Part 1: Learn and Practice

Goal: Multiply rational numbers and write answers in simplest form.

Vocabulary and Help

Rational number: A number that can be written as a fraction, including integers, fractions, mixed numbers, and terminating decimals.

Absolute value: The distance from zero. It is always nonnegative.

Product: The answer to a multiplication problem.

Sign rules:

+ × + = +     − × − = +     + × − = −     − × + = −

Memory tip: Same signs make a positive product. Different signs make a negative product.

Worked Examples

Example 1: (−3)(4)

1. The signs are different, so the product is negative.

2. Multiply the absolute values: 3 × 4 = 12.

3. Answer: −12

Example 2: (2/3)(−6)

1. The signs are different, so the product is negative.

2. Multiply: (2 × 6)/(3 × 1) = 12/3 = 4.

3. Answer: −4

Try It

Directions: Decide the sign first. Then multiply. Show your steps.

Part 2: Explain and Apply

Directions: Read each problem carefully. Use the prompts to organize your work. Write a complete answer when needed.

Sign: __________    Numerator product: __________    Denominator product: __________

Simplified product: ____________________________________

Write a multiplication expression for the temperature change before finding the final temperature.

Helpful plan: Convert the mixed number, multiply by 2/3, then divide by 4.

Part 3: Challenge and Answer Key

First distribute. Then substitute the value of x.

Answer Key

1. −10

2. 18

3. −2

4. −2/3

5. −6

6. 1

7. −0.15

8. −2/3

9. Maya forgot that a negative times a negative is positive. The correct product is 6.

10. The signs are different, so the answer is negative. (2 × −9)/(3 × 4) = −18/12 = −3/2, or −1 1/2.

11. −6 + (−1.5 × 3) + 4.5 = −6 − 4.5 + 4.5 = −6°F.

12. 1 1/2 × 2/3 ÷ 4 = 3/2 × 2/3 × 1/4 = 1/4 cup.

13. (−2/3)(6x) + (−2/3)(−9) = −4x + 6. When x = −3: −4(−3) + 6 = 18.