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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 of an hour, how many miles would it run in 126 hours ? 8. How many fourths are there in 156? 157

In this example, we add the

3-fourths to the fourths produc4

ed by the multiplication of 15 63-fourths.

by 4, and thus obtaine.
Note. A whole number and a fraction expressed to-
gether, thus, 15, is called a mired number.

9. How many eighths of a mile in 57 miles ?
10. Change 86 1; to an improper fraction.
11. Change 463 to an improper fraction.

12. If } of a dollar will pay for 1 gallon of beer, how much beer can be bought for $69?

13. If [ of a dollar will pay for 3 yards of ribbon, how many yards can be bought for $6?

SECTION 15. CHANGE OF FRACTIONS TO WHOLE NUMBERS. 1. How niany whole ones are there in ?? 3)4 2-thirds.

Since make a whole 1, there 14 wholes.

are as many whole ones in 2

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

2. How many whole sheets of paper must be cut into Halves, to make 4 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 1420 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 34 to a whole number.

8. Suppose 8 pounds of sugar can be bought for $1; pow many pounds will 2650 of a dollar

рау

for ? 9. Change 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 2 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 Ź of a dollar, what would be the price of 491 pounds, at the same rate ?

Section 16.
1. Add together , ii, 14, , and Ý:

The sum of these fractions will be an improper frac-
tion, and it must be changed to a mixed number.
2. What is the sum of 491 11, 7511 and 336 ?

In this example, we add together

the elevenths, and find their sum to 836 6

The be 11; which is equal to 21.

11 we write down, and carry the 2 to 140411

the column of units. 3. What is the sum of 419, 185, 124, 85734, 94, 251, 141, and 254 ?

4. Add together 33+ 25, 141, 97012, 28, 1589, 1240 25, , 100, and is 5. Subtract 1976 from 2258. 22583

We cannot take from , therefore, 1876

we join 1 unit with the making ,

and take a from. We then proceen 3813

to take 6 units from 7 units.

9

49111

75 11

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6. Subtract 46031f from 71706. 7. Subtract 6094 from 54200678

8. If 17k 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 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 'n I 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 jacke, 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 86%, multiplied by 9? 864

We multiply 4 by 9 thus, 9 times of 9

is 36 ; equal to 54. Then we write

this under the #, and carry the 5 10 779

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 541 dollars per acre?

4. How much is 4 times 3518?
5 How much is 9 times 14731 44 ?
€ 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 , in a separate 15304

operation, which is not here written.

. How much is 92 times 20516 ? 8. How much is 100 times 14 15 ?

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

10. A merchant paid $75 10% apiece, for 47 mules. What did the whole ainount 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 ģ7 ? 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 mauy bushels will he eat iu 365 days?

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

2. If y of a dollar will pay for travelling 27 miles on a turnpike road, how far can you go for $1?

3. 790 is of what number?

4. If 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 į of a day, what sum of money can he earn in 1 day?

7. If of a yard of gold wire be worth is 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 flour equally among them, each man taking of the four in each barrel. What fraction of a barrel did each man get ? 4. Žof 5 is equal to what part

of 1 ? 5. If you should take it of a bushel of corn from each of 10 bushels, what fraction of 1 bushel would you obtain ?

6. What part of 1 is 16 of 10?

7. What part of 1 is 36 of 2? is 3 of 3 ?' is 3 of 4 ! s of 18? is of 38 ?

8. A tenant raised 28 bushels of corn, and gave

his landlord } of it. What improper fraction of a bushel, (how many thirds of a bushel,] did the landlord receive? How many bushels did the landlord receive?

9. į of 28 is equal to what improper fraction? Then of 28 is equal to how many whole ones?

10. } of 42 is equal to what improper fraction? Then } of 42 is equal to what mixed number?

11. 1'; of 29 is equal to what improper fraction ? Then 1 of 29 is equal to what mixed number?

12. IT $721 should be divided equally among 6 men, how many

sixths of a dollar would each man have > How many dollars would each man have ?

Section 21. 1. Suppose a hogshead of brown sugar to be worth $115; what is the value of of the sugar?

2. What is of 115?

3. 5 men from Connecticut, bought 793 acres of land in Michigan, and divided it into 5 equal farms. How inany acres were there in each farm?

To find } of 793 acres, we divide 793 by 5. The quotient is 158 acres, and there is a remainder of 3 acres. To divide these 3 ar res, we take } of each acre for each farm. } of 3 acres is of 1 acre.

4. What is } of 1315? of 530? of 8201 ?

5. Suppose 12 men to share equally in a prize of $ 551.20; what is each man's share

6. What is ta of 55120? 2 of 967 ? 4 of 700? 7. The Young Ladies' Class Book, which consists of 408 pages of select reading lessons, has been read through by 25 scholars; each reading an equal portion. How many pages did i scholar read?

8. } of £1 [ } of 20s. ) is how many shillings, and what fraction of a shilling?

9. Find of £7 in shillings- that is, reduce £7 to shillings, and find of the number of shillings.

10. of 5 shillings is how many pence?
11. How many grains in To of 6 pennyweights?
12. } of 3 ounces is how many

drams?

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