13. Reduce of a pound, 14. Reduce

of an ounce

"avoirdupois, to the fraction of to the fraction of a pound

an ounce.

15. A man has of a

avoirdupois.
16. A man has

of a pint

hogshead of wine; what part of wine; what part is that of

is that of a pint?
17. A cucumber grew to the
of a mile; what

length of

part is that of a foot?

19. Reduce of of a

a hogshead?

18. A cucumber grew to the length of 1 foot 4 inches of a foot; what part

is that of a mile?

20. 39 of a shilling is of

pound to the fraction of a shil- what fraction of a pound?

ling.

4

21. Reduce of of 3 pounds to the fraction of a penny.

22. 180 of a penny is of what fraction of 3 pounds? 180 of a penny is of what part of 3 pounds? 182 of a penny is of of how many pounds?

¶ 64. It will frequently be It will frequently be rerequired to find the value of a quired to reduce integers te fraction, that is, to reduce a the fraction of a greater de fraction to integers of less de- nomination.

nominations.

1. What is the value of of a pound? In other words, Reduce of a pound to shillings and pence.

2. Reduce 13 s. 4 d. to the fraction of a pound.

13 s. 4 d. is 160 pence⚫ there are 240 pence in a of a pound is 4133 shil-pound; therefore, 13 s. 4 d. is lings; it is evident from of 48 of a pound. That a shilling may be obtained is,-Reduce the given zum or some pence; of a shilling is quantity to the least denomina24 d. That is,-Multiply tion mentioned in it, for a nuthe numerator by that number merator; then reduce an intewhich will reduce it to the next ger of that greater denominaless denomination, and divide tion (to a fraction of which it the product by the denominator; is required to reduce the givif there be a remainder, multiply en sum or quantity) to the and divide as before, and so on; same denomination, for a denomi the several quotients, placed one nator, and they will form the after another, in their order, fraction required.

will be the answer.

6. Reduce 7 oz. 4 pwt. tc the fraction of a pound Troy 8. Reduce 8 oz. 143 dr. to the fraction of a pound avoirdupois.

Note. Both the numerator and the denominator must be reduced to 9ths of a dr.

10. 3 weeks, 1 d. 9 h. 36 m.

ny days, hours, and minutes? is what fraction of a month?

11. Reduce of a mile to its proper quantity.

13. Reduce of an acre to its proper quantity.

15. What is the value of of a dollar in shillings, pence, &c.?

17. What is the value of of a yard

19. What is the value of

of a ton ?

12. Reduce 4 fur. 125 yds. 2 ft. 1 in. 24 bar. to the fraction of a mile.

14. Reduce 1 rood 30 poles to the fraction of an acre.

16. Reduce 5 s. 7 d. to the fraction of a dollar.

18. Reduce 2 ft. 8 in. 14 b. to the fraction of a yard.

20. Reduce 4 cwt. 2 qr. 12 lb. 14 oz. 12 dr. to the fraction of a ton.

Note. Let the pupil be required to reverse and following examples:

21. What is the value of of a guinea?

prove the

22. Reduce 3 roods 17 poles to the fraction of an acre. 23. A man bought 27 gal. 3 qts. 1 pt. of molasses; what part is that of a hogshead?

24. A man purchased 3 of 7 cwt. of sugar; how much sugar did he purchase?

25. 13 h. 42 m. 51 s. is what part or fraction of a day?

SUPPLEMENT TO FRACTIONS.

QUESTIONS.

by the greatest common divisor?

1. What are fractions? 2. Whence is it that the parts into which any thing or any number may be divided, take their name? 3. How are fractions represented by figures? 4. What is the number above the line called?—Why is it so called? 5. What is the number below the line called? -Why is it so called?-What does it show? 6. What is it which determines the magnitude of the parts?-Why? 7. What is a simple or proper fraction? an improper fraction? a mixed number? 8. How is an improper fraction reduced to a whole or mixed number? 9. How is a mixed number reduced to an improper fraction? whole number? 10. What is understood by the terms of the fraction? 11. How is a fraction reduced to its most simple or lowest terms? 12. What is understood by a common divisor? 13. How is it found? 14. How many ways are there to multiply a fraction by a whole number? 15. How does it appear, that diriding the denominator multiplies the fraction? 16. How is a mixed number multiplied? 17. What is implied in multiplying by a fraction? 18. Of how many operations does it consist? What are they? 19. When the multiplier is less than a unit, what is the product compared with the multiplicand? 20. How do you multiply a whole number by a fraction? 21. How do you multiply one fraction by another? 22. How do you multiply a mixed number by a mixed number? 23. How does it appear, that in multiplying both terms of the fraction by the same number the value of the fraction is not altered? 24. How many ways are there to divide a fraction by a whole number?—What are they? 25. How does it appear that a fraction is divided by multiplying its denominator? 26. How does dividing by a

fraction differ from multiplying by a fraction? 27. When the divisor is less than a unit, what is the quotient compared with the dividend? 28. What is understood by a common denominator? the least common denominator? 29. How does it appear, that each given denominator must be a factor of the common denominator? 30. How is the common denominator to two or more fractions found? 31. What is understood by a multiple? by a common multiple? by the least common multiple ?-What is the process of finding it? 32. How are fractions added and subtracted? 33. How is a fraction of a greater denomination reduced to one of a less? of a less to a greater? 34. How are fractions of a greater denomination reduced to integers of a less? integers of a less denomination to the fraction of a greater?

day?

of an hour make how many Ans. to the last, & d.

Ans. to the last, 2011. 2. To of a pound add Amount, 184 s. Note. First reduce both to the same denomination. 3. of a day added to what part of a 4. Add lb. Troy to 7 2

hours?

of an oz.

Amount, 6 oz. 11 pwt. 16 gr.

5. How much is less? Fot? £8? 14 -44 6-43? 148 of 3 of 2?

Ans. to the igsi, 13.
Rem. 5 d.

of a pwt.

Rem. 11 pwt. 3 grs.

h.

Rem. 2 d. 22 h. 20 m.

9. At $ per yard, what costs of a yard of cloth?

165. The price of unity, or 1, being given, to find the cost of any quantity, either less or more than unity, multiply the price by the quantity. On the other hand, the cost of any quantity, either less or more than unity, being given, to find the price of unity, or 1, divide the cost by the quantury.

Ans. $

1. If lb. of sugar cost of a shilling, what will of a pound cost?*

This example will require two operations: first, as above, to find the price of 1 lb.; secondly, having found the price of 1 lb., to find the cost of of a pound. s. (H of 75 s. 1 57) = s. the price of 1 lb. Then, s. X 18 (13 of 9 s. π 53) = 481 s. 4 d. 3487! q., the

After the same manner let the pupil solve the following questions:

2. If 7 lb. of sugar cost of a dollar, what is that pound of how much? What is it for 4 lh. ?4 of how much? What for 12 pounds? of how much? Ans. to the last, $13 3. If 64 yds. of cloth cost $3, what cost 9

4. If 2 oz. of silver cost $224, what costs

yards? Ans. $46269. oz. ? Ans. $84. 5. If oz. costs $1, what costs 1 oz.? Ans. $1'283. 6. If lb. less by costs 13 d., what costs 14 lb. less by of 2 lb. ? Ans. 4. 9 s. 9 d.

7. If yd. cost $, what will 40 yds. cost?

8. If of a ship costs $251, what is

9. At 38. per cwt., what will 93 lb.

Ans. $59'062 +. of her worth? Ans. $53'785 +.

cost?

sold

Ans. 6 s. 3 d. of his share Ans. $1794'375.

10. A merchant, owning of a vessel, for $957; what was the vessel worth? 11. If yds. cost £., what will of an ell Eng. cost? Ans. 17 s. 1 d. 29 q.

*This and the following are examples usually referred to the rule Proportion or Rule of Three. See 195 ex. 35.