Reducing Fractions to Lowest Terms Reduce to lowest terms. 336 2)336 3)168 7)56 8 Divide both terms by common divisors that are easily observed. Shorten the work by using as great common divisors as possible. Exercise 31 (Solve as many as possible at sight.) Reduce each of the following to its lowest terms: This shows the complete work: 1 = = 4444 18 × 4, or 72 18 183 = 72+ Explanation: In one there are four fourths, and in eighteen there are eighteen times four fourths, or seventy-two fourths; and in eighteen and three fourths there are seventy-two fourths plus three fourths, or seventy-five fourths. In practice take (4 × 18) plus 3 for the numerator, and 4 for the denominator. or 75 Read each and give the answer: 41. A 2-foot rope will make how many half-foot pieces? 42. A $5 note is worth how many quarter dollars? 43. A piece of cloth 2 yd. long can be cut into how many pieces each of a yard long? 44. A $2 gold piece is worth how many half dollars? 45. How many one eighth pound packages can be made from 17 pounds of drugs? 46. A line 5 yd. long will make how many half-yard lines? 47. How many times will 4 bu. of potatoes fill a halfbushel measure? 48. $ 12 in half dollars make how many half dollars? $51 in quarter dollars make how many quarter dollars? 49. $21 in quarter dollars make how many quarter dollars? Reducing Improper Fractions to Whole or Mixed Numbers Illustrative Example Reduce 100 to a mixed number. (Solve as many as possible at sight.) Reduce to whole or mixed numbers: Read each and give the answer: 33. 8 half bushels of oats will fill how many bushel sacks? 34. 7 quarter days are how many days? 35. 18 silver half dollars can be exchanged for how many dollar bills? 36. How many quarts of cream are needed to fill 16 one eighth quart bottles? 37. 15 quarter pecks of seed are how many pecks? 38. How many tons of coal will be required to give 21 families each a quarter of a ton? 39. 39 quarter dollars are worth how many dollars? 40. How many yards of ribbon are required to make 40 pieces, each one eighth of a yard long? 4I. How many pints of seed are there in 50 packages each containing pint? Reducing Fractions to a Common Denominator 90. Fractions that have the same number for a denominator are said to have a common denominator. Thus, and have a common denominator. 91. Fractions that have a common denominator are called similar fractions. Thus, and are similar fractions. Illustrative Example Reduce,, and to 12ths. Multiply both terms of by 4; that is, 12÷3. 3 Multiply both terms of by 3; that is, 12÷4. Multiply both terms of by 2; that is, 12÷6. Reducing Fractions to their Least Common Denominator 92. The least common denominator (1. c. d.) of two or more fractions in their lowest terms is the least number that their denominators will divide. Thus, the least common denominator of,, and is 12; for 12 is the least number that 3, 4, and 6 will divide. 93. The least common multiple of the denominators of two or more fractions in their lowest terms is the least common denominator of the fractions. Illustrative Example Reduce,, and to fractions having the least common denominator. The least common multiple of 3, 4, and 8 is 24. Therefore, the 1. c. d. of, 4, and is 24. 16 24 18 24 15 24 |