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Any REMAINDER, which appears after the operation of division, is the numerator of a fraction, the divisor being the denominator; and this fraction forms a part of the quotient. Therefore, place the remainder and the divisor, as a fraction, to the right of the quotient.

2. At $2 per yard, how many yards of cloth can be bought for $49; that is, how many whole yards, and what part of another yard can be bought ?

3. How many times 2 are there in 49 ?

4. How much flour can be bought for $639, at $5 per barrel; that is, how many barrels, and what part of another barrel can be bought ?

5. In 639, how many times 5;- that is, how many fives, and what part of another 5, in 639 ?

6. How much salt can be bought for 87 shillings, at 4 shillings per bushel ?

7. Suppose a rail-way car to run 16 miles an hour; in how many hours will it run 350 miles ?

8. How many times 12 are there in 1049 ?
9. How many times 39 are there in 76800 ?
10. In 438 shillings, how many pounds are there?

Observe that ls. is zo of £1; therefore the remainder in this example, may be expressed as a fraction.

11. How many yards of cloth can be bought for 549 shillings, at £1 per yard ?

12. Suppose a ton of hay to be equal in value to 34 bushels of oats; how many tons of hay must be given for 450 bushels of oats ?

13. How many times 17 are there in 23 times 31 ?

14. How much rice, at $4 per cwt., must be given for 620 lb. of cheese, at 10 cents per pound?

SECTION 14. CHANGE OF WHOLE NUMBERS TO FRACTIONS. 1. How many thirds are there in 14?

In 1 there are 3 thirds, 14

therefore, there are 3 times 3

as many thirds as whole ones, 42-thirds. Ans. ¥. in any whole number.

RULE. To change a whole number to an improper fraction, multiply the whole number by the denominator, and the product will be the numerator.

2. If you cut 17 sheets of paper into half-sheets, how many halves will there be ?

3. How many fifths of a dollar are there $ 16 ?
4. In 31 pounds, how many sixths of a pound?
5. In 73 yards, how many eighths of a yard ?
6. Change 641 to ninths. Change 641 to tenths.

7. If a stage run 1 mile in į of an hour, how many miles would it run in 126 hours ? 8. How many fourths are there in 1522 153

In this example, we add the

3-fourths to the fourths produc4 63-fourths.

ed by the multiplication of 15

by 4, and thus obtain a. Note. A whole number and a fraction expressed together, thus, 15%, is called a mixed number.

9. How many eighths of a mile in 57 miles ?
10. Change 86 17 to an improper fraction.
11. Change 4s to an improper fraction.

12. If } of a dollar will pay for 1 gallon of beer, how much beer can be bought for $65?

13. If į of a dollar will pay for 3 yards of ribbon, how many yards can be bought for $65?

SECTION 15. CHANGE OF FRACTIONS TO WHOLE NUMBERS. 1. How many whole ones are there in 42 ? 3)42-thirds.

Since make a whole 1, there

are as many whole ones in 4 14 wholes.

as there are times 3 in 42. RULE. To change an improper fraction to a whole number, divide the numerator by the denominator, and the quotient will be the whole number. 2. How

many

whole sheets of paper must be cut into halves, to make 48 of a sheet?

3. In 245 of a dollar, how many dollars ? 4. How many pounds are there in 132 of a pound? 5. In 1216 of a yard, how many yards are there?

6. If a stage run 1 mile in of an hour, how many hours would it be in running 126 miles ?

7. Change 312 to a whole number.

8. Suppose 8 pounds of sugar can be bought for $1; how many pounds will 2150 of a dollar pay for ? 9. Change 87 to a mixed number?

We divide the 87-fifths by 5, and 5)87

obtain 17 whole ones: then, there are 17

2-fifths over, making 17. 10. Change 249 to a mixed number. 11. How many dollars are there in 507 of a dollar ? 12. How many gallons in 48 of a gallon ?

13. If } of a dollar will pay for 1 pound of coffee, how many dollars will 312 pounds of coffee cost ?

14. If 1 pound of butter cost } of a dollar, what would be the price of 491 pounds, at the same rate ?

SECTION 16. 1. Add together , ii, 14, 1, 14 and .

The sum of these fractions will be an improper fraction, and it must be changed to a mixed number. 2. What is the sum of 491 ii, 75 i and 336 61? 491 11

In this example, we add together 75 4

the elevenths, and find their sum to 11

be 11; which is equal to 21. The

we write down, and carry the 2 to 140411

the column of units. 3. What is the sum of 419, 184, 124, 85734, 9, 251 %, 141, and 254 ?

4. Add together 33625, 142, 9701 25, 28, 15815, 1240 25, 2}, 10045, and . 5. Subtract 1976 from 2258;. 22583

We cannot take from, therefore, 1876

we join 1 unit with the ; , making a

and take from. We then proceed 3817

to take 6 units from 7 units.

8366

A

6. Subtract 460314 from 71706.
7. Subtract 609 from 542006778.

8. If 175 yards of cloth be cut from a piece contain ing 49 yards, how much will be left?

9. A retailer put into a firkin, 28.1 pounds of butter at one time, 19 pounds at another, and 35 1 pounds at another, and then sold out 25 15 pounds. How many pounds still remained in the firkin?

SECTION 17. 1. Suppose a rail-road car to run of a mile in 1 minute; what distance will it run in 47 minutes ?

2. How many whole ones in 47 times ?

3. If of a yard of broad-cloth will make 1 jacket, how many yards will it take to make 18 jackets ?

4. How many whole ones in 18 times ?

5. If of a pound of gunpowder tea cost 1 dollar, how many pounds can be bought for 50 dollars ? 6. How many whole ones in 50 times ?

Section 18. 1. What is the product of 864, multiplied by 9? 86

We multiply by 9 thus, 9 times $ 9

is 30 ; equal to 57. Then we write

this under the 4, and carry the 5 to 7797

the product of the 6 units. 2. What is the product of 41,, multiplied by 7?

3. What is the value of a field, which contains 5 acres, allowing it to be worth 54 dollars per acre ?

4. How much is 4 times 3517?
5. How much is 9 times 147314?
6. How much is 28 times 54 ?

54 Here we are obliged to multiply by

28 8 units and 2 tens separately, and we 432

cannot well bring in the product of the 108

fraction by the 2 tens. Therefore, 18 we first multiply the whole numbers,

and then find 28 times š, in a separate 15303

operation, which is not here written.

7. How much is 92 times 20514? 8. How much is 100 times 14 15 ?

9. How many gallons of wine are there in 31 casks, each cask containing 54 B6 gallons ?

10. A merchant paid $75 16% apiece, for 47 mules. What did the whole amount to?

11. If a steam-boat run 236 15 miles in 1 day, what distance will it run in 16 days ?

12. How much is 15 times z ? 13. What cost 75 books, at 10% of a dollar apiece?

14. If a horse eat 1% of a bushel of oats a day, how many bushels will he eat in 365 days?

SECTION 19. 1. If } of a chest of tea be worth $6.87}, what is the whole chest worth?

2. If to of a dollar will pay for travelling 274 miles on a turnpike road, how far can you go for $ 1 ?

3. 790 is ] of what number?

4. If 4 of a kite line be 25 yards in length, what is the whole length of the line ?

5. 305 is of what number?

6. If a man can earn 12 cents in jof a day, what sum of

money can he earn in 1 day? 7. If of a yard of gold wire be worth i of a dollar, what is the value of 1 yard of the wire ?

SECTION 20. 1. A boy having $2, gave of his money for a knife. What fraction of 1 dollar did the knife cost ?

2. } of 2 is equal to what part of 1 ?

3. ő men divided 5 barrels of four equally among them, each man taking ; of the flour in each barrel. What fraction of a barrel did each man get ?

4. } of 5 is equal to what part of 1? 5. If

you should take 1 of a bushel of corn from each of 10 bushels, what fraction of 1 bushel would you obtain ?

6. What part of 1 is t of 10?

7. What part of 1 is 3 of 2? is of 3? is of 4 is of 18? is of 38 ?

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