Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

What is of each of the following? 1. 24 2. 16 3. 30 4. 28 12 8 Warm Up What is of each of the following? 1. 24 2. 16 3. 30 4. 28 1 2 12 8 15 14

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.

Learn to multiply 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 1A: 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 = – Simplify. 1 · 4 1 9 Multiply numerators. Multiply denominators. = – = –9 1 The product of two positive proper fractions is less than either fraction. Helpful Hint

Additional Example 1B: Multiplying Fractions Multiply. Write the answer in simplest form. 1 3 · 3 8 1 3 8 · 1 1 3 · 8 = Simplify. 1 1 Multiply numerators. Multiply denominators. = 8

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

Check It Out: Example 1A 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 = – Simplify. 1 · 4 1 4 Multiply numerators. Multiply denominators. = – –4 = 1

Check It Out: Example 1B Multiply. Write the answer in simplest form. 1 6 · 6 9 1 6 9 · 1 1 6 · 9 = Simplify. 1 1 Multiply numerators. Multiply denominators. = 9

Multiply. Write the answer in simplest form. Check It Out: Example 1C Multiply. Write the answer in simplest form. 3 1 – · 7 8 3 7 · 1 8 – The signs are different, so the answer will be negative. 1 8 · 3 7 – = = 3 56 – Multiply numerators. Multiply denominators.

Additional Example 2A: Multiplying Mixed Numbers Multiply. Write the answer in simplest form. 2 2 · 1 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 2B: Multiplying Mixed Numbers Multiply. Write the answer in simplest form. 1 1 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 2C: Multiplying Mixed Numbers Multiply. Write the answer in simplest form. 2 2 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.

Check It Out: Example 2A 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 = · Simplify. 5 3 1 7 2 Multiply numerators. Multiply denominators. = or 1 5 5

Multiply. Write the answer in simplest form. Check It Out: Example 2B Multiply. Write the answer in simplest form. 3 1 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.

Multiply. Write the answer in simplest form. Check It Out: Example 2C Multiply. Write the answer in simplest form. 1 1 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.

Additional Example 3: Transportation Application In 2001, the car toll on the George Washington Bridge was $6.00. In 1995 the toll was 2 of that 3 toll. 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 Divide 4 by 1 to write the fraction as a decimal. The George Washington Bridge toll for a car was $4.00 in 1995.

In 2002, the fee to park in a parking garage was Check It Out: Example 3 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 Divide 3 by 1 to write the fraction as a decimal. The fee to park in the parking garage was $3.00 in 2000.

Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

Lesson Quiz: Part I Multiply. Write each answer in simplest form. 1 5 5 48 1. · 8 6 5 1 2 2. 5 · 35 12 or 11 2 6 1 2 17 2 1 or 8 3. 5 · 1 10 3 3 2 7 8 4. · 4 16 3

Multiply. Write the answer in simplest form. Lesson Quiz: Part II Multiply. Write the answer in simplest form. 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

Lesson Quiz for Student Response Systems 1. Multiply. Write your answer in simplest form. · A. C. B. D. 1 9 4 5 4 45 1 9 1 6 1 10

Lesson Quiz for Student Response Systems 2. Multiply. Write your answer in simplest form. 4 · A. or 5 C. or 1 B. or 3 D. 4 5 1 3 17 3 2 3 8 5 3 5 16 5 1 5 4 5

Lesson Quiz for Student Response Systems 3. Multiply. Write your answer in simplest form. 6 · 1 A. or 8 C. or 5 B. or 6 D. or 4 1 4 2 5 35 4 3 4 26 5 1 5 27 4 3 4 24 4 4 5

Lesson Quiz for Student Response Systems 4. Multiply. Write your answer in simplest form. · 3 A. C. or 1 B. D. 1 5 18 4 5 8 9 19 18 1 18 17 18 1 9

Lesson Quiz for Student Response Systems 3 4 5. To prepare one bowl of salad, 3 pounds of vegetables are required. How many pounds of vegetables are required to prepare one-third bowl of salad? A. 1 lb C. 1 lb B. 1 lb D. 1 lb 1 4 3 4 1 2 3 5