1. Holt CA Course 1 4-4 Multiplying Fractions and Mixed Numbers 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 California Standards

2. Holt CA Course 1 4-4 Multiplying Fractions and Mixed Numbers 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.

3. Holt CA Course 1 4-4 Multiplying Fractions and Mixed Numbers Example 1: Transportation Application In 2001, the car toll on the George Washington Bridge was $6.00. In 1995 the toll was 2 3 of that toll. What was the toll in 1995? 2 3 6  = 2 3 + 2 3 2 3 2 3 2 3 2 3 + ++ + + = 12 3 = 4 1 = $4.00 The George Washington Bridge toll for a car was $4.00 in 1995. +++ + 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 11 1 1 Think: How much is of 6? Use multiplication to find a fraction of a number. 2 3 Write the fraction as a decimal. Simplify

4. Holt CA Course 1 4-4 Multiplying Fractions and Mixed Numbers

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

6. Holt CA Course 1 4-4 Multiplying Fractions and Mixed Numbers Multiply. Write the answer in simplest form. Additional Example 2B: Multiplying Fractions Multiply numerators. Multiply denominators.  4 1 3 5  3 5 1 4 = 3 5  1 4  = 3 20

7. Holt CA Course 1 4-4 Multiplying Fractions and Mixed Numbers Multiply. Write the answer in simplest form. Additional Example 2C: Multiplying Fractions  8 = Divide a numerator and denominator by their GCD, 3. Multiply numerators. Multiply denominators. 3 1 3 1 1 = 1 8 3 8  1 3 1 3  3 8 

8. Holt CA Course 1 4-4 Multiplying Fractions and Mixed Numbers Multiply. Write the answer in simplest form. Check It Out! Example 2A 16  1 4 1 4 = 16 1  1 4 Write 16 as a fraction. = 16  1 1  4 4 1 Divide a numerator and denominator by their GCD, 4. 4 1 = = 4 Multiply numerators. Multiply denominators.

9. Holt CA Course 1 4-4 Multiplying Fractions and Mixed Numbers Multiply. Write the answer in simplest form. Check It Out! Example 2C  9 = Divide a numerator and denominator by their GCD, 6. Multiply numerators. Multiply denominators. 61 6 1 1 = 1 9 6 9  1 6 1 6  6 9 

10. Holt CA Course 1 4-4 Multiplying Fractions and Mixed Numbers Multiply. Write the answer in simplest form. Example 3A: Multiplying Mixed Numbers Write the mixed number as an improper fraction. Divide a numerator and denominator by their GCD, 5. Multiply numerators. Multiply denominators. 2 2 5  1 2 3 = 2 5  5 3 = 2 5  5 3 1 1 5  1 2 3 = 2 3

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

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

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

14. Holt CA Course 1 4-4 Multiplying Fractions and Mixed Numbers 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? Check It Out! Example 1 3 4 4  = 3 4 + 3 4 3 4 3 4 ++ = 12 4 = 3 1 = $3.00 The fee to park in the parking garage was $3.00 in 2000. 3 4 + 1 4 1 4 1 4 1 4 1 4 1 4 + + 1 4 1 4 1 4 1 4 1 4 1 4 1 4 1 4 1 4 1 4 1 4 1 4 1 4 1 4 1 4 1 4 1 4 1 4 111

15. Holt CA Course 1 4-4 Multiplying Fractions and Mixed Numbers Multiply. Write the answer in simplest form. Check It Out! Example 2  8 Multiply numerators. Multiply denominators. 1 3 7 1 8  3 7 = 3 7  1 8  = 3 56

16. Holt CA Course 1 4-4 Multiplying Fractions and Mixed Numbers Multiply. Write the answer in simplest form. Check It Out! Example 3 Write the mixed number as an improper fraction. Divide a numerator and denominator by the GCD, 3. Multiply numerators. Multiply denominators. 3 3 5  2 1 3 = 3 5  7 3 = 3 5  7 3 1 1 5  2 1 3 = or 1 7 5 2 5

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