122 Chapter 2 Fractions and Mixed Numbers: Multiplication and Division Section 2.4 Multiplication of Fractions and Applications . 13 Elija takes 1 3 Max gets of 1 3 1 6 1 2 Figure 2-6 From the illustration, the product Notice that the product is found by multiplying the numerators and multiplying the denominators. This is true in general to multiply fractions. Multiplying Fractions To multiply fractions, write the product of the numerators over the product of the denominators. Then simplify the resulting fraction, if possible. provided b and d are not equal to 0 Multiplying Fractions Example 1 Multiply and write the answer as a fraction. a. b. Solution: a. Notice that the product is simplified completely because there are no common factors shared by 8 and 35. 8 3 b. First write the whole number as a fraction. Multiply the numerators. Multiply the denominators. 40 3 8 5 3 1 5 8 3 5 1 8 35 2 5 4 7 2 4 5 7 8 35 Multiply the numerators. Multiply the denominators. 8 3 5 2 5 4 7 a b c d a c b d 16 1 2 13 16 . The product is not reducible because there are no common factors shared by 40 and 3. Concepts 1. Multiplication of Fractions 2. Fractions and the Order of Concept Connections 1. What fraction is of of a whole? Answers 1. 2. 3. 77 12 10 27 1 8 1. Multiplication of Fractions Suppose Elija takes of a cake and then gives of this portion to his friend Max. Max gets of of the cake. This is equivalent to the expression See Figure 2-6. 12 13 1 2 1 2 1 3 Skill Practice Multiply.Write the answer as a fraction. 2. 3. 7 12 11 2 3 5 9 14 1 2 Operations 3. Area of a Triangle 4. Applications of Multiplying Fractions
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