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MISCELLANEOUS EXERCISES IN FRACTIONS.

1. What are the contents of a field 76,7 rods in length, and 182 rods in breadth? Ans. 8A. 3R. 301p. 2. What are the contents of 10 boxes which are 72 feet long, 12 feet wide, and 14 feet in height?

Ans. 169 cubic feet. of an acre of land there were sold 20 poles and What quantity remained?

3. From

200 square feet.

Ans. 22075ft.

4. What cost

Ans. $236.924.

of a ton at $15 per cwt.?

Ans. $49.7313.

of an acre at $1.75 per square rod?

5. What cost 6. What is the continued product of the following numbers: 142, 113, 5, and 104?

Ans. 9184. 7. From of a cwt. of sugar there was sold of it; what is the value of the remainder at $0.12 per pound?

Ans. $3.183.

8. What cost 19 barrels of flour at $7 per barrel?

Ans. $143.

9. Bought a piece of land that was 475 rods in length, and 2976 in breadth; and from this land there were sold to Abijah Atwood 5 square rods, and to Hazen Webster a piece that was 5 rods square; how much remains unsold?

Ans. 13668 square rods. 10. From a quarter of beef weighing 1753lb. I gave John Snow of it; of the remainder I sold to John Cloon. is the value of the remainder at 82 cents per pound?

What

Ans. $2.0413.

11. Alexander Green bought of John Fortune a box of sugar containing 475lb. for $30. He sold of it at 8 cents per pound, and of the remainder at 10 cents per pound. What is the value of what still remains at 12 cents per pound, and what does Green make on his bargain?

12. What cost

Ans. {

Value of what remains, $13.193. Green's bargain, $16.973. of an acre at $143 per acre?

13. Multiply of 8 of 11 by 1 of 13 of 18.

Ans. $2.

Ans. To

14. What are the contents of a board 11 inches long, and Ans. 4918 square inches.

44 inches wide?

15. Mary Brown had $17.871; half of this sum was given to the missionary society, and g of the remainder she gave to the Bible society; what sum has she left? Ans. $3.57. 16. What number shall be taken from 123, and the remainder multiplied by 10%, that the product shall be 50?

Ans. 813

Ans. 6814

17. What number must be multiplied by 78, that the product may be 20? Ans. 24. 18. What are the contents of a box 85 feet long, 311 feet wide, and 2 feet high? feet. 19. On of my field I plant corn; on of the remainder I sow wheat; potatoes are planted on of what still remains; and I have left two small pieces, one of which is 3 rods square, and the other contains 3 square rods. How large is my field? Ans. 1A. OR. 29p.

REDUCTION OF FRACTIONS OF COMPOUND NUMBERS.

ART. 169. To reduce a fraction of a higher denomination to a fraction of a lower.

Ex. 1. Reduce 160 of a pound to the fraction of a farthing.

OPERATION.

Ans. far.

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OPERATION BY CANCELLATION.

× 20 × 12 × 4

1

2160

9

=

=

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2160

2160

=

2160

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Since 20s. make a pound, there must be 20 times as

far. many parts of a shilling as parts of a pound; we therefore multiply by 20, and obtain s.; and since 12d. make a shilling, there will be 12 times as many parts of a penny as parts of a shilling; hence we multiply by 12, and obtain 2d. Again; since 4far. make a penny, there will be 4 times as many parts of a farthing as parts of a penny; we therefore multiply 2 by 4, and obtain far. far., Ans.

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RULE.-Multiply the given fraction by the same numbers that would be employed in reduction of whole numbers to the lower denomination required.

-

QUESTIONS. Art. 167. What is the rule for reducing a fraction of a higher denomination to the fraction of a lower? Will you explain the operations? Does this process differ in principle from reduction of whole compound numbers?

EXAMPLES FOR PRACTICE.

2. Reduce Tao of a pound to the fraction of a farthing.

Ans.. Ans. 16.

3. What part of a penny is of a shilling?
4. What part of a grain is 640 of a pound Troy?

Ans. 2.

5. What part of an ounce is 1728 of a cwt.? Ans. 3. 6. Reduce 132 of a furlong to the fraction of a foot.

7. What part of a square foot is 5800 of an acre ?

8. What part of a second is go of a day?
9. What part of a peck is

10. What part of a pound is

897

of a bushel?
of a cwt.?

Ans..

Ans..

Ans.

Ans. .

Ans..

ART. 170. To reduce a fraction of a lower denomination

to a fraction of a higher.

Ex. 1. Reduce of a farthing to the fraction of a pound.

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OPERATION BY CANCELLATION.

4

1

=

9 × 4 X 12 X 20

2160£.

Since 4far. make a penny, there will be as many pence as farthings; therefore we divide theby 4, and obtain d. And, since 12d. make a shilling, there will be as many shillings as pence; hence we divide by 12, and obtain 28. Again, since 20s. make a pound, there will be as many pounds as shillings; therefore we divide by 20, and obtain £. for the answer.

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RULE. Divide the given fraction by the same numbers that would be employed in reduction of whole numbers to the higher denomination required.

EXAMPLES FOR PRACTICE.

2. Reduce of a grain Troy to the fraction of a pound.

Ans. 1080

QUESTIONS. Art. 170. Do you multiply or divide to reduce a fraction of a lower denomination to the fraction of a higher? What is the rule?

3. What part of an ounce is
4. What part of a ton is
5. What part of a mile is
6. What part of an acre is

7. What part of a day is 2
8. What part of 3 acres is

9. What part of 3hhd. is

of a scruple?
of an ounce ?
of a rod ?
of a square foot?

Ans.
Ans. 1oooo
Ans. 30.

Ans. 5340.
Ans. goooo

of a second?
of a square foot?

of a quart?

Ans. 294030
Ans. 1323

10. What part of of a solid foot is of a yard solid?

Ans. 2.

ART. 171. To find the value of a fraction in whole numbers of a lower denomination.

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RULE. · Multiply the numerator of the given fraction by the number required to reduce it to the next lower denomination, and divide the product by the denominator.

Then, if there is a remainder, proceed as before, until it is reduced to the denomination required.

QUESTION. Art. 171. What is the rule for finding the value of a fraction in whole numbers of a lower denomination?

EXAMPLES FOR PRACTICE.

2. What is the value of 7 of a cwt.?

3. What is the value of 4. What is the value of

Ans. 3qr. 2lb. 12oz. 74dr.
Ans. 3qr. Ona.

of a yard?

of an acre?

Ans. 1R. 28p. 155ft. 824in.

5. What is the value of of a mile?

Ans. 1 fur. 31rd. 1ft. 10in.

6. What is the value of of an ell English?

Ans. 1qr. 15na.

Ans. 18gal.

7. What is the value of

of a hogshead of wine?

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Ans. 232da. 10h. 21m. 49 sec.

ART. 172. To reduce a simple or compound number to the fractional part of any other simple or compound number of the same kind.

Ex. 1. What part of 1£. is 3s. 6d. 23far.

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Ans. £.

In performing this operation, we reduce the 3s. 6d. 23 far. to .thirds of far., the lowest denom

ination in the question, for the

numerator of the required fraction, and 1£. to the same denomination for the denominator. We then reduce this fraction to its lowest terms, and obtain £. for the answer.

RULE. · Reduce the given numbers to the lowest denomination mentioned in either of them. Then, write the number which is to become the fractional part for the numerator, and the other number for the denominator, of the required fraction.

EXAMPLES FOR PRACTICE.

2. Reduce 4s. 8d. to the fraction of 1£.

Ans. Ans. 2000

487

3. What part of a ton is 4cwt. 3qr. 12lb.?
4. What part of 2m. 3fur. 20rd. is 2fur. 30rd.? Ans. 1.

5. What part of 2A. 2R. 32p. is 3R. 24p.?
6. What part of a hogshead of wine is 18gal. 2qt.?

Ans..

Ans.

QUESTION. Art. 172. What is the rule for reducing a simple or compound number to the fractional part of any other simple or compound number of the same kind?

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