The document provides examples for multiplying rational numbers including fractions, decimals, and integers. It gives step-by-step workings for multiplying fractions and decimals. Examples are provided for multiplying fractions, integers and fractions, and decimals. Applications involving fractions of quantities over multiple days are presented.

1. Warm Up California Standards Lesson Presentation Preview

2. Warm Up Write each number as an improper fraction. 1. 1 3 2 2. 7 8 1 3. 2 5 3 4. 2 3 6 5. 3 8 5 7 3 15 8 17 5 20 3 43 8

3. NS1.2 Add, subtract, multiply , and divide rational numbers (integers, fractions, and terminating decimals) and take positive rational numbers to whole-number powers. California Standards

5. Multiply. Write the answer in simplest form. 6 7 Simplify. 1 8 Multiply numerators. Multiply denominators. Look for common factors: 2. Additional Example 1A: Multiplying Fractions 1(6) 8(7) = 3 28 = = 1(6) 8(7) 3 4

6. Simplify. Multiply numerators. Multiply denominators. Look for common factors: 2, 3. 1 2 2 3 – Additional Example 1B: Multiplying Fractions Multiply. Write the answer in simplest form. 4 – 2(9) 3(2) = = – 2(9) 3(2) 3 1 – 3 = 1 – 1 Write 4 as an improper fraction. 12 1 2 2 3 – 4 9 2 2 3 – =

7. Multiply. Write the answer in simplest form. 5 8 Simplify. 3 5 Multiply numerators. Multiply denominators. Look for common factors: 5. Check It Out! Example 1A 3(5) 5(8) = 3 8 = = 3(5) 5(8) 1 1

8. Simplify. Multiply numerators. Multiply denominators. Look for common factors: 4, 7. 4 7 7 8 – Multiply. Write the answer in simplest form. Check It Out! Example 1B – 7(4) 8(7) = = – 7(4) 8(7) 1 2 1 – 1 1 2 = –

9. To multiply a fraction by an integer, first write the integer as a fraction with a denominator of 1. Then multiply as you would with two fractions.

10. Write the integer 7 as a fraction. 1 20 Additional Example 2: Application = (7) = Multiply numerators and denominators. = Joy completes of her painting each day. How much of her painting does she complete in a 7 day week? 1 20 1 20 71 1 • 7 20 • 1 7 20 Joy completes of her painting in a 7-day week. 7 20

11. Mark runs mile each day. What is the total distance Mark runs in 5 days? Write the integer 5 as a fraction. 1 7 Check It Out! Example 2 = (5) = Multiply numerators and denominators. = 1 7 1 7 51 1 • 5 I 7 • 1 5 7 Mark runs mile in 5 days. 5 7

12. To multiply decimals, first multiply as you would with integers. The number of decimal places in the product is equal to the sum of the number of decimal places in the factors.

13. Multiply. 0 decimal places 2 B. (–0.4)(–3.75) – 3.75   0.4 Additional Example 3: Multiplying Decimals A. 2(–0.51) 1.500  – 0.51 2 decimal places – 1.02 0 + 2 = 2 decimal places. 2 decimal places 1 decimal place 2 + 1 = 3 decimal places or 1.5

14. Multiply. 1 decimal place 3.1 B. (–0.4)(–2.53) – 0.4  – 2.53 Check It Out! Example 3 A. 3.1(0.28) 1.012  0.28 2 decimal places 0.868 1 + 2 = 3 decimal places 1 decimal place 2 decimal places 1 + 2 = 3 decimal places

15. 4. Evaluate 2 ( x ) for x = . 1. Lesson Quiz Multiply. – 1.034 2. 5 8 2 3 – 1 7 9 3. –0.47(2.2) 1 2 2 Edgar runs mile each day. What is the total distance that Edgar runs in a 7-day week? 5. 45 – 5 12 1 2 7 8 9 6 miles 2 9