REDUCTION OF UNLIKE FRACTIONS. 1. Have and like or unlike fractional units? 2. By reduction to higher terms, equals how many sixths? equals how many sixths? 3. Are and like fractions? Why? 4. What, then, is the difference between Like and Unlike fractions? 5. Have and a common denominator? 6. What is the least common dividend of the denominators 2 and 3? DEFINITIONS. 1. Like fractions have the same fractional unit. 2. Unlike fractions have not the same fractional unit. 3. Like fractions have a Common denominator. 4. Like fractions may have a Least common denominator. (L. C. D.) PRINCIPLES. 1. A common denominator of two or more fractions is a common dividend of their denominators. 2. The least common denominator of two or more fractions is the least common dividend of their denominators. EXERCISES. 1. Reduce and to like fractions. Process. Explanation. thereA common dividend of 3 and 8 is 24; fore 24 is a common denominator of and . To reduce to twenty-fourths we multiply both terms by 8; to reduce to twenty-fourths we multiply both terms by 3. 2. Reduce,, and to fractions having their least common denominator. Process. L. C. Dd. of 6, 9, 7 X 4 = 28 9 X 4 = 1 x 3 = 33 Explanation. The least common denominator of the fractions is the least common dividend of their denominators. The L. C. Dd. of 6, 9, 12 is 36. We therefore multiply the terms of by 6, the terms of by 4, the terms of 11 by 3. 30 The same results may be obtained by reasoning thus: Since 1 38, 3, and Reduce the two other fractions in like manner. RULE. Find the L. C. Dd. of the denominators, divide it by each denominator, multiply both terms of each fraction by the quotient obtained by its denominator. State the principle involved. (See page 68.) Brief directions are: 1. Find the L. C. Dd. 2. Divide by the denominators. 3. Multiply the numerators by the quotients. 4. Place the products over the L. C. Dd. Before applying the rule reduce mixed numbers to improper fractions and fractions to their lowest terms. 3. Reduce,, to like fractions having their L. C. D. Process. Introductory, 1⁄2 = 1. 1. L. C. Dd. of 7, 8, 2 is 56. 2. 56, 56, 56 = 8, 7, 28. 3. 3 x 8, 7 x 5, 1 X 28 = 24, 35, 28. 4. Reduce in similar manner the following: 1. What is the sum of 2 books and 3 books? 2. What is the sum of 3. Of and? Of and ? and ? 5 11 4. What is the fractional unit of ? Of 5? Of †? Are these, then, like or unlike fractions? 5. What kind of fractions can be added? 6 6. Can you directly add and ? 7. If these fractions had a like or common denominator, could you add them? 8. How do you reduce unlike fractions to like fractions? PRINCIPLES. 1. Only like fractions can be added. 2. Unlike fractions can be reduced to like fractions and then added. EXERCISES. 1. Find the sum of, and 15 15 Process. † + } + £= }} = 13 = 1 }. State the principle involved. Since the fractions are unlike, we render them like by reducing them to fractions having the L. C. D. 72. 1. Reduce the fractions, giving them a common denominator. 2. Add the integers and the fractions separately, and unite their sums. 7. 113+ 10 + 716 =? 9. 51 +6 +711 + 917 + 311 + 24 =? =? = PROBLEMS. 1. I bought 3 pieces of cloth containing 1257, 963, and 483 yards. How many yards in the three pieces? 2. A merchant sold a customer 22 yards silk, 31 yard; paper muslin, 1 yards silesia, 53 yards cambric, and 5 yards ruffling. How many yards were sold? 3. A farmer divides his farm into 5 fields. The first contains 26 acres, the second 4016 acres, the third 51 acres, the fourth 593 acres, and the fifth 623 acres. acres in the farm? How many |