REDUCTION OF FRACTIONS. 1. Reduce of a pound to the fraction of a penny. We have seen that integers of a higher denomination are brought into integers of lower, by multiplication; (see p. 108,) and also that fractions are multiplied either by multiplying the numerator, or dividing the denominator. (See p. 68.) Pounds are reduced to shillings by multiplying by 20, and shillings to pence by multiplying by 12. Therefore, to reduce of a pound to the fraction of a penny, multiply the fraction by 20 and 12, thus: 28X20×12=248={, Answer. Or thus: |1 6 24 288 20 5 12 65, Answer. As the numerator of the fraction is to be multiplied, place it with its multipliers on the right of the line, and 288, the divisor, on the left. Cross 288 and 12, and write 24 in the place of the larger number; 4 is contained in 20 five times, and in 24 six times. The answer, then, is 5 divided by 6, or, in the lowest terms of the fraction. NOTE. It will be seen, that the only difference between reducing 1 pound to pence, and of a pound, is, that in the latter case the multiplicand is a number divided; consequently, having multiplied the numerator as we should a whole number, we divide the product by the denominator. To divide the product is the same as to divide the multiplicand. To change fractions of a higher denomination into fractions of a lower denomination, we have the following RULE. Multiply the numerator of the fraction, or divide the denominator by all the denominations between it and that denomination into which it is to be reduced, including the lower denomination. EXAMPLES. 1. Reduce of a pound to the fraction of a penny. Answer, 2. 2. Reduce 3. What part of a pound is 504 cwt.? Answer, . of a yard to the fraction of a nail. to the fraction of a farthing. Ans., §. . 4. Reduce Answer, . 5. Reduce 12 of a pound to the fraction of a farthing. Operation. 1920 20 212 4 21=1, Ans. It has been shown (see p. 106) that Far 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. 1×4×12×20=1920' 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. 12×20=40-28: or thus, 65 12 4 20 As the denominator of the fraction is to be multi Answer, 2881. plied for a divisor, 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, 88. 3. Reduce of a penny to the fraction of a pound. Answer, £3. QUESTIONS. 1. What would be your multipliers in reducing the fraction of a pound to the fraction of a penny? 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. 40 ASCENDING. 1. Reduce 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 4. Reduce of a penny to the fraction of a pound. to the fraction of a penny. 6. Reduce of a penny to ea to the fraction of a penny. the fraction of a guinea. 7. Reduce of a guinea to the fraction of a pound. 74 Guinea 128s. 4 5 s 201£ 54, Answer. 8. What fraction of a guin ea is of a pound? 54 £ 120s. 4 7 s. 28 1 guinea. 74=4,Answer. 10. What part of a guinea is 14 of a penny ? 9. Reduce of a guinea to the fraction of a penny. 11. Reduce of a shilling to the fraction of a far-is thing. 12. What part of a shilling of a farthing? 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 6 of a hhd. 16. What fraction of a hhd. of wine to the fraction of a is quart. 17. What fraction of a rod is 764 of an acre? 19. Reduce 9216 of a mile to the fraction of a rod. 20. Reduce 194 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. 23. Reduce 12 of a bushel to the fraction of a gill. 24. Reduce of a gill to the fraction of a bushel. 25. Reduce 3256 of a tun to the fraction of a gill. 27. Reduce of of 4 pounds to the fraction of a penny. 26. Reduce of a gill to the fraction of a tun. 28. of a penny is of of how many pounds? 8 of 1 penny is of what fraction of 4 pounds? 80 of a penny is of what fraction of 4 pounds? 30. Reduce of 14 of 7 of a pound is of of guineas to the fraction of a how many guineas? pound. 29. of a pound is of what fraction of 7 guineas? of a pound is of what fraction of 7 guineas? 31. Reduce 3600 of a 32. Reduce of a second week to the fraction of a sec-to the fraction of a week. ond. 33. Reduce 330 of a 34. Reduce of an hour to year to the fraction of an 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? of a pound reduced to the fraction of a shilling is 20 2. Reduce 13 s. 4 d. to the fraction of a pound. 40 of a shilling-which, re- In £1 there are 240 d.: 1 duced to a mixed number (see penny then is of a pound, p. 64) is 133 s. The of a and 160 d., the number of shilling reduced to the frac-pence in 13 s. 4 d. is 160 of a tion of a penny, is X12-pound, or 160 times as much 24 d. Hence, to reduce as 1 penny. Therefore, to fractions of one denomination reduce integers of lower, to have this to integers of a lower, we fractions of a higher denomination, we have this RULE. Multiply the nu- RULE. Reduce the given merator of the given fraction numbers to the lowest denomby as many of the next lower ination mentioned, for a nudenomination as make 1 of merator, and an integer of that denomination in which the denomination required to the fraction is given, and di-the same denomination for a vide the product by the de-denominator, and they will nominator of the fraction.-form the fraction required. If there be a remainder, pro 7. What is the value of 8. Reduce 8 mi. 5 fur. 20 of a degree? poles, to the fraction of a deg. 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 ? |