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Mastering Dividing Fractions with Reciprocals: A Step-by-Step Guide

In this lesson, learn how to divide fractions using the concept of reciprocals, also known as multiplicative inverses. Understand that two numbers are reciprocals if their product equals one, and discover simple methods to find reciprocals for given fractions. Explore various examples, including how to divide both fractions and mixed numbers, and practice writing answers in simplest form. This guide provides key insights and techniques to make dividing fractions straightforward and effective.

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Mastering Dividing Fractions with Reciprocals: A Step-by-Step Guide

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  1. Dividing Fractions #19

  2. Vocabulary Reciprocals can help you divide by fractions. Two numbers are reciprocals or multiplicative inverses if their product is 1.

  3. 1 __ 9 Example 1: Finding Reciprocals Find the reciprocal.

  4. Example 2 Find each reciprocal. 5

  5. 1 __ 4 Example 3 Find each reciprocal. 2

  6. 4 3 __ __ 3 4 1 __ 4 F.Y.I. Look at the relationship between the fractions and . If you switch the numerator and denominator of a fraction, you will find its reciprocal. Dividing by a number is the same as multiplying by its reciprocal. 24 ÷ 4 = 6 24 • = 6

  7. 8 __ 7 Example 4: Using Reciprocals to Divide Fractions and Mixed Numbers Divide. Write each answer in simplest form. ÷ 7

  8. 2 5 __ __ 3 6 Example 5: Using Reciprocals to Divide Fractions and Mixed Numbers ÷

  9. 1 3 __ __ 12 4 Example 6: Using Reciprocals to Divide Fractions and Mixed Numbers 2 ÷ 1

  10. 1 3 __ __ 8 4 Example 7 Divide. Write each answer in simplest form. 1 ÷

  11. 1 1 __ __ 5 2 Example 8 Divide. Write each answer in simplest form. 2 16 ÷

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