1. Holt CA Course 1 4-5 Dividing Fractions and Mixed Numbers Vocabulary reciprocal multiplicative inverse One of two numbers whose product is 1. (flip a fraction over to find its reciprocal) One of two numbers whose product is 1.

2. Holt CA Course 1 4-5 Dividing Fractions and Mixed Numbers Reciprocals can help you divide by fractions. Two numbers are reciprocals or multiplicative inverses if their product is 1. The reciprocal of is 3 because 1313 1313  3 = 1313  3131 = 3333 = 1. Dividing by a number is the same as multiplying by its reciprocal. 6 ÷ 3 = 2 1313 6  = 2 same answer reciprocals

3. Holt CA Course 1 4-5 Dividing Fractions and Mixed Numbers You can use this rule to divide by fractions.

4. Holt CA Course 1 4-5 Dividing Fractions and Mixed Numbers Example 1: Dividing Fractions Divide. Write each answer in simplest form. A. 3737 ÷ 2525 3737 ÷ 2525 = 3737 · 5252 = 3737 · 5 · 2 = 15 14 or 1 14 1 Multiply by the reciprocal of. 2525 B. 3838 ÷ 12 3838 ÷ = 3838 · 1 = 3838 · 1 1 4 = Multiply by the reciprocal of 12. 1 32 Simplify.

5. Holt CA Course 1 4-5 Dividing Fractions and Mixed Numbers Divide. Write each answer in simplest form. A.5 2323 ÷ 1 1414 5 2323 ÷ 1 1414 = 17 3 ÷ 5454 = 17 3 · 4545 = 68 15 or 4 8 15 Write mixed numbers as improper fractions. Multiply by the reciprocal of 5454 B. 3434 ÷ 2 1212 3434 ÷ 2 1212 = 3434 ÷ 5252 = 3 4 · 2525 = 3 · 2 4·5 1 2 = 3 10 Write 2 as an improper fraction. 1212 Multiply by the reciprocal of. 5252 Simplify.. Example 2: Dividing Mixed Numbers

6. Holt CA Course 1 4-5 Dividing Fractions and Mixed Numbers Example 3: Social Studies Application The life span of a golden dollar coin is 30 years, while paper currency lasts an average of 1 years. How many 1212 times longer will the golden dollar stay in circulation? 30 ÷ 1 1212 = 30 1 ÷ 3232 Write the number as an improper fraction. = 30 1 · 2323 Multiply by the reciprocal of. 3232 = · Simplify. 30 2 1 3 10 1 = 20 1 or 20 The golden dollar will stay in circulation about 20 times longer than paper currency. ·

7. Holt CA Course 1 4-5 Dividing Fractions and Mixed Numbers Check It Out! Example 1 Divide. Write the answer in simplest form. 3535 ÷ 1212 3535 ÷ 1212 = 3535 · 2121 = 3535 · 2 · 1 = 6565 or 1 5 1 Multiply by the reciprocal of. 1212

8. Holt CA Course 1 4-5 Dividing Fractions and Mixed Numbers Divide. Write each answer in simplest form. 3535 ÷ 1 2525 3535 ÷1 2525 = 3535 ÷ 7575 = 3 5 · 5757 = 3·5 5·7 1 1 = 3 7 Write 1 as an improper fraction. 2525 Multiply by the reciprocal of. 7575 Simplify. Check It Out! Example 2

9. Holt CA Course 1 4-5 Dividing Fractions and Mixed Numbers Check It Out! Example 3 The average life of a queen ant is approximately 3 years. The life span of a worker ant is year. How many 3737 times longer will the queen ant live? 3 ÷ 3737 = 3131 ÷ 3737 Write the number as an improper fraction. = 3131 · 7373 Multiply by the reciprocal of. 3737 = · Simplify. 3 7 1 3 1 1 = 7171 or 7 The queen ant will live 7 times longer than the worker ant. ·