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5. If a mason built 3 rods of walk per day, how long did it take him to build 21 rods? 6. B paid 96 cents for glass at 8 cents a pane.

How many panes did he buy?

7. At $9 a cord, how many cords of wood can be bought for $45?

8. If a man earns $11 a week, how many weeks will he require to earn $66?

9. How many lots of 11 acres each can be made from a farm containing 132 acres?

10. If a farmer exchanges 6 firkins of butter worth $20 a firkin for cloth at $4 a yard, how many yards will he receive?

11. My coal cost me $35 at the rate of $7 a ton. How many tons did I purchase ?

12. How many engravings must an artist sell for $12 apiece to realize $84?

13. When sugar is worth 9 cents a pound, how many pounds can be bought for 45 cents ?

14. At the rate of $7 a rod, how many rods of fence can be built for $63?

15. I hired a man for $45 to do a piece of work at the rate of $5 a day. How many days did it take him?

16. A lady bought some silk worth $3 a yard, paying $36 for it. How many yards did she buy?

17. How many barrels of flour at $8 a barrel can be bought for $48?

18. How many pounds of nails can be bought for 75 cents at the rate of 4 pounds for 20 cents?

19. I bought 6 sheep for $30. How much did I pay per head?

20. At $5 per head, how many head of sheep can be bought for $37?

Ans. 7 sheep and $2 left. 21. A man whose wages were $4 a day earned in a certain time $33. How many days did he work? Ans. 84 days.

91. From examples 20 and 21 it is apparent that the remainder may be written either after the quotient, as in the answer to the 20th, or as a part of it, as in the answer to the 21st.

When written as a part of the quotient, the remainder is expressed by placing the divisor under it with a line between them. Such an expression shows that each unit of the remainder is to be divided into as many equal parts as there are units in the divisor.

.When any thing is divided into two equal parts, each of the parts is called one half.

When into three equal parts, each part is called one third. When into four equal parts, each part is called one fourth.

When into five, six, seven, etc., equal parts, the parts are called fifths, sixths, sevenths, etc.

1 expresses one half, or one of two equal parts of any thing.

expresses one fourth, or one of four equal parts of any thing.

expresses two fifths, or two of five equal parts of any thing.

expresses five twenty-sevenths, or five of twenty-seven equal parts of any thing.

92. One or more of the equal parts of any thing is called a Fraction.

93. Read the following fractional expressions:

3 it B ? 융륭 18
註. 19

25

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18

8 94

24

22. If James should divide 25 apples equally among 5 boys, what part of the whole would each receive? How many apples would each receive?

ANALYSIS.If he should divide 25 apples equally among 5 boys, . each boy would receive one-fifth of 25 apples, which is 5 apples.

23. If flour is worth $8 a barrel, what will one-half barrel cost?

24. Mr Smith bought 8 bushels of chestnuts for $24.
How much did he pay per bushel? How much is one-eighth
of 24?

25. What is one-sixth of 36? Of 42? Of 48? Of 60?
26. What is one-tenth of 50? Of 60? Of 70? Of 80?
27. What is one-seventh of 14? Of 28? Of 42?' Of 49?

WRITTEN EXERCISES.

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94. 1. Divide 1396 by 4.
1ST PROCESS.

ANALYSIS.–For convenience we
Divisor. Dividend. Quotient. write the divisor at the left, and the
4) 1396 (300 times. quotient at the right of the dividend,
1200 40 times.

with curved lines between them, and
196
9 times.

begin at the left to divide.

4 is not contained in 1 thousand 160 349 times.

any thousand times, therefore the 36

quotient can not contain units of any
36

order higher than hundreds. Hence
we find how many times 4 is con-
tained in all the hundreds of the

dividend. I thousand plus 3 hun-
2D PROCESS.

dreds equals 13 hundreds. 4 is con4) 1396 (349

tained in 13 hundreds 3 hundred 12

times and a remainder. We write

the 3 hundreds in the quotient and 19

multiply the divisor by it, obtaining 16

for a product 12 hundreds, or 1 thou36

sand 2 hundred, which we write under 36

units of the same order in the divi

dend. Subtracting this product from the partial dividend, there is a remainder of 1 hundred.

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hunds.
tens.
units.

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1 hundred plus 9 tens equals 19 tens. 4 is contained in 19 tens 4 tens times and a remainder. We write the 4 tens in the quotient and multiply the divisor by it, obtaining for a product 16 tens, or 1 hundred, and 6 tens, which we write under units of the game order in the partial ilividend. Subtracting, there is a remainder of 3 tens and 6 units.

3 tens plus 6 units equals 36 units. 4 is contained in 36 units 9 times. We write the 9 units in the quotient and multiply the divisor by it, obtaining for a product 36 units, or 3 tens and 6 units, which we write under units of the same order in the partial dividend. Subtracting, there is no remainder. Hence the quotient is 349.

In the second process all ciphers are omitted from the right of the products and the significant figures are written under units of the same order. The quotient also is expressed by writing the different orders of units in proper succession.

PROOF.—349 the quotient, multiplied by 4 the divisor, is equal to 1396 the dividend.

Hence the work is correct. (Prin. 3.)
Solve in like manner and prove:

2. 738 : 3. 5. 4821 = 3. 8. 7848 - 9.
3. 845 : 5. 6. 3462 ; 6. 9. 8432 : 4.
4. 385 : 7. 7. 3864:8. 10. 8308 : 7.

95. The solution of the preceding examples may be shortened by performing the multiplications and subtractions without writing the results. This process is called Short Division.

The solution of Example 1 by Short Division is as follows: Solve by short division :

PROCESS.

ANALYSIS.—4 is contained in 13 hundred 3 4)1396

hundred times and 1 hundred remainder. We

write 3 hundreds in the quotient under units Quotient 349

of the same order in the dividend. 1 hundred

remainder united with 9 tens makes 19 tens. 4 is contained in 19 tens 4 tens times and 3 tens remainder. We write the 4 tens in the quotient under tens of the dividend. 3 tens remainder united with 6 units make 36 units. 4 is contained in 36 units 9 times. We write the 9 in the quotient. Hence the quotient is 349.

11. 4872 = 4. 17. 3248.
12. 6830 : 5. 18. 5256
13. 2976 ;-6. 19. 49,86
14. 2985 ; 5. 20. 6.7.65
15. 4635 : 3. 21. 3836.
16. 3936 : 4. 22. 9872.

23. 4567 ; 5.
24. 8932 : 6.
25. 8174 ;9.
26. 9185 ; 4.
27. 8436 :- 7.
28. 3885 ; 8.

CASE II.

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96. When the divisor is expressed by more than one figure.

1. How many barrels of flour at $10 a barrel can be bought for $80?

ANALYSIS.—Since 1 barrel costs $10, as many barrels can be bought for $80 as $10 are contained times in $80 which is 8 times. Therefore 8 barrels can be bought for $80.

2. How many pounds of mutton at 10 cents a pound can be bought for 50 cents? How many 10's in 50? In 60? In 70? In 80?

3. A man measured a stick and found it to be 60 inches long. There are 12 inches in a foot. How many feet long

How many 12's in 60? In 72? In 84? In 96? 4. At $13 a ton how much hay can be bought for $26?

5. At 15 cents each how many toys can be bought for 30 cents? For 45 cents? For 60 cents?

6. Mr. Henderson sold 20 lambs for $80. How much did he get apiece for them?

7. 25 cents make a quarter of a dollar. quarters of a dollar has a boy who has 50 cents ?

8. Henry's father gave him a dollar. How many pineapples at 20 cents each can he buy with the money?

9. The railroad fare to a certain place is 35 cents. How many tickets can be bought with 70 cents?

was it?

How many

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