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91

127'

to a simple fraction.

14 13. Change to a simple fraction.

15

to a simple fraction.

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14. Reduce to a simple fraction.

10

6

15. Change

81

16. Change

17. Change

to a simple fraction.

QUESTIONS. complex fractions?

to a simple fraction.

to a simple fraction.

to a mixed number.

to a simple fraction.

Ans..

Ans. 36

Ans. 9.

Ans..

72

82

18. Reduce

993/ 124

19. If 7 is the denominator of the following fraction,

Ans. T

Ans. 20.

Ans. 26.

Ans. 3.

Ans. 1.

Ans..

what is its value when reduced to a simple fraction?

Ans.

Ans. 217.

96

Ans. 12.

20. If † is the numerator of the following fraction,, what is its value when reduced to a simple fraction? Ans. 1.

ART. 166. Complex fractions, after being reduced to simple ones, may be added, subtracted, multiplied, and divided, according to the respective rules for simple fractions.

Art. 166. How do you add, subtract, multiply, and divide

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MISCELLANEOUS EXERCISES IN VULGAR FRACTIONS.

1. What are the contents of a field 7675 rods in length and 182 rods in breadth ? Ans. 8A. 3R. 30 p. 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?

Ans. 22075ft.

3. From 200 square feet. 4. What cost of an acre at $ 1.75 per square rod? Ans. $236.9213. 5. What cost of a ton at $15 per cwt.?

Ans. $49.7313.

6. What is the continued product of the following numbers: 142, 113, 5, and 101? 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. $3.57. barrels of flour at $73 per barrel? Ans. $143. quintals of fish at $3 per quintal ? Ans. $51.

8. What cost 19
9. What cost 138

10. I have two parcels and the other 911 acres. acre?

of land, one containing 7 acres, What is their value at $783 per Ans. $1380.70g.

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

Ans. $2.0413.

12. 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?

Value of what remains, $ 13.193.
Green's bargain, $ 16.973.

Ans. 13. What cost of an acre at $ 143 per acre?

Ans. $2.00.

Ans. To

14. Multiply off of 14 by 7 of 17 of 19. 15. What are the contents of a board 11 inches long, and 44 inches wide?

Ans. 491

square inches.

in length and 9
17. What cost 19

16. How many square rods in a garden
rods wide?
acres of land at $17

18. What cost 14

tons of coal at $7

19. What cost 131

tons of hay at $87

20. What cost 17 bushels of corn at $17

which is 183 rods Ans. 1783 rods. per acre?

of a dollar?

of a dollar?

Ans. $350. per top? Ans. $11117.

per ton?

Ans. $120. per bushel ?

21. What is the value of 22. What is the value of 23. What is the value of 24. What is the value of

Ans. $333. Ans. $0.56. Ans. $0.211. Ans. $0.25§.

of a dollar?

of a dollar? Ans. $0.51%. 25. Bought a cask of molasses, containing 87 gallons; of it having leaked out, the remainder was sold at 274 cents per gallon; what was the sum received ? Ans. $15.0332.

26. Bought of L. Johnson 73yd. of broadcloth at $3 per yard, and sold it at $ 43 per yard; what was gained?

Ans. $3.683.

27. Bought a piece of land that was 47 rods in length and 29 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. 1366

square rods. 28. Bought a tract of land that was 97 rods long and 481 rods wide, and from this I sold to John Ayer a house-lot, 1812 rods long, and 143 rods wide; the remainder of my purchase was sold to John Morse, at $ 3.75 per square rod; what sum shall I receive? Ans. $16717.3015.

29. What are the contents of 10 boxes, each of which is 72 feet long, 4 feet wide, and 3 feet high?

Ans. 1312 feet.

30. Mary Brown had $17.87; 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.

31. What number shall be taken from 128, and the remain der multiplied by 10%, that the product shall be 50?

Ans. 81. 32. What number must be multiplied by 73, that the product may be 20? Ans. 243. 33. Bought of John Dow 97 yards of cloth at $4.62 per yard; what was the whole cost? Ans. $45.67%.

34. Bought of John Appleton 472 gallons of molasses for $12.37; what cost one gallon? What cost 123 gallons? Ans. $3.33.

35. When $15.87 are paid for 123 bushels of wheat, what costs one bushel ? What cost 11 bushels? Ans. $ 14.11. 36. When $19.18 are paid for 38 cords of wood, what cost one cord? What cost of a cord? Ans. $2.136.

37. What are the contents of a box 85 feet long, 311 feet wide, and 2 feet high? Ans. 6814 feet,

38. 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 which is 3 rods square, and the other contains 3 square rods. How large is my field ? Ans. 1A. OR. 29p.

of

REDUCTION OF FRACTIONS OF COMPOUND NUMBERS.

ART. 167. To reduce a fraction of a higher denomination to a fraction of a lower.

Ex. 1. Reducer of a pound to the fraction of a farthing. Ans. qr.

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OPERATION.

OPERATION BY CANCELLATION.

× 20 × 12 × 4

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Since 20s. make a pound, = ‡qr. there must be 20 times as many parts of a shilling as parts of a pound; we therefore multiply

240

£. by 20, and obtains.; and since 12d. make a shilling, there will be 12 times as many parts of a penny as parts of a shilling; hence we multiplys. by 12, and obtain 2d. Again; since 4qr. make a penny, there will be 4 times as many parts of a farthing as parts of a penny; we therefore multiplyd. by 4, and obtain = qr., Ans.

960

RULE. Multiply the given fraction by the numbers that would be employed in reduction of whole numbers to reduce the denomination of the fraction 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 num. bers?

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