4-7 Multiplying Fractions and Mixed Numbers Warm Up Problem of the Day Course 2 Warm Up Problem of the Day Lesson Presentation

4-7 Multiplying Fractions and Mixed Numbers Warm Up 1. What is Course 2 4-7 Multiplying Fractions and Mixed Numbers Warm Up 1. What is 2. What is 3. What is 1 of 24? 12 2 1 of 16? 8 2 1 of 30? 15 2 1 4. What is of 28? 7 4

4-7 Multiplying Fractions and Mixed Numbers Problem of the Day Course 2 4-7 Multiplying Fractions and Mixed Numbers Problem of the Day Caitlin was watching television. In a weather forecast at midnight the forecaster indicated that it would be cloudy for exactly 72 hours and then would be sunny. Caitlin called the station to tell the forecaster he was wrong. How did she know? There are 24 hours in a day, so 72 hours equals 3 days. In 3 days it would be midnight again, not sunny.

4-7 Learn to multiply fractions and mixed numbers. Course 2 4-7 Multiplying Fractions and Mixed Numbers Learn to multiply fractions and mixed numbers.

4-7 Multiplying Fractions and Mixed Numbers Course 2 4-7 Multiplying Fractions and Mixed Numbers The San Francisco-Oakland Bay Bridge, which opened in 1936,is a toll bridge used by drivers traveling between the two cities. In 1977 , the toll for a car crossing the bridge was of the toll in 2001. 3 8 To find the toll in 1977, you will need to multiply the toll in 2001 by a fraction.

Additional Example 1: Transportation Application Course 2 4-7 Multiplying Fractions and Mixed Numbers 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 the 3 toll in 2001. What was the toll in 1995? 2 3 6 · = + 1 3 + 1 3 + 1 3 + 1 3 + 1 3 + 1 3 = 12 3 1 3 = 4 1 Simplify. 1 1 1 1 = $4.00 Write the fraction as a decimal. The George Washington Bridge toll for a car was $4.00 in 1995.

4-7 Multiplying Fractions and Mixed Numbers Try This: Example 1 Course 2 4-7 Multiplying Fractions and Mixed Numbers Try This: 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 Simplify. = $3.00 Write the fraction as a decimal. The fee to park in the parking garage was $3.00 in 2000.

To multiply fractions, multiply the numerators to find the product’s Course 2 4-7 Multiplying Fractions and Mixed Numbers To multiply fractions, multiply the numerators to find the product’s numerator. Then multiply the denominators to find the product’s denominator.

Additional Example 2A: Multiplying Fractions Course 2 4-7 Multiplying Fractions and Mixed Numbers Additional Example 2A: Multiplying Fractions Multiply. Write the answer in simplest form. 3 A. –12 · 4 3 12 3 –12 · = – · Write –12 as a fraction. 4 1 4 3 12 · 3 = – Simplify. 1 · 4 1 9 Multiply numerators. Multiply denominators. = – = –9 1 You can write any integer as a fraction with a denominator of 1. Remember!

Additional Example 2B: Multiplying Fractions Course 2 4-7 Multiplying Fractions and Mixed Numbers Additional Example 2B: Multiplying Fractions Multiply. Write the answer in simplest form. 1 3 B. · 3 8 1 3 8 · 1 1 3 · 8 = Simplify. 1 1 Multiply numerators. Multiply denominators. = 8

Additional Example 2C: Multiplying Fractions Course 2 4-7 Multiplying Fractions and Mixed Numbers Additional Example 2C: Multiplying Fractions Multiply. Write the answer in simplest form. 2 4 C. · – 3 5 The signs are different, so the answer will be negative. 4 5 · 2 3 – = 2 3 · 4 5 – = 8 15 – Multiply numerators. Multiply denominators.

4-7 Multiplying Fractions and Mixed Numbers Try This: Example 2A Course 2 4-7 Multiplying Fractions and Mixed Numbers Try This: Example 2A Multiply. Write the answer in simplest form. 1 A. –16 · 4 1 16 1 –16 · = – · Write –16 as a fraction. 4 1 4 4 16 · 1 = – Simplify. 1 · 4 1 4 Multiply numerators. Multiply denominators. = – –4 = 1

4-7 Multiplying Fractions and Mixed Numbers Try This: Example 2B Course 2 4-7 Multiplying Fractions and Mixed Numbers Try This: Example 2B Multiply. Write the answer in simplest form. 1 6 B. · 6 9 1 6 9 · 1 1 6 · 9 = Simplify. 1 1 Multiply numerators. Multiply denominators. = 9

4-7 Multiplying Fractions and Mixed Numbers Try This: Example 2C Course 2 4-7 Multiplying Fractions and Mixed Numbers Try This: Example 2C Multiply. Write the answer in simplest form. 3 1 C. · – 7 8 The signs are different, so the answer will be negative. 1 8 · 3 7 – = 3 7 · 1 8 – = 3 56 – Multiply numerators. Multiply denominators.

Additional Example 3A: Multiplying Mixed Numbers Course 2 4-7 Multiplying Fractions and Mixed Numbers Additional Example 3A: Multiplying Mixed Numbers Multiply. Write the answer in simplest form. 2 2 · 1 A. 5 3 2 2 2 5 Write the mixed number as an improper fraction. · 1 = · 3 5 3 5 1 2 5 = · Simplify. 5 3 1 2 Multiply numerators. Multiply denominators. = 3

Additional Example 3B: Multiplying Mixed Numbers Course 2 4-7 Multiplying Fractions and Mixed Numbers Additional Example 3B: Multiplying Mixed Numbers Multiply. Write the answer in simplest form. 1 1 B. 4 · 2 5 7 1 1 21 15 4 · 2 = · Write the mixed numbers as improper fractions. 5 7 5 7 3 3 21 15 · = Simplify. 5 7 1 1 9 Multiply numerators. Multiply denominators. or 9 = 1

Additional Example 3C: Multiplying Mixed Numbers Course 2 4-7 Multiplying Fractions and Mixed Numbers Additional Example 3C: Multiplying Mixed Numbers Multiply. Write the answer in simplest form. 2 2 C. 6 · 4 3 5 2 2 20 22 Write the mixed numbers as improper fractions. 6 · · 4 = 3 5 3 5 4 20 22 = · Simplify. 3 5 1 3 = 88 or 29 1 Multiply numerators. Multiply denominators.

4-7 Multiplying Fractions and Mixed Numbers Try This: Example 3A Course 2 4-7 Multiplying Fractions and Mixed Numbers Try This: Example 3A Multiply. Write the answer in simplest form. 3 1 · 2 A. 5 3 3 1 3 7 Write the mixed number as an improper fraction. · 2 = · 3 5 3 5 1 3 7 = · Simplify. 5 3 1 7 2 Multiply numerators. Multiply denominators. = or 1 5 5

4-7 Multiplying Fractions and Mixed Numbers Try This: Example 3B Course 2 4-7 Multiplying Fractions and Mixed Numbers Try This: Example 3B Multiply. Write the answer in simplest form. 3 1 B. 3 · 1 6 3 3 1 21 4 3 · 1 = · Write the mixed numbers as improper fractions. 6 3 6 3 7 2 21 4 · = Simplify. 6 3 3 1 = 14 3 or 4 2 Multiply numerators. Multiply denominators.

4-7 Multiplying Fractions and Mixed Numbers Try This: Example 3C Course 2 4-7 Multiplying Fractions and Mixed Numbers Try This: Example 3C Multiply. Write the answer in simplest form. 1 1 C. 3 · 1 6 3 1 1 19 4 Write the mixed numbers as improper fractions. 3 · · 1 = 6 3 6 3 2 19 4 = · Simplify. 6 3 3 9 = 38 or 4 2 Multiply numerators. Multiply denominators.

4-7 Multiplying Fractions and Mixed Numbers Lesson Quiz: Part 1 Course 2 4-7 Multiplying Fractions and Mixed Numbers Lesson Quiz: Part 1 Multiply. Write each answer in simplest terms. 1 5 5 48 1. · 8 6 5 1 2 35 12 or 11 2 2. 5 · 6 1 2 17 2 1 or 8 3. 5 · 1 10 3 3 2 7 8 4. · 4 16 3

4-7 Multiplying Fractions and Mixed Numbers Lesson Quiz: Part 2 Course 2 4-7 Multiplying Fractions and Mixed Numbers Lesson Quiz: Part 2 Multiply. Write the answer in simplest terms. 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