1. 5-5 Multiplying Fractions by Whole Numbers Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

2. 5-5 Multiplying Fractions by Whole Numbers Warm Up Multiply. 30 96 144 66 120 1. 15  2 2. 12  8 3. 9  16 4. 6  11 5. 8  15

3. 5-5 Multiplying Fractions by Whole Numbers Problem of the Day The length of three dowels are 13 inches, 27 inches, and 19 inches. How can you use the three dowels to mark off a length of 5 inches? 13 + 19 – 27

4. 5-5 Multiplying Fractions by Whole Numbers Recall that multiplication by a whole number can be represented as repeated addition. For example, 4 5 = 5 + 5 + 5 + 5. You can multiply a whole number by a fraction using the same method. + + = 3 = 1414 __ 1414 1414 1414 3434 + + =

5. 5-5 Multiplying Fractions by Whole Numbers 3 1 __ 1 4 3 1 1 4 ______ 3 4 __ There is another way to multiply with fractions. Remember that a whole number can be written as an improper fraction with 1 in the denominator. So 3 =. 3 1 __ == Multiply numerators Multiply denominators Notice that when you multiply a proper fraction and a number greater than 1, the product is between the factors.

6. 5-5 Multiplying Fractions by Whole Numbers Additional Example 1A: Multiplying Fractions and Whole Numbers Multiply. Write each answer in simplest form. Method 1: Use repeated addition. 1 9 __ 1 9 7 9 = = 7 Write 7 as addition. Add the numerators. 1 9 __ 1 9 + + + 1 9 __ 1 9 1 9 1 9 1 9 1 9 7

7. 5-5 Multiplying Fractions by Whole Numbers Additional Example 1B: Multiplying Fractions and Whole Numbers Multiply. Write each answer in simplest form. Method 1: Use repeated addition. 1 8 __ 1 8 6 8 = = 3 4 __ = Write your answer in simplest form. 6 1 8 __ + + + + + 1 8 __ 1 8 1 8 1 8 1 8 Write 6 as addition. Add the numerators. 1 8 __ 6

8. 5-5 Multiplying Fractions by Whole Numbers Additional Example 1C: Multiplying Fractions and Whole Numbers Multiply. Write each answer in simplest form. Method 2: Multiply. 2 3 __ 2 3 8 1 16 3 ___ = 1 3 __ =5 8 Multiply. Write your answer in simplest form.

9. 5-5 Multiplying Fractions by Whole Numbers Check It Out: Example 1A Multiply. Write each answer in simplest form. 3 4 __ 27 4 __ or 9 3 4 __ 6

10. 5-5 Multiplying Fractions by Whole Numbers Check It Out: Additional Example 1B Multiply. Write each answer in simplest form. 2 5 __ 8 5 or 4 3 5 __ 1

11. 5-5 Multiplying Fractions by Whole Numbers Check It Out: Additional Example 1C Multiply. Write each answer in simplest form. 5 6 __ 25 6 __ or 5 1 6 __ 4

12. 5-5 Multiplying Fractions by Whole Numbers Additional Example 2A: Evaluating Fraction Expressions Evaluate 4x for each value of x. Write each answer in simplest form. 1 10 ___ 4 1 __ 1 10 ___ 4 10 ___ = Write the expression. 4x4x 4 1 10 ___ = 2 5 __ Multiply. Substitute for x. 1 10 ___ Write your answer in simplest form. x =x =

13. 5-5 Multiplying Fractions by Whole Numbers Additional Example 2B: Evaluating Fraction Expressions Evaluate 4x for each value of x. Write each answer in simplest form. 3 8 __ 4 1 3 8 12 8 ___ = Write the expression. 4x4x 4 3 8 __ = 3 2 Multiply. Substitute for x. 3 8 __ Write your answer in simplest form. 1 2 __,or 1 x =x =

14. 5-5 Multiplying Fractions by Whole Numbers Check It Out: Example 2A Evaluate 3x for each value of x. Write each answer in simplest form. 1 9 __ 1 9 3 = 1 3 __ x =x =

15. 5-5 Multiplying Fractions by Whole Numbers Check It Out: Example 2B Evaluate 3x for each value of x. Write each answer in simplest form. 2 5 __ 2 5 3 x =x = = 1 5 __ 6 5 or 1

16. 5-5 Multiplying Fractions by Whole Numbers Check It Out: Example 2C Evaluate 3x for each value of x. Write each answer in simplest form. 5 6 __ 5 6 3 x =x = = 1 2 __ 15 6 __ or 2

17. 5-5 Multiplying Fractions by Whole Numbers Sometimes the denominator of an improper fraction will divide into the numerator without a remainder. When this happens, the improper fraction is equivalent to a whole number, not a mixed number. 12 3 ___ = 4 means 12 ÷ 3. 12 3 Remember!

18. 5-5 Multiplying Fractions by Whole Numbers Additional Example 3: Music Application There are 25 students in the music club. Of those students, are also in the band. How many music club students are in the band? 3 5 __ 5 3 To find of 25, multiply. 25 1 ___ 3 5 __ 25 = 3 5 __ 75 5 ___ = = 15 There are 15 music club students in the band. Divide 75 by 5 and write your answer in simplest form.

19. 5-5 Multiplying Fractions by Whole Numbers Check It Out: Example 3A There are 50 people on the football team. Of those people, are also on the basketball team. How many people on the football team are also on the basketball team? 1 5 __ = 1 5 50 10

20. 5-5 Multiplying Fractions by Whole Numbers Check It Out: Example 3B There are 16 players on the baseball team. Of these players, are girls. How many girls play on the baseball team? 1 4 __ = 1 4 _ 16 4

21. 5-5 Multiplying Fractions by Whole Numbers Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

22. 5-5 Multiplying Fractions by Whole Numbers Lesson Quiz Multiply. Write each answer in simplest form. 1. 2. Evaluate 6x for each value of x. Write your answer in simplest form. 3. 4. 5. Alicia spent 15 minutes making a pizza. Of those minutes were spent rolling out the crust. How many minutes did Alicia spend rolling out the crust? 5 minutes 5 4 3 5 __, or 1 1 2 __ 3 2

23. 5-5 Multiplying Fractions by Whole Numbers 1. Multiply and identify the answer in simplest form. A. 10 C. 6 B. 8 D. 4 Lesson Quiz for Student Response Systems

24. 5-5 Multiplying Fractions by Whole Numbers 2. Multiply and identify the answer in simplest form. A. C. B. 1 D. Lesson Quiz for Student Response Systems

25. 5-5 Multiplying Fractions by Whole Numbers 3. Evaluate and identify the answer in the simplest form. A. C. B. D. Lesson Quiz for Student Response Systems

26. 5-5 Multiplying Fractions by Whole Numbers 4. Evaluate and identify the answer in the simplest form. A. 5 C. 3 B. 4 D. 1 Lesson Quiz for Student Response Systems

27. 5-5 Multiplying Fractions by Whole Numbers 5. Peter spent 40 minutes doing his math homework. Of those minutes, were spent referring to additional materials. How many minutes did he spend referring to additional materials? A. 10 min C. 20 min B. 15 min D. 25 min Lesson Quiz for Student Response Systems