1. 4-9 Multiplying Fractions by Whole Numbers Course 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day

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

3. 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 Course 1 4-9 Multiplying Fractions by Whole Numbers

4. Learn to multiply fractions by whole numbers. Course 1 4-9 Multiplying Fractions by Whole Numbers

5. Course 1 4-9 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 = 3 4 __ 1 4

6. Course 1 4-9 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

7. Course 1 4-9 Multiplying Fractions by Whole Numbers Additional Example 1A: Multiplying Fractions and Whole Numbers Multiply. Write the answer in simplest form. 1 9 __ 1 9 7 1 7 1 1 9 ______ 7 9 __ = = Write 7 as a fraction. Multiply numerators and denominators. A. 7

8. Course 1 4-9 Multiplying Fractions by Whole Numbers Additional Example 1B: Multiplying Fractions and Whole Numbers Multiply. Write the answer in simplest form. 1 8 __ 1 8 6 1 6 1 1 8 ______ 6 8 __ = = Write 6 as a fraction. Multiply numerators and denominators. 3 4 __ = Write your answer in simplest form. B. 6

9. Course 1 4-9 Multiplying Fractions by Whole Numbers Additional Example 1C: Multiplying Fractions and Whole Numbers Multiply. Write the answer in simplest form. 2 3 __ 2 3 8 1 8 2 1 3 ______ 16 3 ___ = = Write 8 as a fraction. Multiply numerators and denominators. 1 3 __ or 5 C. 8

10. Course 1 4-9 Multiplying Fractions by Whole Numbers Try This: Example 1A Multiply. Write the answer in simplest form. 1 5 __ 1 5 4 1 4 1 1 5 ______ 4 5 __ = = Write 4 as a fraction. Multiply numerators and denominators. A. 4

11. Course 1 4-9 Multiplying Fractions by Whole Numbers Try This: Example 1B Multiply. Write the answer in simplest form. 1 6 __ 1 6 3 1 3 1 1 6 ______ 3 6 __ = = Write 3 as a fraction. Multiply numerators and denominators. 1 2 __ = Write your answer in simplest form. B. 3

12. Course 1 4-9 Multiplying Fractions by Whole Numbers Try This: Example 1C Multiply. Write the answer in simplest form. 3 4 __ 3 4 9 1 9 3 1 4 ______ 27 4 ___ = = Write 9 as a fraction. Multiply numerators and denominators. 3 4 __ or 6 C. 9

13. Course 1 4-9 Multiplying Fractions by Whole Numbers Additional Example 2A: Evaluating Fraction Expression Evaluate 4x for the value of x. Write the 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. A. x =

14. Course 1 4-9 Multiplying Fractions by Whole Numbers Additional Example 2B: Evaluating Fraction Expression Evaluate 4x for the value of x. Write the 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 B. x =

15. Course 1 4-9 Multiplying Fractions by Whole Numbers Try This: Example 2A Evaluate 3x for the value of x. Write the answer in simplest form. 1 9 __ 3 1 1 9 3 9 = Write the expression. 3x3x 3 1 9 __ = 1 3 Multiply. Substitute for x. 1 9 __ Write your answer in simplest form. A. x =

16. Course 1 4-9 Multiplying Fractions by Whole Numbers Try This: Example 2B Evaluate 3x for the value of x. Write the answer in simplest form. 4 7 __ 3 1 4 7 12 7 ___ = Write the expression. 3x3x 3 4 7 __ = Multiply. Substitute for x. 4 7 __ Write your answer in simplest form. 5 7 __ 1 B. x =

17. Course 1 4-9 Multiplying Fractions by Whole Numbers Sometimes the denominator of an improper fraction will divide evenly into the numerator. When this happens, the improper fraction is equivalent to a whole number, not a mixed number. This makes sense if you remember that the fraction bar means “divided by”. 12 3 ___ = 4

18. Course 1 4-9 Multiplying Fractions by Whole Numbers Additional Example 3: 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.

19. Course 1 4-9 Multiplying Fractions by Whole Numbers Try This: Example 3 There are 18 saltwater fish in the aquarium. Of those fish, are blue. How many fish in the aquarium are blue? 2 3 __ 2 3 To find of 18, multiply. 18 1 ___ 2 3 __ 18 = 2 3 __ 36 3 ___ = = 12 There are 12 blue fish in the aquarium.

20. Course 1 4-9 Multiplying Fractions by Whole Numbers Lesson Quiz Multiply. Write each answer in simplest form. 1. 10 2. 6 Evaluate 6x for each value of x. Write your answer in simplest form. 3. x = 4. x = 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? 2 5 __ 1 10 __ 1 4 5 6 1 3 5 minutes 5 4 3 5 __, or 1 1 2 __ 3 2