5c. 3 3 7 ÷ 7 15 = 24 7 · 15 7 = 24 · 15 7 · 7 Write 3 3 7 as 24 7 and multiply by the reciprocal of Multiply the numerators and denominators. = 360 49 or 7 17 49 Simplify the products. The answer can be written as either an improper fraction or as a mixed number. Student Check 5 Divide the fractions and write each answer in lowest terms. a. 12 15 ÷ 30 24 b. 6 7 ÷ 12 c. 5 2 3 ÷ 4 1 9 Adding and Subtracting Fractions with Like Denominators One common method for adding or subtracting fractions requires that the denominators of the fractions be the same. If the denominators are the same, we simply add or subtract the numerators and place this number over their common denominator. For example, 2 7 + 1 7 = 2 + 1 7 = 3 7 �������������������� Adding or Subtracting Fractions with Common Denominators a b + c b = a + c b , for b ≠ 0 a b - c b = a - c b , for b ≠ 0 �� ������������������������ ������������������ Add or subtract the fractions and simplify the result. 6a. 5 8 + 2 8 6b. 1 1 3 + 6 2 3 6c. 8 9 - 2 9 6d. 5 1 7 - 4 3 7 5 8 Solutions 6a. + 2 8 = 5 + 2 8 = 7 8 Simplify the numerator. 6b. 1 1 3 + 6 2 3 = 4 3 + 20 3 Write each mixed number as an improper fraction. = 4 + 20 3 = 24 3 Simplify the numerator. =8 Simplify the fraction. 8 9 6c. - 2 9 = 8 - 2 9 = 6 9 Simplify the numerator. = 2 · 3 3 · 3 Factor the numerator and denominator. = 2 3 Divide out the common factor of 3. 7 15 , which is 15 7 . Objective 6 ▶ Add or subtract fractions with like denominators. Add the numerators and place over the common denominator. Add the numerators and place over the common denominator. Subtract the numerators and place over the common denominator. 20 Chapter 1 Real Numbers and Algebraic Expressions
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