18 Chapter 1 Real Numbers and Algebraic Expressions Multiplying Fractions We can multiply fractions by multiplying the numerators of the fractions and by multiplying the denominators of the fractions. We always want to express the answers in lowest terms. �������������������� Multiplying Fractions For b, d ≠ 0, a b · c d = a · c b · d �� ������������������������ ������������������ Multiply the fractions and write each answer in lowest terms. 4a. 3 4 · 5 2 4b. 10 3 · 18 25 4c. 2 2 3 · 5 3 4 3 4 Solutions 4a. · 5 2 = 3 · 5 4 · 2 Multiply the numerators and denominators. = 15 8 Simplify the products. 4b. 10 3 · 18 25 = 10 · 18 3 · 25 = 2 · 5 · 2 · 3 · 3 3 · 5 · 5 = 2 · 2 · 3 5 = 12 5 4c. 2 2 3 · 5 3 4 = 8 3 · 23 4 = 28 · 23 3 · 41 = 46 3 Student Check 4 Multiply the fractions and write each answer in lowest terms. a. 5 8 · 3 7 b. 4 9 · 15 14 c. 1 3 7 · 2 1 10 Dividing Fractions Before we can divide fractions, we must discuss the concept of reciprocals. Two numbers are reciprocals if their product is 1. Some examples are shown. Number Reciprocal Their Product 6 1 6 6 · 1 6 = 6 1 · 1 6 = 1 4 5 5 4 4 5 · 5 4 = 1 Objective 4 ▶ Multiply fractions. Multiply the numerators and denominators. Write the prime factorization of each number. 10 = 2 · 5, 18 = 2 · 3 · 3, 25 = 5 · 5 Divide out the common factors of 5 and 3. Multiply the remaining factors. Convert the mixed fractions to improper fractions. 2 2 3 = 8 3 nd 5 3 4 = 23 4 Multiply the numerators and denominators. Divide out the common factor of 4 from the numerator and denominator. Multiply the remaining factors. Objective 5 ▶ Divide fractions.
hendricks_beginning_algebra_1e_ch1_3
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