1. 5-6 Multiplying Fractions Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

2. 5-6 Multiplying Fractions Warm Up 1. What is of 12? 2. What is of 100? 3. What is of 120? 4. What is of 100? 5. What is of 480? 6 50 60 1 2 __ 1 2 1 2 1 4 1 4 25 120

3. 5-6 Multiplying Fractions Problem of the Day Your favorite uncle left one-fifth of his estate to each of his three children and the rest to his favorite charity. If his estate was worth $105,000, how much was given to charity? $42,000

4. 5-6 Multiplying Fractions MA.6.A.1.2 Multiply and divide fractions…efficiently. Also MA.6.A.1.3 Sunshine State Standards

5. 5-6 Multiplying Fractions On average, people spend of their lives asleep. About of the time they sleep, they dream. What fraction of a lifetime does a person typically spend dreaming? 1 3 __ 1 4 1 4 1 3 = 1 12 __ 1 3 1 4 1 4 1 3 One way to find of is to make a model. Find of. Notice that there is 1 section where the shading overlaps, and the product of the numerators is 1. Notice that there are 12 sections in the model, and the product of the denominators is 12. You can use these observations to write a rule for multiplying fractions.

6. 5-6 Multiplying Fractions 1 4 __ 1 3 1 1 4 3 _____ 1 12 __ = = Multiply the numerators. Multiply the denominators. A person typically spends of his or her lifetime dreaming. 1 12 __ The answer is in simplest form. Helpful Hint Notice that when you multiply two proper fractions, the product is less than either factor.

7. 5-6 Multiplying Fractions Additional Example 1A: Multiplying Fractions Multiply. Write each answer in simplest form. 1 4 __ 2 5 _____ = = Multiply numerators. Multiply denominators. 2 20 __ 1 2 4 5 1 4 __ 2 5 __ The GCF of 2 and 20 is 2. The answer is in simplest form. = 1 10 __

8. 5-6 Multiplying Fractions Additional Example 1B: Multiplying Fractions Multiply. Write each answer in simplest form. 5 7 __ 4 15 __ _____ = = Use the GCF to simplify the fractions before multiplying. The greatest common factor of 5 and 15 is 5. 4 21 __ 1 4 7 3 5 7 __ 4 15 __ Multiply numerators. Multiply denominators. The answer is in simplest form. 1 7 __ 4 3 __ 1 3 =

9. 5-6 Multiplying Fractions Additional Example 1C: Multiplying Fractions Multiply. Write each answer in simplest form. 4 9 __ 6 10 __ ______ = = Multiply numerators. Multiply denominators. 24 90 __ 4 6 9 10 4 9 __ 6 10 __ The GCF of 24 and 90 is 6. The answer is in simplest form. = 4 15 __

10. 5-6 Multiplying Fractions Check It Out: Example 1A Multiply. Write each answer in simplest form. 15 63 __ ____ 5 21 __ 3 5 7 9 3 7 __ 5 9

11. 5-6 Multiplying Fractions Check It Out: Example 1B Multiply. Write each answer in simplest form. 6 14 __ ____ 3 7 __ 1 6 2 7 1 2 __ 6 7

12. 5-6 Multiplying Fractions Check It Out: Example 1C 5 8 __ _____ 1 4 1 1 4 __ 1 1 2 5 5 8 2 5 Multiply. Write each answer in simplest form. 1 4

13. 5-6 Multiplying Fractions Additional Example 2A: Evaluating Fraction Expressions 2 5 __ 1 3 b 2 5 2 5 1 3 _____ 1 2 3 5 2 15 __ Substitute for b. 1 3 __ Multiply. The answer is in simplest form. b = Evaluate the expression b for each value of b. Write each answer in simplest form.

14. 5-6 Multiplying Fractions You can look for a common factor in a numerator and a denominator to determine whether you can simplify before multiplying. Helpful Hint

15. 5-6 Multiplying Fractions Additional Example 2B: Evaluating Fraction Expressions b = 3 8 __ b 2 5 2 5 3 8 _____ 3 1 4 5 3 20 __ Substitute for b. 3 8 __ Use the GCF to simplify. The answer is in simplest form. 1 4 2 5 __ 3 8 Multiply.

16. 5-6 Multiplying Fractions Additional Example 2C: Evaluating Fraction Expressions b = 5 7 __ b 2 5 2 5 5 7 _____ 5 2 7 5 10 35 __ Substitute for b. 5 7 __ Multiply. The GCF of 10 and 35 is 5. The answer is in simplest form. 2 7 __

17. 5-6 Multiplying Fractions Check It Out: Example 2A Evaluate the expression c for each value of c. Write each answer in simplest form. c = 1 4 __ 1 7 1 7 4 1 28 __ _____

18. 5-6 Multiplying Fractions Check It Out: Example 2B Evaluate the expression c for each value of c. Write each answer in simplest form. c = 1 4 __ 4 5 4 20 __ 1 4 __ 4 5 1 5

19. 5-6 Multiplying Fractions Check It Out: Example 2C Evaluate the expression c for each value of c. Write each answer in simplest form. c = 1 4 __ 2 3 2 12 __ 1 4 __ 2 3 1 6

20. 5-6 Multiplying Fractions Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

21. 5-6 Multiplying Fractions Lesson Quiz Multiply. Write each answer in simplest form. 1. 2. Evaluate the expression x for each value of x. Write the answer in simplest form. 3. x =4. x = 5. At a particular college of the students take a math class. Of these students, take basic algebra. What fraction of all students take basic algebra? 3 5 __ 1 4 5 7 __ 3 10 __ 1 8 __ 4 5 1 8 2 5 1 4 3 20 __ 3 14 __ 1 10 __ 1 64 __ 1 10 __

22. 5-6 Multiplying Fractions 1. Multiply and identify the answer in simplest form. A. C. B. D. Lesson Quiz for Student Response Systems

23. 5-6 Multiplying Fractions 2. Multiply and identify the answer in simplest form. A. C. B. D. Lesson Quiz for Student Response Systems

24. 5-6 Multiplying Fractions 3. Evaluate the expression and identify the answer in simplest form. A. C. B. D. Lesson Quiz for Student Response Systems

25. 5-6 Multiplying Fractions 4. Evaluate the expression and identify the answer in simplest form. A. C. 1 B. D. 5 Lesson Quiz for Student Response Systems

26. 5-6 Multiplying Fractions 5. At a particular school of the students take chemistry class. Of these students, take organic chemistry. What fraction of all students take organic chemistry? A. C. B. D. 1 Lesson Quiz for Student Response Systems