Preview Warm Up California Standards Lesson Presentation

Warm Up Multiply. 1. 2. 3. 4. 7 18 27 7 or 1 20 2 77 or 15 5 25 1 or 3

NS2.1 Solve problems involving addition, subtraction, multiplication, and division of positive fractions and explain why a particular operation was used for a given situation. Also covered: NS2.2, NS2.4 California Standards

Vocabulary reciprocal multiplicative inverse

Reciprocals can help you divide by fractions 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 1 3 1 3  3 =  1. Dividing by a number is the same as multiplying by its reciprocal. reciprocals 1 3 6  = 2 6 ÷ 3 = 2 same answer

You can use this rule to divide by fractions.

Additional Example 1: Dividing Fractions Divide. Write each answer in simplest form. 3 7 2 5 ÷ A. 3 7 2 5 3 7 5 2 2 5 ÷ = · Multiply by the reciprocal of . 3 7 · 5 = · 2 1 15 14 14 = or 1 3 8 B. ÷ 12 3 8 1 12 3 8 Multiply by the reciprocal of 12. ÷ 12 = · 1 3 8 1 · Simplify. = 12 4 1 = 32

÷ A. B. ÷ ÷ Check It Out! Example 1 Divide. Write each answer in simplest form. 3 5 1 2 ÷ A. 3 5 1 2 3 5 2 1 1 2 ÷ = · Multiply by the reciprocal of . 3 5 · 2 = · 1 1 6 5 = or 1 3 4 5 B. ÷ 3 3 4 3 4 · 1 3 Multiply by the reciprocal of 3. ÷ 3 = 1 3 4 1 · Simplify. = 3 1 1 = 4

Additional Example 2: Dividing Mixed Numbers Divide. Write each answer in simplest form. 2 3 1 4 Important: Write mixed numbers as improper fractions. A. 5 ÷ 1 2 3 1 4 17 3 5 4 5 ÷ 1 = ÷ 5 4 = 17 3 · 4 5 Multiply by the reciprocal of . 68 15 8 15 = or 4 3 4 1 2 B. ÷ 2 3 4 1 2 3 4 5 2 Write 2 as an improper fraction. 1 2 ÷ 2 = ÷ 5 2 3 4 2 5 = · Multiply by the reciprocal of . 1 3 · 2 Simplify. = 4 · 5 2 3 10 =

Check It Out! Example 2 Write mixed numbers as improper fractions. ÷ ÷ Divide. Write each answer in simplest form. 2 3 1 2 A. 3 ÷ 1 Write mixed numbers as improper fractions. 2 3 1 2 11 3 3 2 3 ÷ 1 = ÷ 11 3 3 2 = · 2 3 Multiply by the reciprocal of . 22 9 4 9 or 2 = 3 5 2 5 B. ÷ 1 3 5 2 5 3 5 7 5 Write 1 as an improper fraction. 2 5 ÷ 1 = ÷ 7 5 3 5 5 7 = · Multiply by the reciprocal of . 1 3 · 5 Simplify. = 5 · 7 1 3 7 =

Additional 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 1 2 times longer will the golden dollar stay in circulation? 1 2 30 1 3 2 30 ÷ 1 = ÷ Write the number as an improper fraction. 30 1 2 3 3 2 · = Multiply by the reciprocal of . 10 30 · 2 = Simplify. 1 · 3 1 20 1 = or 20 The golden dollar will stay in circulation about 20 times longer than paper currency.

The queen ant will live 7 times longer than the worker ant. 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 3 7 times longer will the queen ant live? 3 7 3 1 3 7 3 ÷ = ÷ Write the number as an improper fraction. 3 1 7 3 3 7 · = Multiply by the reciprocal of . 1 3 · 7 = Simplify. 1 · 3 1 7 1 = or 7 The queen ant will live 7 times longer than the worker ant.

Divide. Write each answer in simplest form. Lesson Quiz Divide. Write each answer in simplest form. 4 5 1. 8 ÷ 10 5 9 4 9 40 or 2. 1 8 ÷ 1 10 3. 3 5 ÷ 6 3 4. 2 1 ÷ 7 35 44 1 4 3 4 5. There are 5 yards of silk in a roll. If it takes of a yard to make one designer scarf, how many scarves can be made from the roll? 7