CASE VII. To reduce a fraction of one denomination to the fraction of another denomination of equal value. 66 RULE. (1). When it is from the less to a greater denomination, Multiply the denominator by all the denominations from that given to the one sought." Thus, to reduce of a penny to a fraction of a pound, the answer will be 3 = 3 4 X 12 X 20 960 (2). When it is from a greater to a less denomination, Multiply the numerator by all the denominations, from that given to the one sought." Thus, to reduce 6 X 20 X 12 X 4 7 2. Reduce 8 of a pound to the fraction of a farthing, 5760 7 Ex. 1. Reduce 23 of a farthing to the fraction of a pound. of a penny to the fraction of a shilling. of a pound to the fraction of a farthing. of a pound to the fraction of a penny. of a pound to the fraction of a farthing. shillings to the fraction of a pound. of a dwt. to the fraction of a lb. Troy. 8. Reduce of a cwt. to the fraction of an ounce. of a week to the fraction of an hour. of a mile to the fraction of a yard. 6. Reduce 3 9. Reduce 10. Reduce 11. Reduce of a pipe to the fraction of a gallon. 12. Reduce a pint to the fraction of a hhd. of ale. CASE VIII. To find the value of a fraction in numbers of inferior denomination. RULE. Multiply the integer, or its value in the next lower denomination, by the numerator, and divide by the denominator: Thus, the value of of a pound is equal to 3 X 20 12 shillings, 5 2 X 12 and of a shilling is equal to 2323 8 pence. 3 Ex. 1. What is the least number that can be divided by 4, 6, and 10, without a remainder? 2. What is the least number that can be divided by 3, 5, 8, and 10, without a remainder? 3. What is the least number that can be divided, without a remainder, by 3, 4, 8, 10, and 16? of a pound ?* Ex. 1. What is the value of 2. What is the value of 15 of a shilling? 3. What is the value of 1% of half a crown? 5. What is the value of of a cwt. ? 6. What is the value of g of a mile? 7. What is the value of 1⁄2 of a barrel of beer? CASE IX. To reduce a complex fraction to an equivalent simple fraction. RULE. If the numerator, or denominator, or both, be whole or mixed numbers, reduce them to improper fractions; and multiply the denominator of the lower fraction into the numerator of the upper, for a new numerator, and the denominator of the upper fraction into the numerator of the lower, for a new denominator. * Where there is a remainder we proceed as in Compound Division; 5 X 20 100 thus of a pound = 11s. 1d.-3. See p. 83. 9 ADDITION OF FRACTIONS. RULE. Reduce mixed numbers to improper fractions, and compound or complex fractions to simple ones, and bring them all to their least common denominator. Add all the nemerators together, and write the sum over the common denominator. Ex. Add 3, 4, 51, and together; which is thus performed:,, '2', 3 X 3 X 2 X 4 = 72 This may be performed by bringing the given fractions to the least common denominator: See p. 213. Thus,,,,, then 5, 3, 1, 2)5, 3, 2, 4 and the new deno minator 60; the fractions will be 36 + 18 + 3.30 + 18 Ex. 1. Add 4, f, aud & together. 2. Add 2, 3, and 4 together. 3. What is the sum of 3, 4, and 41 ? 4. Add together 35, 43, and .* NOTE. * When there are two or more mixed numbers, as in the 4th example, the fractions may be first added, and join these to the sum of the whole numbers: thus, I add, 3, and 2 together which are and the answer 3+ 4+1 8133. 137 and Ex. 5. Add, &, 21, and 51 together. 6. What is the sum of 7%, 31, and ? 7. What is the sum of and ** 8. What is the sum of of a guinea, of a shilling, of a penny? 9. What is the sum of and of a penny? 10. If I have of a coasting vessel, and purchase an other share of, what part of her will belong to me? 11. Add of a yard, and of a mile together. 12. What is the sum of of a yard, of a foot, and 3 of an inch? 13. Add of a lb. troy to 3 of an ounce. 14. What is the sum of of a hhd. of beer, and of a barrel? 15. Add of a chaldron to of a bushel? SUBTRACTION OF FRACTIONS. RULE. Reduce the given fractions to the same denominator, as in Addition, then subtract the lesser numerator from the greater, and under the difference place the common denominator. Ex. Take from: and, from ¦¦. * To add fractions of different integers, find their respective values by Case VII., and proceed as in Compound Addition: thus, 11. From 12 take §.‡ of a pound. of a pound. 12. From 101. take of a pound.§ 13. From of a pound take of a pound. NOTES. *In mixed numbers, the subtraction may frequently be performed without reducing them to improper fractions. After the fractions are brought to a common denominator, subtract the numerator of the lower fraction from the common denominator; to the remainder add the numerator of the upper fraction, and carry one to the lower whole number: thus, 93 - 47 = 93 — 4 } = 43. Here and being brought to a common denominator, as 3 X 81 24- 28 6- 7 7 X 4 4 X 8 = ; therefore 4 4/ To subtract a proper fraction from an unit: Subtract the numerator from the denominator; the remainder being placed over the denominator, gives the answer required: thus, take 3 from 1, answer 2. To subtract a proper fraction from any whole number: Subtract the numerator from the denominator, and the remainder placed over the denominator, gives the fraction which is to be annexed to the whole number made less by 1: thus, take from 11, the answer 10. § To subtract fractions of different integers: Find their respective values, and proceed as in Compound Subtraction: See p. 68. From of a pound, take of a shilling. will be 6s. old. 68. Sd.; and 5 X 12 8 7d.; therefore the answer |