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5. Reduce 192ʊ of a pound to the fraction of a far

thing.

Operation.
1

1920 20

212

4

21 Ans.

It has been shown (see p. 65) that Reduction Ascending is the reverse of Reduction Descending, and also, (p. 93) that a fraction is divided, either by dividing its numerator, or multiplying its denominator. Farthings are reduced to pence by dividing by 4, and pence to shillings

by dividing by 12; shillings to pounds by dividing by 20. Therefore-To reduce of a farthing to the fraction of a pound, divide the fraction by 4, 12 and 20.

1. What part of a pound is of a farthing?

Operation.
×4×12×20=1920

: or thus, 2

4

12

20

1920|1=1920 Answer.

To change fractions of lower, into fractions of higher denominations, we have, then, this

RULE.

Multiply the denominator of the fraction by all the denominations between it and that into which it is to be reduced, and write the product under the numerator of the given fraction.

2. Reduce of a penny to the fraction of a pound.

Operation.

X12×20=1440-2 or thus, 65

12 4 20

Answer, 288 1.

As the denominator of the fraction is to be multiplied for a di

visor, place it with its multipliers on the left of the line. Then, by cancelling 5 on the right of the line, and 20 on the left, equal, therefore cross 5 and 20, and write 4 on the left. Multiply the remaining numbers on the left together, for a divisor. We have, then, the answer in the lowest terms of the fraction, zģg.

QUESTIONS. 2. What would be your multipliers in reducing the fraction of a pound to the fraction of a penny?

3. Reduce

of a penny to the fraction of a pound. Answer, £30.

4. Reduce of a farthing to the fraction of a pound. Answer, 3360

5. What part of a cwt. is of a pound? Ans., 504. 6. Reduce of a nail to the fraction of a yard.

REDUCTION.

Answer, 24

DESCENDING.

ASCENDING.

1. Reduce 14 of a pound 2. Reduce of a farthing to the fraction of a farthing. to the fraction of a pound.

3. Reduce

of a pound

to the fraction of a penny.
5. Reduce of a guin-

4. Reduce of a penny to the fraction of a pound.

6. Reduce ğ of a penny to

ea to the fraction of a penny. the fraction of a guinea. 7. Reduce of a guinea

8. What fraction of a

to the fraction of a pound. guinea is of a pound?

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to the fraction of a penny.

11. Reduce of a shil

10. What part of a guinea

of a penny?

12. What part of a shilof a farthing?

ling to the fraction of a far-ling is thing.

13. Reduce of a pound 14. What part of a pound Troy to the fraction of an Troy is § of an ounce?

ounce.

15. Reduce 6432 of a hhd. 16. What fraction of a of wine to the fraction of ahhd. is 4 of a quart?

quart.

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19. Reduce 216 of a mile to the fraction of a rod.

18. What fraction of an acre is of a rod?

20. Reduce of a rod to the fraction of a mile.

22. Reduce of a foot to

21. Reduce 550440 of a degree to the fraction of a the fraction of a degree.

foot.

J

23. Reduce iz of a bushel to the fraction of a gill. 25. Reduce 32256 of a ton to the fraction of a gill.

27. Reduce of 3 of 4 pounds to the fraction of a

penny.

29. of a pound is of what fraction of 7 guineas?

of a pound is what fraction of 7 guineas? of a pound is of

of how many guineas?

of

24. Reduce of a gill to the fraction of a bushel.

26. Reduce of a gill to the fraction of a ton. 28. 2 of a penny is of of how many pounds? 8 of 1 penny is of what fraction of 4 pounds? 8 of a penny is of of what fraction of 4 pounds? 30. Reduce of 14 of 7 guinea to the fraction of a pound.

31. Reduce 4233600 of a 32. Reduce of a second

week to the fraction of a sec-to the fraction of a week. ond.

33. Reduce 4200 of a 34. Reduce of an hour year to the fraction of an to the fraction of a year. hour.

NOTE. All practical questions in the several foregoing Rules,viz. Multiplication and Division of Fractions by Whole Numbers; Multiplication and Division of Whole Numbers by Fractions; Multiplication and Division of Fractions by Fractions; also, Reduction of Fractions Ascending and Descending, may be solved by one uniform mode of stating said questions, which will be given in the Rule of Three, and which supersedes the above Rules in Fractions.

The foregoing Rules have been given as profitable exercises for the student. In practice, however, the student will be found to recur to the uniform rule stated and explained in the Rule of Three, as the most simple and expeditious process, and which he will always be able readily to retain in memory.

To reduce Fractions to integers of lower denominations, and the reverse.

1. What is the value of

of a pound?

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

In £1 there are 240d.: 1

of a pound reduced to the fraction of a shilling is penny then is of a pound, X20-40 of a shilling,- and 160d., the which, reduced to a mixed pence in 13s.

:

number of 4d. is 168 of

number (see p 89) is 133s. a pound,or 160 times as much The of a shilling reduced as 1 penny. Therefore, to to the fraction of a penny, is reduce integers of lower, to X1224d. Hence, to fractions of a higher denomreduce fractions of one de-ination, we have this nomination to integers of a lower, we have this

RULE. Reduce the given numbers to the lowest denomRULE. Multiply the nu-ination mentioned, for a numerator of the given fraction merator, and an integer of by as many of the next lower the denomination required to denomination as make 1 of the same denomination for a that denomination in which denominator, and they will the fraction is given, and di- form the fraction required. vide the product by the de- 4. Reduce 7d. 2qrs. to the nominator of the fraction.-fraction of a shilling. If there be a remainder, proceed as before, until it is reduced to the lowest denomination. If there be still a remainder, place it at the

Integer.

1s.

Operation.

d.

qrs.

7

12

4

right of the last answer.

12

6)30(5

3. What is the value of §

4

Ans.

48(8

[blocks in formation]

Or, we may reduce the farthings to the fraction of a penny, and reduce the whole to an improper fraction. Operation by cancelling. 215 5

Thus 7

4 121

85 ğ An.

6. Reduce 6 furlongs, 26

5. What is the value of po. 11 ft. to the fraction of a

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7. What is the value of 8. Reduce 8 mi. 5 fur. 20 of a degree? poles, to the fraction of a

9. What is the value of mile. of a ton?

10. Reduce 16 cwt. 1 qr.

QUESTIONS. 1. Rule for reducing fractions to integers of lower denominations? 2. Rule for reducing integers of lower denominations to a fraction of a higher?

11. What is the value of 12 lbs. 11 oz. 10 dr. of a dr. to the fraction of a ton.

of a month?

13. What is the value of of a pound Troy?

15. What is the value of of an acre?

17. What is the value of of a yard of cloth?

19. What is the value of of a dollar in shillings?

21. What is the value of of a ton?

23. What is the value of of a hogshead?

12. Reduce 3 w. 1 d. 9 h. 36 m. to the fraction of a month.

14. Reduce 8 oz. 11 pwt. 10 grs. to the fraction of a pound.

16. Reduce 3 roo. 13 ro. 90 feet, 108 in. to the fraction of an acre.

18. Reduce 3 qrs. 2 na. to the fraction of a yard.

20. Reduce 4s. 6d. to the fraction of a dollar.

22. Reduce 11 cwt. 0 qr. 12 lbs. 7 oz. 17 drs. to the fraction of a ton.

24. Reduce 49 gals. to the fraction of a hogshead.

Reduction of Vulgar Fractions to Decimal. RULE. Divide the numerator by the denominator. 1. Reduce to a decimal fraction.

Operation. 2)10

In this example, being a proper fraction, the numerator will not contain the denominator, but, by adding a cipher, ,5 we obtain the quotient 5, which is 5 tenths. (See the Rule for pointing off, in Division of Decimals, p. 52.) As many ciphers, therefore, as are added to the numerator, so many decimal places must be in the quotient. If, after the division, the quotient does not contain so many, supply the deficiency by prefixing ciphers. 2. Reduce to a decimal fraction. Answer, ,75. 3. Reduce ğ, and 3, to decimal fractions.

Answer, ,625,125,6. 4. Reduce 3, 3, 2, 1, and 1, to decimal fractions.

Answer, ,875,375,75,25,5.

QUESTIONS. 1. Rule for reducing a vulgar fraction to a decimal? 2. How many decimal places must there be in the quotient? 3. If the quotient does not contain a sufficient number of figures, what is to be done?

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