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Preview Warm Up California Standards Lesson Presentation

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**What is of each of the following? 1. 24 2. 16 3. 30 4. 28 12 8**

Warm Up In Spiral What is of each of the following? 1 2 12 8 15 14

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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: NS2.4, NS2.2 California Standards

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**Recall that multiplication can be written as repeated addition**

Recall that multiplication can be written as repeated addition. For example, 5 = = 15. You can use repeated addition to multiply a whole number by a fraction.

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**Additional Example 1: Transportation Application**

In 2001, the car toll on the George Washington Bridge was $6.00. In 1995 the toll was 2 of that toll. 3 What was the toll in 1995? Think: How much is of 6? Use multiplication to find a fraction of a number. 2 3 2 3 6 = + 1 3 + 1 3 + 1 3 + 1 3 + 1 3 + 1 3 = 12 3 1 3 = 4 1 1 1 1 1 = $4.00 The George Washington Bridge toll for a car was $4.00 in 1995.

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**In 2002, the fee to park in a parking garage was **

Check It Out! Example 1 In 2002, the fee to park in a parking garage was $4. In 2000 the fee was of the fee in 2002. What was the fee in 2000? 3 4 3 4 4 = + + 1 4 = 12 4 1 4 = 3 1 1 = $3.00 The fee to park in the parking garage was $3.00 in 2000.

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**Additional Example 2A: Multiplying Fractions**

Multiply. Write the answer in simplest form. 3 12 4 3 12 3 12 = Write 12 as a fraction. 4 1 4 3 12 3 Divide a numerator and denominator by their GCD, 4. Pre-reduce = 1 4 1 9 Multiply numerators. Multiply denominators. = = 9 1 Remember! Use the GCD of a numerator and denominator to simplify before multiplying.

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**Additional Example 2B: Multiplying Fractions**

Multiply. Write the answer in simplest form. 4 1 3 5 3 5 1 4 Multiply numerators. Multiply denominators. 3 5 1 4 = = 3 20

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**Additional Example 2C: Multiplying Fractions**

Multiply. Write the answer in simplest form. 1 3 3 8 1 Divide a numerator and denominator by their GCD, 3. 3 8 1 1 3 8 = 1 1 Multiply numerators. Multiply denominators. = 8

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Check It Out! Example 2A Multiply. Write the answer in simplest form. 1 16 4 1 16 1 16 = Write 16 as a fraction. 4 1 4 4 16 1 Divide a numerator and denominator by their GCD, 4. = 1 4 1 4 Multiply numerators. Multiply denominators. = = 4 1

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**Multiply. Write the answer in simplest form.**

Check It Out! Example 2B Multiply. Write the answer in simplest form. 3 1 7 8 3 7 1 8 Multiply numerators. Multiply denominators. 1 8 3 7 = = 3 56

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Check It Out! Example 2C Multiply. Write the answer in simplest form. 1 6 6 9 1 6 9 1 1 6 9 Divide a numerator and denominator by their GCD, 6. = 1 1 Multiply numerators. Multiply denominators. = 9

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**Additional Example 3A: Multiplying Mixed Numbers**

Multiply. Write the answer in simplest form. 2 2 1 5 3 IMPORTANT: Write the mixed number as an improper fraction. 2 2 2 5 1 = 3 5 3 5 1 2 5 Divide a numerator and denominator by their GCD, 5. = 5 3 1 2 Multiply numerators. Multiply denominators. = 3

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**Additional Example 3B: Multiplying Mixed Numbers**

Multiply. Write the answer in simplest form. 1 1 4 2 5 7 1 1 21 15 4 2 = Write mixed numbers as improper fractions. 5 7 5 7 3 3 21 15 Divide numerators and denominators by their GCDs, 5 and 7. = 5 7 1 1 9 Multiply numerators. Multiply denominators. or 9 = 1

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**Additional Example 3C: Multiplying Mixed Numbers**

Multiply. Write the answer in simplest form. 2 2 6 4 3 5 2 2 20 22 Write mixed numbers as improper fractions. 6 4 = 3 5 3 5 4 Divide a numerator and denominator by their GCD, 5. 20 22 = 3 5 1 3 = 88 or 29 1 Multiply numerators. Multiply denominators.

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Check It Out! Example 3A Multiply. Write the answer in simplest form. 3 1 2 5 3 3 1 3 7 Write the mixed number as an improper fraction. 2 = 3 5 3 5 1 3 7 = Divide a numerator and denominator by the GCD, 3. 5 3 1 7 2 Multiply numerators. Multiply denominators. = or 1 5 5

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**Multiply. Write the answer in simplest form.**

Check It Out! Example 3B Multiply. Write the answer in simplest form. 3 1 3 1 5 3 3 1 18 4 3 1 = Write mixed numbers as improper fractions. 5 3 5 3 6 18 4 Divide a numerator and denominator by their GCD, 3. = 5 3 1 = 24 5 or 4 4 Multiply numerators. Multiply denominators.

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**Multiply. Write the answer in simplest form.**

Check It Out! Example 3C Multiply. Write the answer in simplest form. 1 1 3 1 6 3 1 1 19 4 Write mixed numbers as improper fractions. 3 1 = 6 3 6 3 2 Divide a numerator and denominator by their GCD, 2. 19 4 = 6 3 3 9 = 38 or 4 2 Multiply numerators. Multiply denominators.

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**Multiply. Write each answer in simplest terms.**

Lesson Quiz Multiply. Write each answer in simplest terms. 5 48 35 12 or 11 2 1. 2. 17 2 1 or 8 7 8 3. 4. 1 5. A recipe for clam chowder calls for 2 pounds of 4 butter. If you prepare one-half of the recipe, how much butter do you need? 1 8 pounds

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