CASE III. To reduce an improper fraction to its equivalent whole or mixed number RULE.-Divide the numerator by the denominator, and the quotient will be the whole or mixed number required. 16 EXAMPLES. 1. Reduce 981 to its equivalent whole or mixed number. 16)981(61 2. Reduce ber. 96 21 16 the answer. 5 or 981-981-16-61 48 3. Reduce 126 to its equivalent whole or mixed number. Ans. 25. 4. Reduce 56 to its equivalent whole or mixed number. Ans. 7. 5. Reduce $21613 to its proper terms. Ans. 120987. 514 CASE IV. To reduce a whole number to an equivalent fraction, having a given denominator. RULE.-Multiply the whole number by the given denominator, and place the product over the said denominator, and it will form the fraction required. 9. EXAMPLES. 1. Reduce 7 to a fraction, whose denominator shall be 7x9=63, and 63 Answer. And 3=63÷9=7 Proof. 2. Reduce 13 to a fraction, whose denominator shall be 12. Ans. 156. 3. Reduce 746 to a fraction, whose denominator shall .be 60. Ans. 44760. CASE V. To reduce a compound fraction to an equivalent single one. RULE.-Multiply all the numerators together for the numerator, and all the denominators together for the denominator, and they will form the fraction required. If part of the compound fraction be a whole or mixed number, it must be reduced to an improper fraction by one of the former cases. When it can be done, divide any two terms of the fraction by the same number, and use the quotients instead thereof. EXAMPLES. 1. Reduce of of of to a single fraction. 2x3x4x8 3x4x5x+1 23 192 660 equal numerators and equal denominators, the answer will be as before,=. 16 2 Reduce of of to a single fraction. Aus. 4. 3. Reduce of 12 4. Reduce of of of of 10 to a single fraction. 19 to a single fraction. CASE VI. Ans. 1540. To reduce fractions of different denominators to equivalent fractions, having a common denominator. RULE.-Maltiply each nomerator into all the denominators except its own, for a new numerator; and all the denominators continually for the common denominator ! first reducing the fractions to their lowest terms, &c. NOTE. By Note 9, in case 1, it will be seen, that several fractions of different denominators may be readily reduced to a common denominator. Thus may be reduced to the same denominator as 3, by multiplying its terms by 3, by which it becomes 3. Also, 2, and, may be reduced to a common denominator, by multiplying the terms of the first fraction by 6, of the second by 3, and dividing those of the last by 5. And so of others. EXAMPLES. 1. Reduce,, and to equivalent fractions, having a common denominator. 1×5×7=35 the new numerator for 1. 3×2×7=42 do. 4×2×5=40 do. do. 용. do. 2×5×7=70 the common denominator. Therefore the equivalent fractions are 48, 48, and 48, the answer. 2. Reduce,,, and ing a commou denominator. 3 Reduce 1, 2 of 4, 52 nator. to equivalent fractions, havAns. 378 315 838, 70, and 48. 30, 630, 630' 57 60 and 2 to a common denomiAns. 198, 348, 3435, 70 4. Reduce 1, 2 of 11, and to a common denominator. Ans. 18818, 18818, 18016, 16618. CASE VII. To find the value of a fraction in any known parts of the integer. RULE.-Multiply the numerator by the parts in the next inferiour denomination, and divide the product by the denominator; and if any thing remain, multiply it by the next inferiour denominator, and divide by the denominator as before; and so on, as far as necessary; and the quotients placed after one another, in their order, will be the answer required, EXAMPLES. 1. What is the value of of a shilling? Ans. 44d. 3 12 8)36(4d. 4 4 8) 16(2qrs. 2. What is the value of of a dollar? Ans. 41cts. 6mills. 3. What is the value of of a mile ? Ans. 4fur. 22pol. 4yds. 24 feet. 4. What is the value of of a month? 5. What is the value of Ans. 3w. 1d. 9h. 36m. of an acre? Ans. Irood, 30poles. 6. What is the value of of of 3 of $49,95cts.? Ans. $5,55cts. CASE VIII. To reduce a fraction of one denomination to that of another, retaining the same value. RULE. Make a compound fraction of it, and reduce it to a single one. EXAMPLES. 1. Reduce of a penny to the fraction of a pound. of And of 2=1440=28 the answer. of 20 of 12-348-3d. the proof. 2. Reduce of a farthing to the fraction of a pound. Ans. 1920 3. Reduce of a mill to the fraction of a dollar. Ans. 2750 4. Reduce to the fraction of a penny. Ans. 40-134d. 5. Reduce of a pound Avoirdupois to the fraction of an cwt. Ans. 78382 6. Reduce of a month to the fraction of a day. Ans. 46. 7. Reduce 7s. 3d. to the fraction of a pound. 3. Reduce 6 furlongs, 16 poles to the fraction of a mile. Ans.. ADDITION OF VULGAR FRACTIONS. RULE.-Reduce compound fractions to single ones; mixed numbers to improper fractions: fractions of different integers to those of the same; and all of them to a common denominator; then the sum of the numerators, written over the common denominator, will be the sum of the fractions required. NOTE 1.-In adding mixed numbers that are not compounded with other fractions, find first the sum of the fractions, to which add the whole numbers of the given mixed number. NOTE 2.-When adding fractions of money, weight, &c. reduce fractions of different integers to those of the same integer. Or, find the value of each fraction by Case 7, in Reduction, and then add them in their proper terins. EXAMPLES. 1. Add 3,, of and 7 together. First, 353, of 7=28=76, 7=1. Then the fractions are 29, 4, and 1. 29x8x10x 1=2320 7x8x10x 1= 560 7x8x 8x 1 = 448 7x8x 8×10=4480 7808 8x8x10x1=640 2. Add §, 71, and of 2 together. 12428-12 Ans. Ans. 83. Ans. 4311. Ans. 263. Ans. 18. 3. What is the sum of of 95 and 7 of 14? 5. Add and 171 together. 6. What is the sum of £4, s. and of a penny? Ans. s. or 3s. 1d. 1qrs. 7. Add of 15£. £87, 4 of 4 of 3 of a pound and of of a shilling together. 8. Add of a yard, of a foot and of a mile toAns. 660yds. 2ft. 9in. Ans. £7 17s. 54d. gether. 9. Add of a week, of a day and of an hour toAns. 2days, 144hours. gether. |