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Warm Up

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

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Warm Up

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  1. Preview Warm Up California Standards Lesson Presentation

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

  3. California Standards NS2.1 Solve problems involving addition, subtraction, multiplication, and division of positive fractions and explain why a particular operation was used for a given situation. Also covered: NS2.4, NS2.2

  4. Recall that multiplication can be written as repeated addition. For example, 3  5 = 5 + 5 + 5 = 15. You can use repeated addition to multiply a whole number by a fraction.

  5. 2 Think: How much is of 6? Use multiplication to find a fraction of a number. 3 2 2 2 2 2 2 2 6  + + + = + + 3 3 3 3 3 3 3 12 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 = 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 = 1 Additional Example 1: Transportation Application In 2001, the car toll on the George Washington Bridge was $6.00. In 1995 the toll was 2 of that toll. 3 What was the toll in 1995? + + + + + 1 1 1 1 = $4.00 The George Washington Bridge toll for a car was $4.00 in 1995.

  6. 3 3 3 3 3 4  + + = + + + + 4 4 4 4 4 12 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 = 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 1 1 1 = 1 Check It Out! Example 1 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 = $3.00 The fee to park in the parking garage was $3.00 in 2000.

  7. Additional Example 2A: Multiplying Fractions Multiply. Write the answer in simplest form. 3 12  4 3 12 3  = Write 12 as a fraction. 12  4 1 4 3 Divide a numerator and denominator by their GCD, 4. 12 3 = 1 4 1 9 Multiply numerators. Multiply denominators. = = 9 1 Remember! Use the GCD of a numerator and denominator to simplify before multiplying.

  8. 3 1  5 4 1 3   4 5 3 = 1 3 20  5 4 Additional Example 2B: Multiplying Fractions Multiply. Write the answer in simplest form. Multiply numerators. Multiply denominators. =

  9. 3 1  3 1  3 8 8 3  Additional Example 2C: Multiplying Fractions Multiply. Write the answer in simplest form. 1 3  3 8 1 Divide a numerator and denominator by their GCD, 3. = 1 1 Multiply numerators. Multiply denominators. = 8

  10. Check It Out! Example 2A Multiply. Write the answer in simplest form. 1 16  4 1 16 1 = Write 16 as a fraction.  16  4 1 4 4 Divide a numerator and denominator by their GCD, 4. 16  1 = 1  4 1 4 Multiply numerators. Multiply denominators. = = 4 1

  11. 1 3 1 3  =  7 8 8 7  3 = 56 Check It Out! Example 2B Multiply. Write the answer in simplest form. 3 1  7 8 Multiply numerators. Multiply denominators.

  12. 6 1  6 1  6 9  9 6 Check It Out! Example 2C Multiply. Write the answer in simplest form. 1 6  6 9 1 Divide a numerator and denominator by their GCD, 6. = 1 1 Multiply numerators. Multiply denominators. = 9

  13. Additional Example 3A: Multiplying Mixed Numbers Multiply. Write the answer in simplest form. 2 2 1  5 3 2 2 5 Writethe mixed number as an improper fraction. 2 1  =  5 3 3 5 1 Divide a numerator and denominator by their GCD, 5. 2 5 =  5 3 1 2 Multiply numerators. Multiply denominators. = 3

  14. Additional Example 3B: Multiplying Mixed Numbers Multiply. Write the answer in simplest form. 1 1 4  2 7 5 1 1 21 15 4 = Write mixed numbers as improper fractions. 2   5 7 7 5 3 3 21 15 Divide numerators and denominators by their GCDs, 5 and 7.  = 5 7 1 1 Multiply numerators. Multiply denominators. 9 or 9 = 1

  15. 88 1 = or 29 3 3 Additional Example 3C: Multiplying Mixed Numbers Multiply. Write the answer in simplest form. 2 2  4 6 3 5 2 2 20 22 Write mixed numbers as improper fractions.  4 6  = 3 5 3 5 4 Divide a numerator and denominator by their GCD, 5. 20 22 =  3 5 1 Multiply numerators. Multiply denominators.

  16. Check It Out! Example 3A Multiply. Write the answer in simplest form. 3 1 2  5 3 1 3 7 Writethe mixed number as an improper fraction. 3  2 =  5 3 3 5 1 3 7 =  Divide a numerator and denominator by the GCD, 3. 5 3 1 7 2 Multiply numerators. Multiply denominators. = or 1 5 5

  17. 4 24 or 4 = 5 5 Check It Out! Example 3B Multiply. Write the answer in simplest form. 3 1 3  1 3 5 3 1 18 4  1 3 = Write mixed numbers as improper fractions.  5 3 3 5 6 18 4 Divide a numerator and denominator by their GCD, 3.  = 5 3 1 Multiply numerators. Multiply denominators.

  18. 38 2 = or 4 9 9 Check It Out! Example 3C Multiply. Write the answer in simplest form. 1 1 3 1  6 3 1 1 19 4 Write mixed numbers as improper fractions. 1 3 =   6 3 6 3 2 Divide a numerator and denominator by their GCD, 2. 19 4 =  6 3 3 Multiply numerators. Multiply denominators.

  19. 5 48 35 12 11 12 or 2 1 8 1 pounds 1 2 17 2 or 8 Lesson Quiz Multiply. Write each answer in simplest terms. 1. 2. 7 8 3. 4. 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?

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