d : 

Example II. Divide ;^i64 iis. 4M. by 7. 

£ s. d. ^^e divide 164 by 

7 )164 II 4i 7^ and find the quo- 

23 10 2J : f remainder. tient to be ;£23 with 

a remainder, jQ^. 

Xow £^ and iis. reduced to shillings make 71 shil- 
lings. 

The seventh of 71 is 10, with a remainder of i shilling. 

One shilling and fourpence make 1 6 pence. 

The seventh of 16 is 2, with a remainder of 2 pence. 

2 pence and Jd. reduced to farthings make i o farthings. 

The seventh of 10 is i, with 3 farthings remainder. 

The nearest answer therefore is ^£^23 los. 24d., with 
three farthings remaining undivided. 

Exercise XL. 

1. What is the fourth part of ;£"i los. I 

2. Divide ;£26 by five. 

3. Add the half of ;£"io los. to the third part of the 
same sum. 

4. If ;£'25o I OS. are left to be divided among 6 persons, 
how much will each receive ? 

5. ;£"i8 have to be divided among 10 persons : how 
much will each receive ? 



coMPOTUfD Dinsioy. 63 

6. From the half of five guineas take the third of five 
guineas. 

^ s. d. £ s. d. 

7. 8)7 2 6 7)23 10 4 



;^ S. d. £ S. d. 

8. 10)123 16 8 11)25 2 9 



9. ^18 I2S. 6d.-Mo; ;^24 5s. 7d.-f 7. 

10- ^38 17s. 3<i-^ii j ;^i9 6s. 5d. --I2. 

11- £37 15s- 3^.-5; £^^4 10S.-8. 

12. ;£'207 15s. 6d.-6; ^£'327 14s. 8d.^9. 

13. Add together the eighth and the tenth parts of 

^53 I 28. 6d. 

14. Take the twelfth part of ^126 33. from the whole 
of that sum. 

15. A gentleman bequeaths ^2^1250, of which one-half 
is given to his eldest son, one-third to his second son, and 
the remainder in charities ; how much money is given to 
each purpose ? 

16. ^213 17s. 6d. + ^519 I2S. 8d. 

12 

17. ^504 IPS. -^196 13s. 4d. 

8 

18. ^27 15s. 6^d. + £196 i8s. 7d. - ^59 IPS. 4ld. 

7 + 4 

19. ;^325 163. 7d. X 10 

7 

20. Find the difference between the eighth and the 
twelfth parts of ;£i25o. 

21. K the sum of ^1827 193. 6d. be divided into nine 
parts, of which A receives five, and B four, what is the 
share of each % 

22. Divide a legacy of ;£^8757 2s. among three persons, 
so that the first shall have five parts, the second four 
parts, and the third two parts . 



61? AUITHMETIC FOR BEGIKNEES. 



DIYISOX OF MOXEY {continued). 

So* When the divisor is greater than 12, each remain- 
der must be set down separately, and the work done as in 
Long Division (22). 

Example. Divide £713$ i6s. 4d. by 27. 

We first divid e;^7i35by27, 
as in 2'£. 

The quotient is ;^2 64, and 
^j are left undivided. 

We next reduce these ^j 
and the i6s. to shillings. They 
make 156 shillings. 

On dividing 156 by 27, the 
nearest answer is 5 s., and 21 
shillings remain undivided. 

We next reduce these 21 
shillings and 4d. to pence. 
They make 256 pence. 

On dividing 256 by 27 we 
find the quotient to be 9 pence, 
and 13 pence remain undivided. 

We next reduce the 13 pence 
to 52 farthings. 

On dividing these 52 by 27 

we find the quotient i, and 

a remainder of 25 farthings 

- which cannot be divided by 27. 



25 farthings remain undivided. 

The answer is, therefore, ;£"2 64 5s. 9^d., and 25 re- 
mainder. 



£ s. 

7)7135 i6 

54 


4(264 


173 
162 




115 

108 




7 

20 




27)156(5 
135 


shillings. 


21 




12 




27)256(9 
243 


pence. 


13 
4 




27)52(1 
•27 


farthing. 



compound division. 1 ' ' 65 

Exercise XLT. 

1. Find the thirteen tli part of ;£"3co. 

2. Divide ^£^2^ los. by sixteen, and by eighteen. 

3. Add together £ti6 ios, and;^i38 4.S. yd., and 
divide the snm by nineteen. 

4. Find the difference between the fifteenth and the 
sixteenth of ;^ 1 000. 

5. A gentleman leaves ^^10,000, of Avhich one-half is 
to be paid to his widow, one-third to be equally divided 
among his six children, and the rest among his four 
nephews : how much is received by each child and by 
ecch nephew ^ 

6. ^834 ics. 4-^17 i6s. -t-pfi47 i2s. 8d.-M7. 

7. ;^i25o -J- 24 ; ^£638 IOS. 6d. -f- 27. 

8. ;£"i39 2S. 4d.--i5; ;£"3i68 i6s. 2d. ~ 2>Z- 

9. ^274 r2s. od. -^ 29; ^835755.-52. 

10. ^^7265 14s. 6d. -f- 37 ; ^1273 4s. 6d. -f- 45. 

11. ^^2198 14s. 6d. -4- 18; ;^3i25 I2S. 6d.-4- 29. 

12. ;£3i86 i2s. lod. -- 65 ; ;£"2 5oo -f- 73. 

13. Add together ^^568 13?. 7d.; £2/^6 los. 5d. ; and 
;;^i20o ; and divide the sum by 24. 

14. If a prize equal in value to ^^1728 is captured at 
sea, and one-third is distributed among the officers, and 
the remainder among 68 men, what is each seaman's 
share ? 

15. Divide the sum of ;^583 into 960 equal parts. 

16. ;^i38 i6s. 7d. -f ;^i53 14s. 10 

29 

17. ^1347 5s. 6^d. - ^216 5s. 8 d. 

47 

18. Add together the thirty-second and forty-eighth 
parts of ^1625. ' 

19. Divide ^2^3147 15s. by forty-seven, and reduce the 
quotient to farthings. 

20. Part ;^iooo between two persons in such a way 
that fifteen parts shall be received by one for every seven- 
teen parts received by the other. 



66 ARITHMETIC TOE BEGmNERS. , 

EEDUCTION, A:N'D OTHER USES OF DIVISION^. 

30. When it is required to reduce any number of 
farthings into pence, or any sum of money into another of 
higher value, the sum must be worked by Division. 

Example I. What is the value of 10,000 farthings % 

4)10,000 farthings. 



12)2,500 pence. 



20)208 shillings, and 4 pence remaining. 



10 pounds, and 8 shillings remaining. 

Because 4 farthings are i penny ; 

Therefore we divide 10,000 farthings by 4. 

There are 2,500 pence in 4 farthings. 

But because 1 2 pence make one shilling ; 

We divide 2500 pence by 12 to reduce it to shillings. 

There are 208 shillings and 4 pence in 2500 pence. 

But because there are 20 shillings in ;^i, 

AYe divide 208 shillings by 20. 

There are ;£"io and 8 shillings in 208 shillings. 

Therefore ten thousand farthings are found to equal 
;^io 8s. 4d. 

•JY. When it is required to find how many sums of one 
value are contained in another, both sums must be reduced 
to the same name before the division is worked. 

ExamjjU II. How many times can I take 4s. 3d. out of 
£S los. 1 

By 33 we find that ;£"5 los. contains 1320 pence ; and 
4s. 3d. contains 51 pence. 

The question is, therefore, how many times are 51 
pence contained in 1320 pence? 

We divide 1320 by 51. 1320 -^ 51 z=: 25 times and 49 
remainder. The answer is therefore 25 times, leaving a 
remainder of 49 pence. 



EEDTJCTION BY DIVISION. 67 



Exercise XLIL 



1. How many pence are there in ^^ los. ? 

2. How many pounds are there in 1683 farthings ? 

3. Eeduce 22,840 pence to shillings and pounds. 

4. How many coins worth five farthings each could 
I have in change for ^£4 1 

5. What is the difference between 5000 halfpence and 
7350 farthings 1 

6. Eeduce to pounds, shillings, and pence, the following 
sums : — 

(a) 18,364 farthings; 23,086 halfpence; 4196 
pence. 

(h) 27,463 fourpenny pieces; 8165 sixpences; 
12,796 farthings. 

7. How many articles worth 3^d. each can I buy for 
^20] 

8. To how many persons can I give 3s. 6d. out of 

9. In 1728 sixpences how many guineas ] 

10. 25 francs are worth an English sovereign : what is 
the value in English money of 17,287 francs? 

11. What is the difference between the number of 
farthings in five guineas and the number of pence in the 
same sum ? 

12. How many articles worth 33. 4d. each can I buy 
for y^79 I OS. ? 

13. A prize fund of ^£"500 is so distributed that one- 
fourth of it falls to the share of the officers, and the rest 
is given in sums of ^£2 los. each to the seamen ; how 
many seamen share it I 

14. In 12,350 farthings how many sixpences? How 
many half-crowns? 

15. If there were a coin worth 2|d., how many could 
I obtain in change for ^^50 ? 

16. If a million farthings were divided into 12 parts, 
of which one person received 7 and another 5, what would 
be the share of each ? 



63 ARITHMETIC FOIl BEGIXNERS. 

MISCELLANEOUS EXERCISES.— XLIIL 

1. Eind the price of 12 articles at 3^d. each, and of five 
at 7 J-d. each, and add them together. 

2. Add together five half-crowns, seven sliilKngs, nine 
sixpences, and fifteen pence. 

3. If I have in my purse a ^£"5 note, four sovereigns, 
seven half-sovereigns, a crown, five florins, seven shillings, 
three fourpenny pieces, and nine threepenny pieces, what 
sum have I in all ] 

4. What is the difiference between 172 sixpences and 
1720 pence? 

5. Make out a bill for 4 pairs of shoes at 12s. 6d. each 
pair, 2 of boots at 19s. 6d. each, 3 pairs of slippers at 
3s. 9d., and repairs amounting to 12s. lod. 

6. A man earns 27s. per week, his wife 30s. per calendar 
month, and three children 3s. Qd. per week each : what is 
the income of the whole family per annum 1 

7. When the income tax is at 5d. in the pound, what 
amount of tax does a gentleman pay whose income is 
;2fi2 5o per annum? 

8. At a church offertory j^zS los. were collected, and 
it was calculated that on an average 4d. had been given by 
each person : how many were there in the congregation 1 

9. What is the difference between the number of far- 
things in ;£"53, and the number in ;^24 7s. 6d. 1 

TO. Out of an income of ;£^8oo per annum a man saves 
;j{^i2 every quarter : what does he spend per week 1 

11. Find the sum of three guineas and ^£6 14s. 8Jd., 
and reduce the whole to farthings. 

12. If I pay for 56 yards of cloth at 2s. 8Jd. per yard, 
wliat sum will remain out of a ;^20 note 1 

13. Eind the total cost of a score of articles at 3s. gd. 
each, and of a gross at 5s. 2d. each. 

14. If an equal number of men, women, and children 
recpive each a gift, the men of 5s., the women of 2s. 6d., 
and the children of is. each, and if the whole sum dis- 
tributed amounts to ;£6^ os. 6d., how many persons in 
all are relieved. 



EXERCISES I2f '.rElGHT. 6D 



WEIGHT. 

38. The common table in use in England, for weighincj 
all articles of ordinary sale, is as follows : — It is called 
Acoiiflupois weight; other weights, such as Troy, and 
Apothecaries*, being only used in special trades. 

The fottmcinff should he learned by heart : — 

1 6 Drams make one Ocxce. 

i6 Ounces make one Pound. 

28 Pounds make one Quarter. 

4 Quarters (or 112 lbs.) make one Hundredweight. 

20 Hundredweights make one Ton.* 

Multiply 7 cwt. 3 qrs. 13 lbs. 6 oz. by 5, or 

Five times 6 oz. are 30 oz. But 
because 16 oz. make i lb., 30 oz. 
^ I lb. 14 oz. Set down 14 oz. 
and carry i lb. 

Eive times 13 lbs. are 65 lbs., 
which added to i lb. make 66 lbs. 
But as 28 lbs. = I qr., 66 lbs. 
518 o 410 are 2 qrs. and 10 lbs. Set down 

10 lbs. and carry 2 qrs. 
Five times 3 qrs. :ii= 15 qrs., T^hich with 2 makes 17 
qrs. But since 4 qrs. = i cwt., 17 qrs. ziz 4 cwt. i qr. 
Set down the i qr. and cany 4 cwt. 

Five times 7 cwt. are 35 cwt, which added to 4 make 
39 cwt. But 39 cwt. equal i ton 19 cwt. 

In like manner on multiplying i ton 19 cwt. i qr. 
10 lbs. 14 oz. by 3, we find the answer to be 5 tons 18 cwt. 
o qr. 4 lbs. 10 oz. 

* The full tables of weight and measure, for purpose? of reference, 
will be found on p. 70 of the " School Arithmetic," and an explana- 
tion showing the rise and history of our system of weighing on 
p. 332 of the " Science of Arithmetic." 



Example I. 


Mu 


Itip 


Y 5 and 3. 






cwt. qrs. 


lbs. 


oz. 


7 3 


13 


6 

5 


119 I 


10 


14 






3 



70 AKITHMETIC TOR BEGINNERS. 

Example II. Find tlie difference between one ton, and 
17 cwt. 3 qrs. 12 lbs. 9 oz. 

ton. cwt. qrs. lbs. oz. Add 16 oz. to the npper 
-10 000 line. 9 from 16 leaves 7 oz. 
17 312 9 Set down 7. 

^dj 4 lbs. to the low^er line, 

2 015 7 and 28 lbs. to the upper. 13 

from 28 leaves 15 lbs. Set 

do^vn 15. 
Add I qr. to the lower line, and 4 qrs. to the upper. 
4 qrs. from 4 leaves nothing. Set down o. 

Add I cwt. to the lower line, and 20 cwt. to the upper. 
I 8 cwt. from 20 leaves 2 cwt. Set down 2. 

Add I ton to the lower line, i from i leaves o. 

The difference is 2 cwt. 15 lbs. 7 oz. 

Exercise XLIY. 

1. Add together 2 lbs. 6 oz., 14 oz., and 12 lbs. 

2. Find the difference between the weight of one parcel 
of 5 lbs., and that of two weighing j lb. 9 oz. each. 

3. What will three pounds of tea cost at 3 jd. per oz. % 

4. Add together 7 cwt. 3 qrs., 2 tons 5 cwt., and 
3 cwt. I qr. 19 lbs. 

5. Find the total weight of five parcels, weighing 
respectively 5 J lbs., 2 lbs. 4 oz., 15 lbs., 3 lbs. 12 oz., and 
29 oz. 

6. Reduce 3 cwt. 2 qrs. 1 9 lbs. to pounds and ounces. 

7. How many ounces are there in 3 qrs. 1 1 lbs. ? 

8. Eeduce 1000 ounces to pounds. 

9. How much butter at lod. per lb. can I buy for 
£a ios. % 

10. How many parcels of sugar weighing 4 lbs. 4 oz. 
each can be made up out of a hogshead weighing 3 cwt. 
2 qrs. 1 5 lbs. "? 

11. Find the price of 7 cwt. 3 qrs. 16 lbs. at five 
farthings per lb. 

12. What is the difference between 1000 lbs. and 
1000 ounces % 



EXERCISES IN WEIGHT. /i 

13. Find the price of 7 cwt. 3 qrs. of sugar at 4.Jd. 
per lb. 

14. How many three-ounce packets can be filled up 
from a box of lozenges weighing 3 qrs. of a hundred- 
weight 1 

tons. cwt. qrs. lbs. oz. tons. cwt. qrs. lbs. oz. 

15. 7 I 19 6 35290 

3 18 5 8 I 15 II 

5 10 o o o 10 3 19 o 

3140 I 20 7 

6 o 18 5 



16. 7 tons 3 cwt. 18 lbs. + 19 lbs. 12 oz. + 3 qrs. 
18 lbs. 7 oz. + 19 cwt. 19 lljs. 

17. 2 cwt. 14 lbs. 7 oz. + 25 lbs. II oz. + I cwt. 

1 qr. I lb. + 3 qrs. 12 lbs. 

18. 5 tons 7 cwt. + 6 cwt. I qr. 23 lbs. — 17 cwt. 

2 qrs. 18 lbs. 

19. 18 c^vt. 2 qrs. 9 lbs. X 6 ; 5 tons 3 cwt. 2 qrs. 
9 lbs. XII. 

20. From four tons take thirty-nine cwt. three qrs. 
seventeen lbs. 

21. How many j)arcels weighing 2 J lbs. each can be 
made up out of 1 7 cwt. 3 qrs. ? 

22. At 8|d. per lb. what quantity can I buy for 
^79 6s. 8d.'? 

23. At ^£^224 per ton what is the price of coffee 
per oz. 1 

24. Find how many times a pound and a half is con- 
tained in 3 1 cwt. 

25. What is the difference between 32 lbs. and 132 
ounces ? 

26. Find the price of one hundred and thirty-seven 
lbs. at fourpence farthing per oz. 

27. Eeduce 11,100 oz. to hundredweights and tons. 

28. Eeduce 5^ tons to ounces and drams. 

29. What is the difference in ounces between 3I tons 
and 39I cwt. 



72 AllITUMETIC FOR BEGINNERS, 

LEXGTH. 

39. The me^ures of length in use in England are 
chiefly the Inch, Foot, Yard, and ]\Iile. Other denomina- 
tions are only occasionally used. 

To he leanied hy heart : — 

Twelve Inches make one Foot. 
Three Feet make one Yard. 
Five and a half Yards make one Polf. 
Forty Poles make one Furlong. 
Eight Furlongs make one Mile. 

It is also useful to remember that — 

Two hundred and twenty Yards make one Furlong.* 
Seventeen hundred and sixty Yards make one Mile. 

Example I. Add together the lengths of 5 roads, of 
which the first is f of a mile long; the second i mile 

3 furlongs ; the third, 2 \ miles ; the fourth, 7 furlongs 
20 poles; and the fifth, i mile i furlong 30 pole^ 

4 yards. 

miles, furlongs, poles, yards. There are only 4 yards 

in the right-hand column. 
Set down 4 yards. 

30 and 20 make 50 
poles. But as 40 poles 
make i furlong, 50 poles 
are i furlong 10 poles. 
Set do^vn 10 poles. 

I and I and 7 and 4 

and 3 and 6 are 22 fur- 

js make i mile, 22 furlongs 

2 and I and 2 and i make 6 



The answer is 6 miles 6 furlongs 10 poles 4 yards. 

* Unless poles are expressly mentioned in the sum, always use the 
number 220 as multiplier or divisor, and proceed at one step from 
furlongs to yards. 5^ is an inconvenient number ; and " poles " are 
every day less and less used in practice as measures of lengtb. 



I 

2 

I 


6 
3 

4 

7 

I 








20 

30 4 


6 


6 


10 4 


longs, 
make 
miles. 


But since 8 furloi 
2 miles 6 furlongs. 
Set do\\Ti 6 miles. 



EXAMPLES IN LENGTH. 



73 



Example II. How many feet are there in 7 J miles ] 



miles, furlongs. 
1 6 

8 

62 furlongs. 
220 



1240 
124 



13640 yards. 
3 



40920 feet. 



Since 8 furlongs are i mile, 
j of a mile equals 6 furlongs. 
8 X 7 +6 = 62 furlongs, the 
number of furlongs in 7 miles 
6 furlongs. 

Since 220 yards make one 
furlong we multiply 62 by 220, 
and find that there are 13,640 
yards in 62 furlongs, or in 7 
miles 6 furlongs. 

Since 3 feet make one yard, 
we multiply 13,640 yards by 3, 
and thus hnd that 40,920 feet 
= 13,640 yards = 62 furlongs 
= 7 miles 6 furlongs. 



Example III. AYhat will be the cost of a wall 2 miles 
and a half long, at 2s. 9d. per yard i 

2)1760 

4 



3520 
880 


z= yards in 2 miles. 
Sz „ half a mile. 


4400 


1=. a 2 1 miles. 


zz 




12)145200 


= cost of the wall in pence. 


20)12100 


= „ ghillings. 


605 


= „ pounds. 



Since there are 1760 yards in a mile, there are 4400 
yards in 2 J miles. 

In 2S. gd. there are 33 pence. 

The whole cost must therefore be 4400 x 33 pence. 

And this product is (by 3«J) equal to jC^^S' 



-UlITmrETIC FOR BEGIXXISRS. 



Exercise XLV. 



1. How many inches are there in 3 yards 2 feet ? 

2. Eeduce 7 furlongs to feet and inches. 

3. In 100,000 feet how many miles 1 

4. Add together 29 yards, 17 j^ards 8 inches, 15 yards 
3 feet 4 inches, and 2 feet 1 1 inches. 

5. What is the dift'erence between 27 yards and 
2 7 inches ? 

6. How many lengths measuring 5 inches each can be 
cut off two balls of string, of which the one measures 178 
3'ards and the other 256 feet? 

7. What is the cost of 17^^ yards of gold thread at a 
halfpenny an inch ? 

8. There are three roads, of which the first measures 
I mile 870 yards ; the second, 1260 yards; and the third 
is as long as the other two put together. Express their 
united lengths in miles, furlongs, and yards. 

9. Suppose it cost 6d. per foot to pave the three roads 
in the last sum : what will be the total cost of the 
paving 1 

10. How many hurdles measuring 3 feet 4 inches each 
will be required to surround an oblong patch of ground, of 
which the two long sides measure 360 yards each, and the 
two short ones 270 yards 2 feet each? 

11. From a road two miles and a half long, two por- 
tions are paved measuring 1500 yards and 7 furlongs 120 
yards respectively : what length remains unpaved ? 

12. Find how many lengths of 3 feet 6 inches each can 
be cut off from a wirei mile 6 furlongs long. 

13. If the telegraphic wire be supported by poles at in- 
tervals of TOO yards, how many such poles will there be 
along a railroad 67^ miles long ? 

14. What Avill it cost to put up a fence on each side of 
a path three-quarters of a mile long at g^d. per foot. 

15. How many times Avill a wheel which is 5 feet 6 
inches in circumference revolve in a journej^ of 7 J miles 1 



SURFACE 3iEASlIRE3fEXt. 75 

SUEFACE. 
40. ^Vlien square or oblong surfaces are measured, it is 
usual to multiply the length by the number representing the 
breadth. The reason of this will be seen from the diagram. 

^ B If A B were three feet long, and 

B G 2 feet long, the whole space 
would be divided into six spaces 
(3x2), each being one foot square. 
The units of surface chosen for 
*^ measurement are always squares 
formed upon the units of length. 

To he learned hy liexui : — 

144 SQUMiE INCHES make one square foot. 
isine SQUARE feet make one square yard. 

Example I. How many square yards of carpet will be 
required to cover a floor measuring i8 feet long and J5 
feet mde ? 

18 X 15=1270 square feet. 
But because 9 square feet make i square yard, 
270 _;. 9 :r:: 30 square yards. 

Example II. How many yards of paper J a yard wide 
will be required to cover the walls of a room 12 feet high, 
which measures 21 feet by i8 feet? and what will it cost 
at 7 ^d. per yard ? 

There are four walls in the room. 

The dimensions of each of the longer walls are 2 1 feet 
by 12, or 21 X 12 = 252 square feet. 

The dimensions of each of the shorter walls are 18 feet 
by 12, or 18 X 12 zr 216 square feet. 

The total dimensions of ihe four walls therefore are 
252 + 252 + 216 -f 216 zz: 936 square feet. 

But 936 square feet =936-^9== 104 square yards. 

And if the paper is half a yard wide, twice this number 
of yards will be required, or 104 x 2 or 208 yards of paper. 

But 208 x 7jd. zi i56od. z=l ^6 los., which is the 
cost of papering the room. 



76 ABITHlEEtlC FOR BEGDTSfEBS. 



Exercise XLYL* 



1. How many square feet are there in the floor of a room 
9 yards long and 4 yards wide ? 

2. Find the dimensions of the ceiling, and of each of the 
four walls of a room 65 feet long, 34 feet broad, and 16 
feet high. 

3. How many square inches are there in a sheet of paper 
I foot 3 inches long and 7 inches broad ? 

4. If floorcloth costs 4d. per square foot, what will it 
cost to cover a passage fifteen yards long and 7 feet wide ? 

5. If 8 square feet of space be allowed for each child in 
a schoolroom, how many children can be accommodated 
in a room 90 feet long and 40 broad ? 

6. How much space wiU be enclosed if 40 hurdles mea- 
suring 3 feet long are arranged so as to include an oblong 
space, 1 4 hurdles being on each of the longer, and 6 on each 
of the shorter sides 1 

7. A man buys a plot of building ground at is. 3d. per 
square foot; the frontage is 27 yards, and the depth 13 
yards : what does he pay for the land ? 

8. How many square inches are contaiaed in a floor 14 
feet long and 9 feet wide ? 

9. What will be the cost of laying down encaustic tiles 
along a gaUery measuring 35 feet long and 16 feet broad, 
at the rate of i penny per square inctu 

10. 'VVTiat will it cost to paper a room 28 feet long, by 
18 broad, and 13 feet high, if the paper is two feet wide, 
at lod. per yard? 

11. How many spaces containing 20 square feet each are 
equal in area to a space measuring 60 yards by 18 ? 

12. HoAv many paving-stones, measuring 3 feet by 2, 
will be required for a footpath half a mile long and 18 feet 
broad, and what will it cost to lay it down at 3d. per 
square foot. 

* Throughout this exercise no questions involving fractions or the 
technical use of duodecimals are used. For a full explanation and 
advanced exercises in this rule, see " School Aiithmetic," p. 58, and 
** Science of Arithmetic," p. 275. 



SUKPACE MEASUB^3LEXT. 77 

SVBFACE— (continued). 

41. When large surfaces, such as fields, gardens, and 
roads are measured, the following table is used : — 

To be learned by heart : — 

Thirty and a quarter (30 J) square yards make one perch. 

Forty (40) PERCHES make one rood. 

Four (4) ROODS make one acre. 

Six hundred and forty (640) acres make one square mile. 

Example I. How many square feet are there in 17 
acres 3 roods ? 

17 acres 3 roods. 
4 

7 1 roods in 1 7 acres 3 roods. 
40 



2840 perches in 17 acres 3 roods. ' 
3oi 



>52oo = 30 times 2840. 
710 = a quarter of 2840. 



85910 — 30 and a quarter times 2840. 
9 



7 73 1 9Q = number of square feet in 1 7 acres 3 roods. 



AVe multiply the acres by 4, and add in the 3 roods. 

There are 71 roods in 17 acres 3 roods. 

We multiply 71 by 40 because 40 perches make i rood. 

There are 2840 perches in 17 acres 3 roods.. 

We multiply 2840 by 30^ because 30 j square yards 
make i perch. 

We multiply 85910, the number of square yards in 17 
acres 3 roods by 9 in order to reduce to square feet. 

The answer is 773190, the number of square feet in 17 
acres 3 roods, 



78 ABJTHMETIC TOR BEGINNERS. 

Example II. What are the dimensions of three fieldsj 
measuring respectively 29 acres 3 roods 27 poles; 15 
acres 2 roods 18 poles; and 31 acres 3 roods 39 poles. 

acres, roods, perches. On adding 39, 18, and 27 toge- 
29 3 27 tlier, we find they make 84. 

15 2 18 But because 40 perches make i 

31 3 39 rood, 84 perches = 2 roods 4 per- 

dies. Set down 4 perches and 

77 2 4 caiTy 2 roods. 

• 2 and 3 and 2 and 3 make 10. 

roods, 
liut because 4 roods make i acre, 10 roods make 2 acres 
2 roods. Set down 2 roods and carry 2 acres. 
2 and 31 and 15 and 29 make 77. 

The answer is 77 acres 2 roods 4 perches. 

Exercise XL VII. 

I. Find the difference in size between a field measuring 
100 acres, and one measuring 79 acres 2 roods 18 perches. 
.. 2. What is the total area covered by five garden plots 
measuring i rood 1 9 perches each ? 

3. How much should I give for a square mile of waste 
ground at j£t, ios. per acrel 

4. How many plots of land measuring 1 1 yards square* 
can be taken out of 15 acres % 

5. If a plot of ground measures one mile long and a 
quarter of a mile broad, how many acres does it contain 1 

6. A man buys a piece of land for a house, measuring 
15 yards in frontage and 14 yards in depth, at 2s. 6d. 
per square foot : what does the land cost ? 

7. Find the rent of five fields, measuring respectively 
17 acres 2 roods; 14 acres 20 perches; 7I acres; 12 
acres 8 poles; and 19 acres 2 roods 12 poles; at 15 shil- 
lings an acre. 

* Obsei-ve the difference between 11 square yards and 11 yards 
square. The first means 11 spaces measuring I square yard each; 
the second means one square space having 1 1 yards as the length of 
its side, or 11 x 11, or 121 square yards. 



-y^—^ 



Hi 



\/ 



CAPACITY OR BULK. 79 

CAPACITY OR BULK. 

42. Wlien a solid mass has to be measured, its length, 
breadth, and thickness have to be separately calculated. 

If a cube measures three inches 
each way, it would, if cut into 
pieces of one inch each wa}^, be 
found to contain th'ree times three 
times three such pieces, or twenty- 
seven cubic inches; i. e., nine in 
each of three layers, as shown in the 
diagram. For this reason twenty- 
seven is often called the cube of three. 

And lo X lo X lo, or looo, is the cube of lo. 
Hence, to find the cubic units in any solid mass we 
measure the length by the breadth and by the height. 

To be learned hy heart : — 

1728 CUBIC INCHES (i 2 X 12 X 1 2) make one CUBIC FOOT. 

27 cubic feet (or 3 x 3 X 3) make one cubic yard. 

Example. How many cubic inches are there in a block 
of stone measuring 14 feet long, 7 feet wide, and 10 feet 
deep 1 

14x7X10 = 980 = the number of cubic feet in the 
block of stone. Therefore 1728 x 980= 1,693,440 or 
the number of cubic inches in the block. 

Exercise XLYIII. 

1. How many cubic feet of air are contained in a room 
measuring 21 feet long, 18 feet wide, and 11 feet high? 

2. How many bricks containing 108 cubic inches each 
can be cut out of a mass of clay measuring 20 feet long, 
16 wide, and 8 deep 1 

3. A reservoir of water is 36 feet long, 30 feet wide, 
and 5 feet deep : how many cubic feet does it contain ? 

4. What will a block of marble cost which measures 
I foot and a half long, 7 inches wide, and 1 1, inches deep 
at lid. per cubic inch ? 



b'O ARITHMETIC FOR BEGINNERS. 

CAPACITY OR BVI.K~(cantinued). 

4*$. AVlien the bulk of liquids, of seeds or of corn, 
has to be measured it is more convenient to employ the 
names of vessels which are in common use. 

To he learned hy heart : — 

Two pints make one quart. 

Four quarts make one gallon. 

Two gallons make one peck. 

Four pecks make one bushel. 

Eight bushels make one quarter (of com). 
Exanqyle. What will ly-J gallons of wine cost at 3s. 6d. 
per pint ? 

17 gallons 2 quarts. Eeduce the gallons to 

4 pints. 

— There are 140 pints in 

70 quarts in 17^ gallons. 17!^ gallons. 
2 Because 3s. 6d. equal 

— 42 pence, 

140 pints in 17 J gallons. Therefore 140 x 42 m 
42 5880 pence = price of 17^ 

gallons in pence. 

12 )5880 

20) 49.0 5880 pence = £2^ los. 
24.10 

Exercise XLIX. 

1. Add together 3 pints, 13 quarts, and 12 gallons. 

2. How many pints are contained in 17 quarters of 
wheat ? 

3. How many bottles containing a pint and a half can 
be filled from 3 casks containing 4J gallons, 6 gallons, and 
8 gallons respectively 1 

4. Find the difference between the contents of a vessel 
of 28 gallons I peck, and one of 19 gallons 3 quarts. 

5. AVhat will be the total capacity of 15 casks contain- 
ing 5 gallons 3 quarts i pint each ? 

6. In 23^ bushels how many pints ] 

7. Eeduoe 10,000 half-pints to gallons. 

8. Divide 17 quarters 7 bushtls 3 pecks by seven. 



LONG IIULTIPLICATIOX. 57 



Exercise XXXVII. 

I. Multiply £^ los. 4d. by thirteen. 
2- Multiply ;;^2 6 15s. 3^d. by seventeen. 

3. Multiply £S4 15s. 8id. by nineteen. 

4. Add together live times ^2 3s. 6d., and twenty- 
three times 17 s. 9d. 

5. What will 47 paire of boots cost at ^i is. 6d. per 
pair? 

6. Find the price of three dozen articles at ^£2 15 s. gd. 
each. 

7. What will 59 acres of land cost at ;£^2 2 los. per 
acre ? 

8. ]Srultiply ^37 15s. 6d. by 73, and subtract 
^1250 65. 4d. from the product. 

9. £28 13s. 6d. X 19; ^12 14s. 7^d. X 23. 

10. ;£"22o los. 4|d. X 41; £tS3 i6s. 8id. x 26. 
II- ;^274 los. 2d. X 30; ,^832 15s. 2-|d. x 23. 
12. £1 i6s. 5jd. X 37 ; ^1862 I2S. 4id. X 53. 

13- ^'216 los. io|d. X 17; ^10 12s. aid. X 29. 

14- ;^io7 3S. iiid. X 53; ^617 2S. gd. x 46. 



;f s. d. 

(>^3 5 2 

31 


£ «. d. 
7294 10 4-1- 
19 





16. Find the total cost of twenty-three articles at 
£1 9s. 6d. each, and of thirty-five articles at 17s. 8 Ad. 
each. 

17. What is the value of 24 casks of wine, each worth 

.£1545. 7d.? 

18. Deduct fifteen times ;^23 4s. 6d. from ^£^1000. 

19. If a draper buys seventy-live shawls at;^3 17s. 6d. 
each, and sells them at four guineas and a half each, what 
profit does he gain 1 

20. AVhat is the cost of 19 tons of iron at £g gs. 6d. 
per ton ? 

]. 2 



58 



AKITH3IETIC TOR BZGIXXEBS. 



HOUSEHOLD ACCOUNTS AXD SIMPLE BILLS. 

3S. The most fireqnent use to Trhicli easy Multiplica- 
tion and Addition of money are put is the calculation of 
small accounts after making purchases at shops. 

Example I. If I buy at a stationer's six quires of note- 
paper at 4jd., three packets of envelopes at 8d. each, some 
drawing-paper for is. 3d-, five black-lead pencils at 3id., 
two boxes of steel pens at is. 6d. each, and an inkstand 
for 4s, 6d., how much do I spend % 

It is usual to arrange such an account thus : — 





s. 


d. 


6 quires of note-paper at 4jd. 


.. 2 


3 


3 packets of envelopes at 8d. 


2 





Drawing-paper 


I 


3 


5 pencils at 3 Jd. 


. I 


5l 


2 boxes steel pens at is. 6d. 


. 3 





Inkstand .... 


.. 4 


6 



14 5^ 



Exercise XXXYin. 
Compute and finish the following accounts: — 



s. 



5 lbs. of rice at 3|d. per lb. 

6 lbs. of soap at 5d. 

8 lbs. of Valencia raisins at 6 id. 

3 packets of starch at 5|d 

6 tablets of soap at 3d. 
5 quires of paper at 7d. 

2 quires of foolscap at 9|d. 
8 packets of envelopes at 4d. 

4 magazines at pd. .. . 

7 prayer-books at 2s. 3d. ... 



BILLS AND ACCOUNTS. 59 



4 lbs. of tea at 3s. 6d. 

5 lbs. of coffee at is. 8l1. 

7 lbs. of loaf sugar at 6 Ad. 

6 lbs. of moist sugar at 4.^d. .. 

3 pairs of gloves at 3s. Qd'. 

2 neckties at is. 6d. ... .. 

4 pairs of stockings at 2s. 2d... 

3 silk handkerchiefs at 3s.- 6d. . , 



3. 13 yards longcloth at 3|d., 25 yards shirting at 8.^d., 
2 dozen napkins at is. 4d. each, 3 tablecovers at 8s. od. 
each. 

4. 19 yards black silk at 5s. 2d. per yard, 5 yards crape 
at 6s. 6d,, 12 yards black alpaca at is. yd., and 3 pairs kid 
gloves at 2s. 8d. 

5. 2 bottles of pickle at lojd.. 3 of fruit at Qd., i bottle 
of blacking; at is. 2d., 9 lbs. of candles at 6^d. per lb. 

6. 5 pairs cotton hose at is, 9d., 6 pairs worsted at 
2S. 3|d., 4 pairs merino at 3s. 2d. per pair, and 2 dozen 
children's socks at 7|d. per pair. 

7. 27^ yards of carpet at 4s. 9d. per yard, 27^ of felt 
at 9|d., making the same 27 1 yards at 4d. per yard; stair 
carpet, 27 yards at 3s. 9d. ; two dozen stair rods at 2|cL 
each. 

8. Two dozen port at 48s. per dozen, 2 dozen pale 
sherry at 46s., 3 dozen Sauterne at 24s., 4 dozen pints of 
claret at 13s. 

9. 3 pairs lace curtains at 23s. 9d. j^er pair; tapes, 
rings, &c., for the same, 6s. 6d. ; making up and fixing 
same, i8s. 6d. 18 yards grey silk at 6s. gd.; 14 yards of 
muslin at 8Jd. 

10. Making and fixing 3 window-blinds for drawing- 
room (2 at i8s. 4d. each, i at 12s. lod.); 7 blinds for 
bedrooms (viz., 2 at iis. 8d. each, i at 7s. 6d., and 4 at 
6s. 2d. each) ; rods, screws, lines, &c., for fixing, 6s. 6d. 
Altering spring rollers, 4s. 6d., cleaning and repairing 
outside blinds, £1 3s. 



CO 



ARITHMETIC FOR BEGINNERS. 



Si:srPLE EEDCCTIOX, AND OTHER USES OF 

MULTIPLICATION. 
i%Sm Example I. How many pence are there in £2t, 1 



20 



shil- 



460 = shillings in ;!^ 2 3. 
12 

5520 = pence in jQ2t,. 



Because there are 
lings in ;£i: 

There arein ;£"2 3 20 times 
23 shillings, or ^6o shillings. 

And because there are 12 
pence in a shilling, there are 
in 460 shillings 1 2 times 460, 
or 5520 pence. 



Hence there are 5520 pence in ^23. 

£xainplG II. Eeduce ^^59 i6s. 2|d. to farthings. 



1196 
12 



14354 
4 



shillings in £$() i6s. 



pence in ^59 i6s. 2d. 



57417 farthings in £^g i6s. 2\<1. 



£S9 i6s. 2|d. We multiply y;59 

20 by 20, and add in 

the 16 shillings. 

There are thus 
II 96 shillings in 
^59 i6s. 

We multiply 11 96 
by 12, and add in 
the 2 pence. 

There are thus 
14354 pence in ;£"59 
16s. 2d. 
We multiply 14354 by 4, and add in the i farthing. 
There are thus 57417 farthings in £^<) i6s. 2jd. 

Example III. How many fourpenny pieces are there in 

-^'139. 15s- ^ 

We multiply £i^g by 20, and add 
in the 15 shillings. There J\re 2795 
shillings in ;£"i 3 9 15s. 

Eut there are three fourpenny pieces 
ill a shilling. Therefore we multiply 
2795 shillings by 3. 

There are thus 8385 fourpenny pieces 
S3S5 in £139 15s- 



£ 


s. 


d, 


139 


15 





20 






2795 






3 







SIMPLE REDUCTION. 61 



Exercise XXXIX. 

1. Eeduce ^i']^^ to shillings; ;^i8 los. to pence: 

2. How many sixpences are there in jQi2)^S 5^- ^ 

3. If there were a coin worth two pence, how many 
could I have in change for two guineas ] 

4. Eeduce £2> ^9S- 6|d. to farthings. 

5. Find the price of 17 articles at 2|d. each. 

6. How many things worth three halfpence each can I 
buy for 5s. 1 

7. Find the difference between the number of four- 
penny jDieces and the number of threepenny pieces in 

£^ 15s. 

8. In seventeen half-crowns how many pence 1 

9. If I changed a five-pound note into threepenny 
jneces, how many should I have? 

10. How many more shillings are there than half- 
crowns in twenty guineas % 

11. Eeduce the two sums ;!^i 2 1 6s 3 ^d. and £2^ 7s. gd. 
to farthings. 

12. Find the difference in pence between ;£^6 14s. 8d. 
and;£'5o. 

13. Divide ;^i75 i6s. Qd. by 3, and give the answer in 
farthings, 

14. How many halfpence are equal in value to twelve 
bags of money containing jQi i6s. 3d. each 1 

15. Multiply ;£^763 i8s. 4d. by 15, and reduce the 
answer to pence. 

16. How many halfpence are there in seventeen guineas '? 

17. How many farthings are there in seven times 
^i8 6s. 4id? 

18. Find the total number of farthings in nine guineas, 
three half-sovereigns, and fifteen half-crowns and seven 
sixpences. 

19. How many articles worth three halfpence each 
could I buy for ;^57 los. ? 

20. Add the number of farthings in seven hundred and 
fifty I'ounds to the number of shillings in the same sum. 



62 - AKITHilETIC FOR BEGrN'>T:RS. 

divisio:n^ of money. 

34:. In dividing a sum of money, pounds, skillings, 
pence, and farthings must be separately divided in succes- 
sion, and when there is any remainder, it must be reduced 
to the term next below it. 

Example I. Divide £^^ 6s. 3d. by three. 

jQ s. d. AYe find one-third of £2)2> ^7 *^^® 
2,)^2> 6 3 method of simple division, lO. 

• The answer is ;£i i. 

1 1 2 I A third of 6s. is 2s. 

The third of 3d. is i penny. 



The answer is jQi i 2s. 3d : 

Example II. Divide jQi6^ iis. 4M. by 7. 
;^ s. d, ^Ye divide 164 by 

7 )164 II 4i 7^ and find the quo- 

23 10 2J : I remainder. tient to be ^£"23 with 

a remainder, jQt^ 
J^ow jQ^ and us. reduced to shillings make 71 shil- 
lings. 

The seventh of 71 is 10, with a remainder of i shilling. 
One shilling and fourpence make 1 6 pence. 
The seventh, of 16 is 2, with a remainder of 2 pence. 
2 pence and Jd. reduced to farthings make 10 farthings. 
The seventh of 10 is i, with 3 farthings remainder. 

The nearest answer therefore is ;£22, los. 24d., with 
three farthings remaining undivided. 

Exercise XL. 

1. "Wliat is the fourth part of ;?^i los. ? 

2. Divide ;£'26 by five. 

3. Add the half of ;£"io los. to the third part of the 
same sum. 

4. If ;£^25o I OS. are left to be divided among 6 persons, 
how much will each receive ? 

5. ;£i8 have to be divided among 10 persons: how 
much will each receive % 



COMPOUND DIVISION. 



63 



6. From the half of five guineas take the third of five 
guineas. 

;£■ s. d. . ^ s. d. 

7. 8)7 2 6 7)23 10 4 



8. 10)123 16 



£ s. 

11)25 2 



9. ;^i8 I2S. 6d.-f-io; ^2453. 7d. 47. 
10. £3^ lys- 3^.-11; £19 6s. 5d.-f-i2. 
II- ;^f37 15s. 3^.-5; £^H 10S.-8. 

12. ;£"207 15s. 6d. -6; ;£"327 14s. Sd.^g. 

13. Add together the eighth and the tenth parts of 
£S3 I2S. 6d. 

14. Take the twelfth part of ^126 3s. from the whole 
of that sum. 

15. A gentleman bequeaths ^1250, of which one-half 
is given to his eldest son, one-third to his second son, and 
the remainder in charities ; how much money is given to 
each purpose 1 

16. ;^2i3 17s. 6d. + ^519 I2S- 8d. 

12 

17. ; ^5o4 108.-^196 13s. 4d. 

8 

18. ;^27 15s. 6id. + ^^196 i8s. 7d. - £s9 los. 4$^- 



19- ;£"325 i6s. 7d. x 10 



7 +4 



20. Find the difference between the eighth and the 
twelfth parts of ^£1250. 

21. If the sum of ^1827 19s. 6d. be divided into nine 
parts, of which A receives five, and B four, what is the 
share of each 1 

22. Divide a legacy of ^8757 2s. among three persons, 
so that the first shall have five parts, the second four 
parts, and the third two parts . 



64 ARITHMETIC FOR BEGINNERS. 



DIVISON OF MONEY {contmmd). 

3o« Wlien the divisor is greater than 12, each remain- 
der must be set down separately, and the work done as in 
Long Division (2S). 

Example. Divide ;£7i35 i6s. 4d. by 27. 

AVe first divide ;£"7 1 3 5 by 2 7, 
asin2?. 

The quotient is ^£"264, and 
;£'] are left undivided. 

AVe next reduce these ^£'7 
and tlie i6s. to shillings. They 
make 156 shillings. 

On dividing 156 by 27, the 
nearest answer is 5 s., and 21 
shillings remain undivided. 

"We next reduce these 21 
shillings and 4d. to pence. 
They make 256 pence. 

On dividing 256 by 27 we 
find the quotient to be 9 pence, 
and 13 pence remain undivided. 

We next reduce the 13 pence 
to 52 farthings. 

On dividing these 52 by 27 
we find the quotient i, and 
a remainder of 25 farthings 
which cannot be divided by 27. 



25 farthings remain undivided. 

The answer is, therefore, ;£264 5s. 9|d., and 25 re- 
mainder. 



£ s. 

7)7135 16 
54 


d. £ 
4(264 


173 
162 




115 

108 




7 
20 




27)156(5 
135 


shillings. 


21 
12 




27)256(9 
243 


pence. 


13 
4 

27)52(1 
27 


farthing. 



MISCELULSTEOrS EXEKCISES. 89 

3. To how many persons can I give 5Jd. out of ;^46ol 

4. How many lengths of 8§^ inches can be cut from a 
piece 172 yards long? 

5. There are 30 J square yards in a perch : how mauy 
perches are there in 5289 yards 1 

6. 32067 -^ 6f; 5183-1. I li. 

7. 41682 -i. i5|; 31625 -f- 8^. 

8. 2 196 + 578; 516382 - 29547. 

i5§ 172I 

9. Find the total number of shillings in 28 half-crowns, 
twelve half-sovereigns, and 17 ^£"5 notes. 

10. What is the worth of a 17 lb. bag of tea at ^{d. 
per oz. ? 

1 1. How many persons can receive 4jd. each out of a 
sum of ;£"i2 i8s. ] 

12. Multiply the product of 712 and 518 by the differ- 
ence between these numbers. 

13. Add together 45 pence, 45 farthings, and 45 shil- 
lings. 

1 4. Take seventeen thousand four hundred and nineteen 
jwunds fourteen shillings and fourpence three farthings 
from a million pounds. 

15. How many halfpence are there in fifteen guineas? 

16. How many packages weighing 2^ oz. each can be 
made up out of two chests of tea weighing i cwt. 3 qrs. 
17 lbs. each? 

1 7. Add together f of is., ^ of ;£"i, 4 of a crown, and 

A of ^5- 

18. What would it cost to put up a fence a mile and 
three-quarters long at is. 7|d. per yard? 

19. If I draw off from a vessel successively a third, a 
fourth, and a sixth of its contents, what portion of the 
whole remains ? 

20. How many yards of velvet trimming j^ of a yard 
wide can be cut from a piece 31!^ yards long and f of a 
yard wide ? 

2 1. How often does a clock which chimes every quarter 
of an hour chime in 17 weeks 3 days ? 



90 

ANSWERS TO EXEECISES. 

VII.-(i) 12. (2) 8. (3) 17. (4) 14. 4. (7) 8 

(8) 13. (9) 15. (10) 8. (11) 8. 7. 8. (12) 14. (13) 7 
VIII. — (i) II. 12. 16. II. 13. 10. 12. 13 

(2) 7- 9- 5- 5- 5- 8. 9. 7- 7- 

IX.-(i) 37. 81. 92. 91. 54. 75. 75. 50 

(2) 24. 3y 51- 59- 54- 24. ss- 21. 16. 
X.— 8. 4. 19. 47. 67. 68. 34. 5. 5. (i) 4 

36. 38. (2) 43. (3) 15 pence. (4) 32. (5) 76 

(6) 23. (7) 21. (8) 12. (9) 27. (10) 17. (11) 34. 

XL— (i) 94. 86. 53. (2) 87. 99. 95. (3) 57 

(4) 98. (5) 84- (6) 92. (7) 95 yards. (8) 56 

(9) £ii- (10) 29. 

XII.— (i) 884. 550- 931. (2) 867. 870. 450 

(3) 166. (4) ;^8o4. (5) 96. (6) 270. (7) 115- (8 
49- (9) 102. (10) 46. (11) 775. 

XIV.-959. (2) 35. 286. (3) 161. (4) 22. (5) 
187. (6) 124. (7) 31. (8) 313- (9) ;£i75. (10) 
156. (11) ^39. (12) £39' (13) 174. (14) 295. 
186. 713. (15) 339. 376. (16) 134. 197- 268. 
(17) 482. 167. 487. (18) 257. (19) 665. (20) 119. 
(21) 484. (22) 169. 

XVL— (i) 750. (2) 3561. (3) 4322. (4) ^1392- 
;^io97. (5) 326 mUes. (6) ^387. (7^ 58. (8) B. 
over C 51. B over A 834. C over A 783. (9) 5870. 
'o>034. 4957. (10) 6240. 6044. (11) 1086. 831. 
4375. (12) 2859. 1456. 

XVII.- (i) 12. (2) 15. (3) 16. 24. (4) 24. (5) 
6. 8. 9- 10. (6) 4. 5- 3- 2. (7) 6. 4. (8) 5- 
(9) 7- (10) 4- 6. (11) 3. (12) 2. 3. 

XVIII.-(i) 36. 75- (2) 92. 114. (3) 318. (4). 
906. (5) 735- (6) 507- (7) 79- (8) 187. (9) 34- 
1587. 246. 4218. (10) 1436. 1254. 1578. 

XIX.— (i) 28. 36. 28. (2) 15. 32. 10. 12. (3) 
20. 25. 45. (4) 36. 28. 12. 24. (5) 20. 36. 
16. (6) 18. 24. 30. 12. (7) 4. 4. 7. 2. (8) 5. 



AXSWEBS TO EXERCISES. 91 

4- (9) 32. (10) 48. (11) 60. (12) 55. 33. 44. 

(13) 5136. 10,196. 28,484. (14) 20,240. 6355. 
(15) 32,484- 3126. 35,480. (16) 24,508. 24,579. 
(17) 606. 5135. 12,648. (18) 9820. 2876. 

XX.-(i) 56- 18. 36. (2) 35- (>Z' (3) 72. 35- (4) 
6. 8. 9. (5) 6. 10. 5. 3. (6) 6. 4. 3. 2. 12. 

(7) 28. 40. (8) 6:^. (9) 4. 12. 2. 24. 3. 16. 
8. 6. 

XXI.— (i) 2065. 2473. (2) 10,450. (3) 156. 324. 
567. 2076. (4) 136. 312. 1736. (5) 114. 674. 
(6) 168. 708. 7500. (7) 711 pounds. (8) 239. (9) 
623. (10) 116. 2152. 2856. (ii) £i^,SZ^. (12) 
The latter by 31. (13) 7808. (14) 1404. (15) 3640. 
67,529- 3336. (16) 7360. 5778. 62,998. (17) 9582. 
103,500. 15,183. (18) 49,626. 28,728. 12,168. (19) 
33.304- 10,980. 35,889. (20) 16,335. 24,822. 16,136. 
(21). 8274. 56,980. 74,136. (22) 36,141. 72,369 
62.064. 

XXIII. — ii) 170. 280. 3100. (2) 2160. 2i,6oo- 
216,000. (3) 195,200. (4) 1,245,600. (5) 76,700. 
(6) 326,480. (7) 32,500. 

XXIV.-(i) 1206. (2) 11,310. (3) 1850. (4) 
64,625. (5) 923,601. (6) 8820. (7) 1904. 35,280. 

(8) 308. 812. (9) 3540. (10) 2560. 43>26o. (11) 
58,473. (12) 557. (13) 13,232. 19,776. (14) 546,936. 
98,268. (15) 900,798. 624,085. (16) 660,969. 22,790. 
(17) 2,195,095. 437,525- (18) 643,282. 821,016. (19) 
15,310,600. 6,621,534. 

XXV.~(i) 17,496. 311,148. (2) 819. (3) 67,284. 
495,648. (4) 1 128. 7632. (5) 612. 3888. 3384. 
(6) 83,020. 1,373,247. (7) 383,760. 1,580,040. (8) 
2,535,162. 93,984. (9) 55,530. 5,126,247. (10) 
778,185. 159,350. (11) 2,302,016. 1,229,984. (12) 
3,064,320. 3,342,800. (13) 391,068. 33,477,138. 

(14) 14,784. (15) 60,903. (16) 62,720. 
XXVI.-(i) 21,182. 53. (2) ^40. ^20. (3) 

412. (4) 42. 132. 266. (5) 125. (6) 305. (7) 
150. 200. 120. 300. (8) ;£2,434. (9) 209. (lo) 



92 AIUTIIMETIC rOR BEGIXNEIIS. 

21,130. (11) 21,423. (12) IT93. (13) 84,011-3. 
9805-3. (14)4526-3.7198-6. (15)3997-5- 725.460-1. 

(16) 89..962-3. 5332-3. (17) 3962-2. 4802-5. (18) 
8134-3. 68,474-3. 

XXVII.-(i) 40. (2) 52-20.(3) 81. (4) 42,533-9- 
(5) 33^- (6) 31- (7) 1980. (8) 178. (9) 15 and 
55 remainder. (10) 7. (11) 20. (12) 157-108. (13) 
453-15- 3478-3- 1267-15. (14) 492-194. 627-58. 
2976-9. (15) 285,448-2529. 2415-164. 4807-10. 
(16) 880-372. 5891-76. 2599-205. (17) 1345-3- 
761-25. 4010-16. (18) 34,346-20. (19) 394. 

XXVII [.-(1)32-79. (2)392-185. (3)176,938-2; 

17,693-82 ; 1769-382; 176-9382. (4) 17-69; 3^3-5^ y 
526-84; 4793-82. (5) 10; 1000; 100. (6) 7-59. 

(7) 59, ^ith 763 remaining. (8) 204-143. (9) 1383- 
16; 13-23,256. (10) 383-365. (11) ;^54; ;£"ii8 10 
shillings. (12) ^^122 and 4c foiirpences ; ^^682 and 
40 fourpences. (13) 17-136. (14) 276. (15) 568-320. 
(16) 811-222; 64-4665. (17) 61-4870; 86-29,175. 
(18) 17-14,438; 1774-248. (19) 1265-187; 58-676. 
(20) 175,990. (21) 1173—614. 

xxix.-(i) 39. (2) 30. (3) 80; 2. (4) 5; 16. 

(5) 20. (6) 160. (7) 442. (8) 262. (9) 160. (10) 
4. (it) 13; 73-246. (12) 31,860; 630. (13) 268. 
(14) 69,592, (15) 149,076. 

XXX.— (i) 4064 grs. (2) 1867. (3) 66 yrs. (4) 
884 shillings. (5) 900 ; 21,600. (6) 45 yds. (7)35- 

(8) 1232. (9) 608. (10) 132. (11) ^12,280. (12) 
;£2oo. (13) 139-668. (14) 313. (15) 28,830. (16) 
332. (17) 1568; 1848. (18)22,222—2. (19)47,520; 
31,680. (20) 25,908. (21) 384. (22) 1279. (23) 
3,652,264. (24) 273. (25) 45j904. (26) 10,000. 
(27) 541,985; 660,372. (28) 157,030. (29) 6878. 
(30) 7168. (31) 41,879. (32) 22,704,108. (33) 
50,000. 

XXXIL— (i) 8—18. (2) 15 pence. (3) 2^,d. (4) 
5d. (5) 3d.; IS. 3d. (6)2s. 7d. (7) 8|d. (8) I Id. 

(9) 15- (10) 2d. (II) 6d. (12) 15. 



Ai»S\rERS TO EXERCISES. 93 

XXXlII.-(i) £2 14s. 7d. (2) £zz 19s. lod. 
(3) £'2 8s. 7d. (4) ;^52 75. 5d. (5) ^50 9s. id.; 
^,^381 OS. 3d.; £-7^%2 17s. 8d. (6) ;£i2 5s. 3d.; 
^£'291 3s. 3d.; ^28 6s. i|d. (7) iis. 3^d. (8) 
;^i 8s. 7jd. (9) los. 3d. (lo) £^ i2s. 4d. (11) 
^22 5s. 

XXXIV.— (I) ^6327 i8s. iid. (2) 7:3612 IS. 5id. 
(3) ;^i2,3i7 8s. 4id. (4) ^5199 i6s. 8ld. (5) 
7:8189 8s. I lid. (6) ^4017 15s. 2d. (7) ^22 
103. I id. (8) ;£'68i 1 8s. 7d. (9) £^2 14s. 2d. 
(10) ^2664 IIS. 8|d. ; ;£4367 is. lod. ; ;£"5744 
15s. 5id. (11)^28,923 OS. io|d.;;£'57,5i5 12s. 8id.; 
^29,148 15s. 8id. (12) £2 IS. 8|d. (13) ;^35,58i 
IIS. ii|d. ; ^20,582 14s. 6d. ; ;£"37,5i3 ^Ss- 9^. 

XXXV.-(i) 3S. 8d. (2) ^123 6.. 6d. (3) £s 
i6s. 4d. (4; ^18 5s. 3d. (5) ^518 los. (6) 
^^2386 6s. lo^d. ; ^£"1322 6s. 8M. ; ^^78 os. lod. 
(7) ^2795 4S. 43d.; ^14,888 5s. 9|d.; ^2712 
6s. 5id. (8) ^978 9s. 5id. (9) ^'197 14s. 8d. (10) 
;^i86 los. o.^d. (11) £2 19s. 7|d. (12) 3s. 2d. 
(13) ^74 4S.'55d. (14) £a9 15s. 

XXXVI.— (i) I2S. 6d. ; fy 14s. (2) ^^15 5s. 9£d. ; 
£yZ 7s. 9d. (3) 8s. ijd. (4) £2 3S. (5) ;£io3- 
(6) 17s. 9.|d. (7) ^42 6s. lod. ; £\\ 12s. iid. ; 
;^27 15s. 7id. (8) ^127 17s. 4|d.;^i28 iis. 4d. ; 
;^i53 8s. lod. (9) ;^iio9 17s. 4id.;^i5 15s. 4d. ; 
^196 i8s. 4d. (10) £26 14s.; £1 i6s. 4d. (11) 
^155 i6s. 3d.; ;^i4 los. 7id. (12) ;^io5 8s. 4d. 
(13) ^31 8s. lod.; ^17 15s. 9d. (14) ^474 
7s. 6d.; £c) 2s. (15) ^139 13s. (16) ;£"3i5 4s. 6d. 
(17) ;£545 I7S- 6d. (18) ^5 iis. 8d. (19) £^ 
i2s. 6d. (20) £']% 17s. 3d. (21) ;£"223<2 los. lod. 
(22) ^£4190 5S. 4d- (23) 2741 5s. Zl^' (24) ^655 
i2s. (25) £^, 

XXXVII.-(i) ^45 14s. 4d. (2) ;£454 19s. njd. 
(3) ;£io4o i8s. ofd. (4) £z^ 5S- 9^. (5) ^5° 
los. 6d. (6) ^100 7s. (7) ^1327 los. (8) ^1507 
5s. 2d. (9) ;^544 i6s. 6d. ; ;£292 i6s. 4jd. (10) 



94 AWTHMETIC POR BEGIKNEBS. 

;£904i 5s. 4jd. ; £3999 i3S- lo^d. {n) £^23$ 
5S-; ;f 19,153 9S. 3|d. (12) £67 9s. Sjd.; ^98,718 
15s. io|d. (13) ^3681 4S. 6id. j £soj i6s. 5|d. 
(14) ;^568i 8s. 8id.; ^28,388 6s. 6d. (15) ;^2i,i8i 
OS. 2d.; ^£138,595 17s. i^d. (16) ;£64 i8s. 3|d. 
(17) ^365 los. (18) ^£651 i2s. 6d. (19) ^63 

15s. (20) ;£"l8o OS. 6d. 

XXXVIII.-fi) £1 17s. i|d. (2) ;^3 IS. 9|d. 
(3) ;£3 17s. 9id- (4) ^7 17s. 3d. (5) 10s. ojd. 
(6) £ 210s. 2d. (7) £13 7s. 9|d. (8) ^15 12s. 
(9) ^11 7S. 8d. (10) ^6 19s. 

XXXIX.— (i) 35.380 shillings 4430 pence. (2) 55,410. 
(3) 252. (4) 3819. (5) 3s. 6Jd. (6) 40. (7) 55. 
(8) 510. (9) 400. • (10) 252. (11) 12,302; 23,41?. 
(12)3184. (13)56,268. (14)10,440. (15)2,750,100. 
(16) 8568. (17) 123,095. (18) 12,480. (19) 9200. 
(20) 735>ooo- 

XL.-(i) 7s. 6d. (2) £s AS- (3) £S 15s. (4) £41 
T5S- (5) £^ i6s. (6) 17s. 6d. (7) 17s. 9|d.; £3 7s. 
2ld.-i. (8) ^12 7s. 8d.: £2 5s. 8|d.-9. (9) £1 
17s. 3d.; £3 9s- 4id.-5. (10) £3 los. 7|d.-7; £1 
i2s. 2id.-8. (11) p^7 IIS. oid.-2; £23 is. 3d. (12) 
£34 i2s. 7d.; ^36 8s. 3id.-2. (13) ;^i2 is. 3id. 
(14) £i^S i2S. 9d. (15) ;£625; ;£4i6 13s. 4^. ; 
^208 6s. 8d. (16) ;f6i i2s. 6d. (17) ^38 9s. 7d. 
(18) £^5 OS. 4d. (19) ^465 9S- 4|d.-3. (20) £z2 
IS. 8d. (21) ;£'ioi5 los. lod. A; ;£^8i2 8s. 8d. I 
(22) The first has ^£^3980 los. ; the second, ^^3184 8s. 
the third, ;;^i592 4s. 

XLL— (i) ;^23 IS. 6id.-ii. (2) ^45 4S. 4|d. 
;^40 3S. ioid.-i2. (3) ^44 19s. 8|d.-6. (4) £4 
3s. 4d. (5) Each child ^555 us. i^d. ; each nephew 
;^4i6 13s. 4d. (6) £58 i6s. 4|d. (7) ^^52 is. 8d. ; 
^23 I2S. iifd.-3. (8) £9 5s. 5ld.-7; £9^ os. 5|d. 
-17- (9) £9 9S- 4-3^.-6; ^160 14s. 3jd.-36. (10) 
^196 7s. 5id.-4; £28 5s. ioid.-6. (11) ^122 3s. 
o4d.-6 ; ;£^i07 15s. 7d- 28. (12) ^49 os. 6d.-i6; 
;£34 4S. iid-52. (13) ;^83 19s. 4d. (14) £16 18s. 



ANSWERS TO EXERCISES. 95 

9ld.-36. (15) I2S. i|d. (16) £10 IS. 9i(l.-3. (17) 
£2^ IS. 3id.-7. (18) ^84 I2S. 8id. (19) 64,294. 

(20) The one receives ;£468 15s. 3 and the other ;^53i 5s. 

XLIL— (i) 1320. (2) £1 15s. o|d. (3) ^^95 3S- 
4d. (4) 768. (5) £2 15s. 2jd. {6)a £ig 2s. 7d. 
£^2> IS. I id., ^17 9s. 8d. ; h ^457 14s. 4d., ;£204 2S. 
6d., ^13 6s. 7d. (7) 1280. (8) 522. (9) 4igs. 3s. (10) 
691-12. (11) 4780. (12) 477. (13) 150. (14) 514 
sixpences and 3|d. ; 102 h.-c. 2s. 5.^d. (15) 4800. (16) 
^607 i2s. 8|d.; ^"434 OS. 7|d. 

XLIIL-(i) 6s. 7 id. (2) £1 5s. 3d. (3) ^13 l5s- 
3d. (4) £2 17s. 4d. (5) £s 13s. id. (6) ^117 9s. 
(7) ^26 OS. lod. (8) 17 10 persons. (9) 27,480. (10) 
^14 9s. 2|d. (11) 9491. (12) ;^i2 8s. 4d. (13) 
£"1 IS. (14) 153 of each, or 459 persons in all. 

XLIV.— (i) 15 lbs. 4 oz. (2) I lb. 14 oz. (3) 15s. 
(4) 2 tons 16 cwt. 19 lbs. (5) I qr. 5 oz. (6) 411 lbs. 
6576 ozs. (7) 1520. (8) 62 f lbs. (9) 108 lbs. (10) 95- 
52. (11) £^ i2s. id. (12) 8 cwt. I qr. 1 3 lbs. 8 oz. (13) 
^16 5s. 6d. (14) 448. (15) 6 tons I cwt. 2 qrs. 13 lbs. 
II ozs. ; 4 tons 11 cwt. i qr. 26 lbs. 7 ozs. (16) 8 tons 
3 cwt. I qr. 19 lbs. 3 oz. (17) 4 cwt. i qr. 25 lbs. 2 oz. 
(18) 4 tons 15 cwt. 3 qrs. 5 lbs. (19) 5 tons 11 cwt. i qr. 
26 lbs. ; 56 tons 19 cwt. i qr. 15 lbs. (20) 2 tons 11 lbs. 

(21) 883—5. (22) 2240. (23) ijd. (24) 261-1. 
(25) 23 lbs. 12 ozs. (26) ;^38 i6s. 4d. (27) 6 cwt. 21 
bs. 12 oz. (28) 197,120 ozs. 3,153,920 drs. (29) 5,4656. 

XLV. — (i) 132. (2) 4620 ft. 55,440 ins. (3) 18 miles 
7 furs. 113 yds. i foot. (4) 6^ yds. 11 ins. (5) 26 yds. 
9 ins, (6) 1896. (7) ;^i 6s. 3d. (8) 4 miles 2 furs. 
100 yds. (9) ^568 los. (10). 1135-8. (11) 5 furs. 
140yds. (12)^2640. (13)1188. (14) ;^3i3 los. (15) 
7200. 

XLVI.— (i) 324. (2) Ceiling 245 sq. yds. 5 ft. ; 2 
long walls 115 sq. yds. 5 ft. each ; 2 short walls 60 sq. 
yds. 4 ft. each. (3) 105. (4) £^ 5s. (5) 450. (6) 
84 sq. yds. (7) £i()'j 8s. 9d. (8) 18,144. (9) ^336. 
(10) ^8 i6s. lid. (11) 486. (12) 7920; ;^594. 



7) 

1 



OG ARITHMETIC FOR BEGINNERS. 

XLVII. — (i) 20 a. I r. 22 p. (2) i a. 3 r. 15 p. (3) 
^/:224o. (4) 600. (5) 160 a. (6) ;^236 5s. (7) 

\xLVliL-(i) 4158. (2) 41,960. (3) 5400. (4) 
£8 13s. 3d. 

XLIX.— (i) 15 gal. 29 qt. i pt. (2) 8704. (3) 95— 2< 

(4) 10 gal. I qt. (5) 88 gal. i pt. (6) 1504. (7) 621 
gal. (8) 2 grs. 4 bus. 2 pks. 

L.— (1)8760. (2)2976. (3)9,936,000. (4);£"26i5s.6d- 

(5) 3406. (6) ^35 15s. od. (7) 300,960. (8) 10,950. 
LI.-(i) £6 i6s. 6d. (2) 2346. (3) ;^47 i8s. 6d. 

(4) £9 8s. 4d. (5) £3 13s. ijd. (6) ^276 2S. lojd. 
(7)284. (8)248. (9)676. (10) ;£83 2s. 8id. (11) 
6080 yds. ; ;£'i596. (12) 1800 cub. ft. ; 3,110,406 c. in 
(13)3520. (14) 448; 1792; 35,840. 

LII.-(i) 10; 9. (2) 4; 8. (3) 2; 5. (4) 2. 

(5) 4- (6) 20; 10; 6; 15. (7) 12; 12. (8) 5d.j 15s. 

(9) 2jd. (10)9; 4; 15. (11)15. (12)21. (13)20. 
(14) I; TO-; T- (15) t- (16) 2 feet; 6 furs, j 7 ins. 
(17) 6s. 3d. ; IIS. 8d. ; 8s. 4d. (19) 4 ; 8 ; .10. (20) 

6 furs. ; 1232 yds. ; 550 yds. (21) 14 lb. ; 8 cwt., 2 qrs.^ 

(22) 2 ft. 6 ins. ^Hj 

LIII.-(i)4. (2) J. (3)4. (4)Aor|. (5)8s.4d. 

(6) ^ lb. or 14 oz. (7) 8. (8) 7 ins. (9) 35 minutes. 

(10) 3 qts., ij gills. (11) ^. (12) IS. 8d.; £1 8s. 
LIV.— (i) 621. (2) 66,674. (3) 9570; 14,432; 

2854^. (4)8i6|; 3751; 13,8244. (5) 997J. (6) 9180. 
(7)143,6561. (8) 8858i ; 299,559i. 

I,V.— (i) 1953I. (2)5940; 960 p., 5 yds. (3)19,200. 
(4) 714 and 4 ins. remain. (5) 174; 25^ yds. remain. 
(6)4858-^^; 465-' ^ (7) 2725-^2 ; 3614-2. (8) 
177—3; 2826— 1215. (9) 1890. (lo)' ;^3 13s. 8d. 

(11) 688. (12) 71.550,304. (13) £2 9S. 84d. (14) 
^^982,580 5s. 7|d. (15) 7560. (16) 2478—6. (17) 
£2 IS. iijd. (18) £2So 5s. (19) J. (20) 378. 

(21) II;7I2. 



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