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**Dividing Rational Numbers**

3.4

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**Warm Up Multiply. –2 1. –3 2. –15 – 10 3. 0.05(2.8) 0.14 4. –0.9(16.1)**

5 6 1 2 –2 1. –3 2. 23 –15 – 10 (2.8) 0.14 4. –0.9(16.1) –14.49

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**Learn to divide fractions and decimals.**

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Vocabulary reciprocal

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**A number and its reciprocal have a product of 1**

A number and its reciprocal have a product of 1. To find the reciprocal of a fraction, exchange the numerator and the denominator. Remember that an integer can be written as a fraction with a denominator of 1.

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**Multiplication and division are inverse operations**

Multiplication and division are inverse operations. They undo each other. 1 3 2 5 2 15 = 2 5 = ÷ 2 15 1 3 Notice that multiplying by the reciprocal gives the same result as dividing. 5 2 2 15 2 • 5 15 • 2 1 3 = =

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**Example: Dividing Fractions**

Divide. Write the answer in simplest form. 5 11 1 2 A. ÷ 5 11 ÷ 1 2 5 11 • 2 1 = Multiply by the reciprocal. 5 11 • 2 1 = No common factors. 10 11 = Simplest form

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**Example: Dividing Fractions**

Divide. Write the answer in simplest form. 3 8 B. 2 ÷ 2 3 8 ÷ 2 = 19 8 2 1 ÷ Write as an improper fraction. = 19 8 1 2 Multiply by the reciprocal. 19 • 1 8 • 2 = No common factors 19 16 = 3 16 = 1 19 ÷ 16 = 1 R 3

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**Try This A. ÷ 28 45 Divide. Write the answer in simplest form. 7 15**

3 4 A. ÷ 7 15 ÷ 3 4 7 15 • 4 3 = Multiply by the reciprocal. 7 • 4 15 • 3 = No common factors. 28 45 = Simplest form

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**Try This B. 4 ÷ 3 ÷ ÷ 3 4 1 Divide. Write the answer in simplest form.**

2 5 B. 4 ÷ 3 = 22 5 3 1 ÷ Write as an improper fraction. 2 5 ÷ 3 4 = 22 5 1 3 Multiply by the reciprocal. 22 • 1 5 • 3 = No common factors. 7 15 = or 1 22 15 22 ÷ 15 = 1 R 7

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When dividing a decimal by a decimal, multiply both numbers by a power of 10 so you can divide by a whole number. To decide which power of 10 to multiply by, look at the denominator. The number of decimal places is the number of zeros to write after 1. 1.32 0.4 1.32 0.4 10 13.2 4 = = 1 decimal place 1 zero

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**Example: Dividing Decimals**

Divide. 0.384 ÷ 0.24 0.384 0.24 0.384 ÷ 0.24 = 100 38.4 24 = 38.4 24 = Divide. = 1.6

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Try This Divide. 0.585 ÷ 0.25 0.585 0.25 0.585 ÷ 0.25 = 100 58.5 25 = 58.5 25 = Divide. = 2.34

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**Example: Evaluating Expressions with Fractions and Decimals**

Evaluate the expression for the given value of the variable. 5.25 A. for n = 0.15 n 0.15 has 2 decimal places, so use 5.25 0.15 = 100 525 15 = Divide. = 35

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**Example: Evaluating Expressions with Fractions and Decimals**

Evaluate the expression for the given value of the variable. 4 5 B. k ÷ for k = 5 5 4 = 5 1 • 4 5 5 ÷ 5 • 5 1 • 4 = 254 1 4 6

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**Try This A. for b = 0.75 = = = 3.4 0.75 has 2 decimal places, so use .**

Evaluate the expression for the given value of the variable. 2.55 A. for b = 0.75 b 0.75 has 2 decimal places, so use 2.55 0.75 = 100100 25575 = Divide. = 3.4

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**Try This u ÷ , for u = 9 B. = 9 ÷ = = 15 No common factors.**

Evaluate the expression for the given value of the variable. 4 7 u ÷ , for u = 9 B. = 9 1 9 ÷ 4 7 7 4 Write as in improper fraction and multiply by the reciprocal. 9 • 7 1 • 4 = No common factors. = 3 4 15 63 ÷ 4 = 15 R 3

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**Lesson Quiz: Part 1 Divide. –1 1. 2 –1 2. –14 ÷ 1.25 –11.2**

5 6 1 2 –1 89 1. 2 ÷ –1 2. –14 ÷ 1.25 –11.2 ÷ 0.65 6 112 x 4. Evaluate for x = 6.3. 17.7

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Lesson Quiz: Part 2 5. A penny weighs 2.51 grams. How many pennies would it take to equal one pound (453.6 grams)? 181

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