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. EXAMPLES. 1. Reduce 281 to its equivalent whole or mixed number. 16)981(61 - 21 16 5 or 281-981-16-61 2. Reduce 219 to its equivalent whole or mixed num ber. the answer. Ans. 121. mixed numAns. 28. 3. Reduce 126 to its equivalent whole or ber. 4. Reduce 56 to its equivalent whole or mixed number. Ans. 7. 5. Reduce 621613 to its proper terms. Ans. 120917. 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 3 Answer. And 63-63÷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. 8 1. Reduce of of of to a single fraction. 2×3×4x8 3x4x5x11 183-16 the answer. Or, by expunging equal numerators and equal denominators, the answer will be as before,=1. 2. Reduce of g of § to a single fraction. Ans. 1. 3. Reduce of of of 10 to a single fraction. Ans. 154. 19 4. Reduce of of to a single fraction. Ans. 821 CASE VI. To reduce fractions of different denominators to equivalent fractions, having a common denominator. RULE.-Multiply each numerator 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 by multiplying its terms by 3, by which it becomes 3. Also,, 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, 3, and 4 to equivalent fractions, having a common denominator. 2×5×7=70 the common denominator. Therefore the equivalent fractions are 8, 48, and 48. the answer. 2. Reduce, §, 1, and § to equivalent fractions, having a common denominator. Ans. 838, 815, 7, and 18. 3. Reduce, of 4, 5 and to a common denomi342 Ans. 198, 38, 340, 570. of 14, and to a common denomAns. 13552, 15815, 18014, 11418. nator. 4. Reduce 13, inator. CASE VII. 3135 60 570 1440 6016 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. 1. What is the value of of a shilling? Ans. 44d. 3 12 8)36(4d. 8)16(2qrs. 2. What is the value of of a dollar? Ans. 41cts. 63mills. 3. What is the value of of a mile? Ans. 4fur. 22pol. 4yds. 24 feet. 4. What is the value of of a month? Ans. 3w. 1d. 9h. 36m. 5. What is the value of of an acre? Ans. 1rood, 30poles. 6. What is the value of of § of 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. å of 15 of 20=1410=rss the answer. And of 20 of 12=248=d. 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. 6. Reduce of a month to the fraction of a day. Ans. $461. 7. Reduce 7s. 3d. to the fraction of a pound. s. d. 73 S. 20 in a £ 12 240 denominator. 27-28 Ans. 8. Reduce 6 furlongs, 16 poles to the fraction of a mile. Ans. t. 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 terms. EXAMPLES. 1. Add 3, 7, of 7 and 7 together. First, 32, 4 of 7=28=16, 7=7. 29x8x10x 1=2320 7x8x10x 1= 560 7x8x 8x 1= 448 7x8x 8x10=4480 8x8x10x1=640 2. Add, 7, and of together. 7808 12128-12 Ans. Ans. 83. Ans. 4311. Ans. 263. Ans. 18. ? 3. What is the sum of 3 of 95 and 7 of 14? 4. Add 19, 7, and of together. 5. Add & and 17 together. 6. What is the sum of £4, s. and of a penny Ans. 88s. or 3s. Id. 1qrs. 7. Add 4 of 15£. £34, 3 of 4 of of a pound and of of a shilling together. gether. 9. Add of a week, of a gether. Ans. £7 17s. 54d. foot and of a mile toAns. 660yds. 2ft. 9in. day and of an hour toAns. 2days, 144hours. |