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Preview Warm Up California Standards Lesson Presentation

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

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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

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Vocabulary reciprocal multiplicative inverse

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**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

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**You can use this rule to divide by fractions.**

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**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

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**÷ 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

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**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 =

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**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 =

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**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.

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**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.

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**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

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