1. Course 2 3-10 Multiplying Fractions and Mixed Numbers 3-10 Multiplying Fractions and Mixed Numbers Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

2. Course 2 3-10 Multiplying Fractions and Mixed Numbers Warm Up What is of each of the following? 1. 242. 16 3. 304. 28 128 15 1 2 14

3. Course 2 3-10 Multiplying Fractions and Mixed Numbers Problem of the Day At midnight Caitlin heard a forecaster say that it would be cloudy for exactly 72 hours and then would be sunny. Caitlin knew the forecaster was wrong. Explain. There are 24 hours in a day, so 72 hours equals 3 days. In 3 days it would be midnight again, not sunny.

4. Course 2 3-10 Multiplying Fractions and Mixed Numbers Learn to multiply fractions and mixed numbers.

5. Course 2 3-10 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 1939, the toll for a car crossing the bridge was of the toll in 2005. 2 15 To find the toll in 1939, you would need to multiply the toll in 2005 by a fraction. See Example 1 in your textbook.

6. Course 2 3-10 Multiplying Fractions and Mixed Numbers 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 that toll. 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 Divide 4 by 1 to 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

7. Course 2 3-10 Multiplying Fractions and Mixed Numbers 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? Check It Out: Example 1 3 4 4 · = 3 4 + 3 4 3 4 3 4 ++ = 12 4 = 3 1 Simplify. = $3.00 Divide 3 by 1 to 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

8. Course 2 3-10 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.

9. Course 2 3-10 Multiplying Fractions and Mixed Numbers Multiply. Write the answer in simplest form. Additional Example 2A: Multiplying Fractions –12 · 3 4 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!

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

11. Course 2 3-10 Multiplying Fractions and Mixed Numbers Multiply. Write the answer in simplest form. Additional Example 2C: Multiplying Fractions · 4 The signs are different, so the answer will be negative. Multiply numerators. Multiply denominators. 1 3 5 – · 3 5 1 4 – = 3 5 · 1 4 · – = 3 20 –

12. Course 2 3-10 Multiplying Fractions and Mixed Numbers Multiply. Write the answer in simplest form. Check It Out: Example 2A –16 · 1 4 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.

13. Course 2 3-10 Multiplying Fractions and Mixed Numbers Multiply. Write the answer in simplest form. Check It Out: Example 2B · 9 = Simplify. Multiply numerators. Multiply denominators. 6 1 6 1 1 = 1 9 6 9 · 1 6 1 6 · 6 9 ·

14. Course 2 3-10 Multiplying Fractions and Mixed Numbers Multiply. Write the answer in simplest form. Check It Out: Example 2C · 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 –

15. Course 2 3-10 Multiplying Fractions and Mixed Numbers 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. 2 2 5 · 1 2 3 = 2 5 · 5 3 = 2 5 · 5 3 1 1 5 · 1 2 3 = 2 3

16. Course 2 3-10 Multiplying Fractions and Mixed Numbers Multiply. Write the answer in simplest form. Additional Example 3B: Multiplying Mixed Numbers Write the mixed numbers as improper fractions. Simplify. 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

17. Course 2 3-10 Multiplying Fractions and Mixed Numbers Multiply. Write the answer in simplest form. Additional Example 3C: Multiplying Mixed Numbers Multiply numerators. Multiply denominators. 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

18. Course 2 3-10 Multiplying Fractions and Mixed Numbers Multiply. Write the answer in simplest form. Check It Out: Example 3A Write the mixed number as an improper fraction. Simplify. Multiply numerators. Multiply denominators. 3 3 5 · 2 1 3 = 3 5 · 7 3 = 3 5 · 7 3 1 1 5 · 2 1 3 = or 1 7 5 2 5

19. Course 2 3-10 Multiplying Fractions and Mixed Numbers Multiply. Write the answer in simplest form. Check It Out: Example 3B Write the mixed numbers as improper fractions. Simplify. 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

20. Course 2 3-10 Multiplying Fractions and Mixed Numbers Multiply. Write the answer in simplest form. Multiply numerators. Multiply denominators. 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 Check It Out: Example 3C

21. Course 2 3-10 Multiplying Fractions and Mixed Numbers Lesson Quiz: Part I 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

22. Course 2 3-10 Multiplying Fractions and Mixed Numbers Lesson Quiz: Part II 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