1. 4-7 Multiplying Fractions and Mixed Numbers Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

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

3. 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. Course 2 4-7 Multiplying Fractions and Mixed Numbers

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

5. 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. Course 2 4-7 Multiplying Fractions and Mixed Numbers

6. In 2001, the car toll on the George Washington Bridge was $6.00. In 1995 the toll was Additional Example 1: Transportation Application 2 3 of the toll in 2001. What was the toll in 1995? 2 3 6 · = 2 3 + 2 3 2 3 2 3 2 3 2 3 +++ + + = 12 3 = 4 1 Simplify. = $4.00 Write the fraction as a decimal. The George Washington Bridge toll for a car was $4.00 in 1995. +++ + 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 11 1 1 Course 2 4-7 Multiplying Fractions and Mixed Numbers

7. 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? Try This: Example 1 3 4 4 · = 3 4 + 3 4 3 4 3 4 ++ = 12 4 = 3 1 Simplify. = $3.00 Write the fraction as a decimal. The fee to park in the parking garage was $3.00 in 2000. 3 4 + 1 4 1 4 1 4 1 4 1 4 1 4 + + 1 4 1 4 1 4 1 4 1 4 1 4 1 4 1 4 1 4 1 4 1 4 1 4 1 4 1 4 1 4 1 4 1 4 1 4 111 Course 2 4-7 Multiplying Fractions and Mixed Numbers

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

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

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

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

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

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

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

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

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

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

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

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

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

21. Lesson Quiz: Part 1 Multiply. Write each answer in simplest terms. 1. 1 8 · 5 6 2. 5 5 6 · 1 2 3.5 1 10 ·1 2 3 4. 3 16 · 4 2 3 7878 35 12 or 11 12 2 17 2 1212 or 8 5 48 Course 2 4-7 Multiplying Fractions and Mixed Numbers

22. Lesson Quiz: Part 2 Multiply. Write the answer in simplest terms. 5.A recipe for clam chowder calls for 2 1 4 pounds of butter. If you prepare one-half of the recipe, how much butter do you need? 1 1818 pounds Course 2 4-7 Multiplying Fractions and Mixed Numbers