5 R.1 Fractions, Decimals, and Percents (c) 1 2 3 , 4 1 2 = 5 3 , 9 2 Write each mixed number as an improper fraction. = 5 3 # 2 9 Multiply by 2 9, the reciprocal of 9 2. = 10 27 Multiply. The quotient is in lowest terms. S Now Try Exercises 37, 43, and 49. Adding and Subtracting Fractions If a b and c b are fractions 1b≠02, then add or subtract as follows. a b + c b = a +c b and a b − c b = a −c b That is, to add or subtract two fractions having the same denominator, add or subtract the numerators and keep the same denominator. If the denominators are different, first find the least common denominator (LCD). Write each fraction as an equivalent fraction with this denominator. Then add or subtract as above. EXAMPLE 6 Adding and Subtracting Fractions Add or subtract as indicated. Write answers in lowest terms as needed. (a) 2 10 + 3 10 (b) 4 15 + 5 9 (c) 15 6 - 4 9 (d) 4 1 2 - 1 3 4 SOLUTION (a) 2 10 + 3 10 = 2 + 3 10 Add numerators. Keep the same denominator. = 5 10 = 1 2 Write in lowest terms. 15 = 3 # 5 and 9 = 3 # 3, so the LCD is 3 # 3 # 5 = 45. Write equivalent fractions with the common denominator. Add numerators. Keep the same denominator. (b) 4 15 + 5 9 = 4 15 # 3 3 + 5 9 # 5 5 = 12 45 + 25 45 = 37 45 1 8 3 8 1 4 8 5 1 2 5 Figure 4 Adding Fractions 3 8 1 8 2 2 8 5 1 4 5 Figure 5 Subtracting Fractions Figures 4 and 5 illustrate adding and subtracting fractions.
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