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. OBS.-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. Art. 122. 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. Ans. 2. Reduce 3360 of a pound to the fraction of a farthing. 3. What part of a pound is cwt.? Ans. 2. Ans. 3. 4. Reduce of a yard to the fraction of a nail. Ans. }. 5. Reduce 1920 of a pound to the fraction of a farthing. 1 Art. 123.-It has been shown (see Art. 117) that Reduc Operation. 1 1920 20 212 tion Ascending is the reverse of Reduction Descending, and also, (Art. 68,) 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. ThereforeTo reduce of a farthing to the fraction of a pound, divide the fraction by 4, 12, and 20. 2|1=Ans. 1 What part of a pound is of a farthing? Art. 124. 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. As the denominator of the fraction is to be multiplied 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, 1 3. Reduce of a penny to the fraction of a pound. Ans. £. 4. Reduce of a farthing to the fraction of a pound. Ans. 3360 5. What part of a cwt. is of a pound? 6. Reduce of a nail to the fraction of a yard. Ans. 27. QUESTION.-1. What would be your multipliers in reducing the fraction of a pound to the fraction of a penny? 13. Reduce of a pound Troy to the fraction of an ounce. 8 15. Reduce of a hhd. of wine to the fraction of a quart. 17. What fraction of a rod is 7684 of an acre? 19. Reduce of a mile to the fraction of a rod. 21. Reduce 550440 of a degree to the fraction of a foot. 23. Reduce of a bushel to the fraction of a gill. 25. Reduce 32256 of a tun to the fraction of a gill. 27. Reduce of of 4 pounds to the fraction of a penny. 29. of a pound is of what fraction of 7 guineas? of a pound is fraction of 7 guineas? of what of a pound is of of how many guineas? pound. 4. Reduce of a penny to the fraction of a pound. 6. Reduce of a penny to the fraction of a guinea. is 8. What fraction of a guinea of a pound? £ 120s. 4 7 s.28 1 guinea. 74=Ans. 10. What part of a guinea is 14 of a penny? 12. What part of a shilling is 4 of a farthing? is 14. What part of a pound Troy of an ounce ? 16. What fraction of a hhd. is of a quart? 18. What fraction of an acre is 19 of a rod? 40 1921 144 20. Reduce of a rod to the fraction of a mile. 22. Reduce of a foot to the fraction of a degree. 24. Reduce of a gill to the fraction of a bushel. 26. Reduce of a gill to the fraction of a tun. 28.0 of a penny is of of how many pounds? 3 of 1 penny is of what fraction of 4 pounds? of a penny is of what fraction of 4 pounds? 30. Reduce of of 7 guineas to the fraction of a pound. 31. Reduce 335 of a week to the fraction of a second. 33. Reduce 30 of a year to the fraction of an hour. 32. Reduce of a second to the fraction of a week. 34. Reduce of an hour to the fraction of a year. Comparison of Numbers and Quantities. Art. 127. We compare quantities and numbers, to ascertain what part the one is of the other. Things compared must be of the same kind, or those properties compared must be alike. We do not compare rods with hours, nor minutes with days, but rods with fods, and minutes with minutes. (See Art. 166.) The terms quotient, ratio, value of the fraction, each expresses what part the dividend is of the divisor. What is the quotient of 6 divided by 3 ? What is the ratio of 6 to 3 ? What is the value of the fraction? What is one-third of 6? How many times greater than 3 is 6 ? What part of 3 is 6? Ans. 2. The answer to each question is the same, and obtained by the same process. The quotient expresses what part the dividend is of the divisor. The quotient, with unity over it, expresses what part the divisor is of the dividend, 2, and 3. That is, 6 is twice as large as 3, and 3 is half as large as 6. The numerator of a fraction is the same part of the denominator, that the fraction is of unity. If the numbers consist of different denominations, reduce them to the same, and write that number which the question requires to be a part, as the numerator of a fraction, and the other as a denominator. |