Learn to multiply mixed numbers .

1. Learn to multiply mixed numbers.

2. Remember! To write a mixed number as an improper fraction, start with the whole number, multiply by the denominator, and add the numerator. Use the same denominator. 1 1 • 5 + 1 6 __ _________ __ 5 5 5 = = 1

3. 1 1 __ __ 4 3 1 1 4 1 4 __ __ __ __ __ Write 1 as an improper fraction. 1 = • 3 3 3 4 3 1 • 4 _____ 4 • 3 4 __ 12 1 __ 3 Additional Example 1A: Multiplying Fractions and Mixed Numbers Multiply. Write each answer in simplest form. • 1 Multiply numerators. Multiply denominators. Write the answer in simplest form.

4. 1 4 __ __ 2 5 1 1 7 7 4 __ __ __ __ __ Write 3 as an improper fraction. 3 = • 2 2 2 2 5 7 • 4 _____ 2 • 5 28 __ 10 14 4 __ __ 5 5 Additional Example 1B: Multiplying Fractions and Mixed Numbers Multiply. Write each answer in simplest form. 3• Multiply numerators. Multiply denominators. Write the answer in simplest form. You can write the answer as a mixed number. = 2

5. 12 3 __ __ 13 8 3 3 19 12 19 __ __ __ __ __ Write 2 as an improper fraction. 2 = • 8 8 8 13 8 12 19 __ __ • 13 8 3 • 19 ______ 13 • 2 57 5 __ __ 26 26 Additional Example 1C: Multiplying Fractions and Mixed Numbers Multiply. Write each answer in simplest form. • 2 3 Use the GCF to simplify before multiplying. 2 You can write the answer as a mixed number. = 2

6. 1 1 __ __ 9 2 1 1 3 1 3 __ __ __ __ __ Write 1 as an improper fraction. 1 = • 2 2 2 9 2 1 • 3 _____ 9 • 2 3 __ 18 1 __ 6 Check It Out: Example 1A Multiply. Write each answer in simplest form. •1 Multiply numerators. Multiply denominators. Write the answer in simplest form.

7. 2 5 __ __ 3 6 2 2 8 8 5 __ __ __ __ __ Write 2 as an improper fraction. 2 = • 3 3 3 3 6 8 • 5 _____ 3 • 6 40 __ 18 20 2 __ __ 9 9 Check It Out: Example 1B Multiply. Write each answer in simplest form. 2• Multiply numerators. Multiply denominators. Write the answer in simplest form. You can write the answer as a mixed number. = 2

8. 14 2 __ __ 15 7 2 2 23 14 23 __ __ __ __ __ Write 3 as an improper fraction. 3 = • 7 7 7 15 7 14 23 __ __ • 15 7 2 • 23 ______ 15 • 1 46 1 __ __ 15 15 Check It Out: Example 1C Multiply. Write each answer in simplest form. • 3 2 Use the GCF to simplify before multiplying. 1 You can write the answer as a mixed number. = 3

9. Remember! You can estimate the product to see whether your answer is reasonable.

10. 1 2 __ __ 7 3 Write the mixed numbers as improper fractions. 1 = 2 = 5 15 __ __ • 1 15 2 5 __ 3 7 __ __ __ 7 7 3 3 5 • 15 ______ 3 • 7 75 __ 21 12 __ 21 4 __ 7 Additional Example 2A: Multiplying Mixed Numbers Find each product. Write the answer in simplest form. 1 • 2 Multiply numerators. Multiply denominators. You can write the improper fraction as a mixed number. 3 Simplify. 3

11. 2 3 __ __ 5 8 Write the mixed numbers as improper fractions. 1 = 2 = 11 12 __ __ 2 12 3 11 • __ __ __ __ 8 5 5 5 8 8 11 12 __ __ • 8 5 11 • 3 ______ 2 • 5 33 __ 10 3 __ 10 Additional Example 2B: Multiplying Mixed Numbers Find each product. Write the answer in simplest form. 1 • 2 3 Use the GCF to simply before multiplying. 2 Multiply numerators. Multiply denominators. Simplify. 3

12. 1 3 __ __ 6 4 Write the mixed numbers as improper fractions. 1 = 2 = 7 13 __ __ • 1 13 3 7 __ 4 6 __ __ __ 6 6 4 4 7 • 13 ______ 4 • 6 91 __ 24 19 __ 24 Check It Out: Example 2A Find each product. Write the answer in simplest form. 1 • 2 Multiply numerators. Multiply denominators. You can write the improper fraction as a mixed number. 3

13. 3 2 __ __ 5 9 Write the mixed numbers as improper fractions. 1 = . 3 = 11 18 __ __ 3 18 2 11 • __ __ __ __ 9 5 5 5 9 9 11 18 __ __ • 9 5 11 • 2 ______ 1 • 5 22 __ 5 2 __ 5 Check It Out: Example 2B Find each product. Write the answer in simplest form. 1 • 3 2 Use the GCF to simply before multiplying. 1 Multiply numerators. Multiply denominators. Simplify. 4