1. Rational Numbers & Equations
Lesson 19
Rational Numbers & Equations
Estimating Products and Quotients

2. Warm-Up
Spot the Dog lost 1.85 pounds after his surgery. Two weeks later he had gained back 1.2 pounds. What number represents his total change in weight since the surgery?
Keyla ran miles each day for 5 days. What was the total distance she ran over these 5 days?
79.8 ÷ 3.8

3. Estimating Products and Quotients
Target:
Estimate products and quotients of
rational number operations.

4. Vocabulary
Compatible Numbers: Numbers that are easy to compute mentally.

7. Estimating Using Compatible Numbers
Substitute compatible numbers for one or more rational numbers in the expression.
Find the value of the expression using the compatible numbers.

8. Example 1a Estimate using compatible numbers. 51.2 ÷ 6.94
Round the divisor to the nearest
whole number ÷ 7
Change the dividend to the nearest
multiple of the new divisor ÷ 7
Divide ÷ 7 = 7
51.2 ÷ 6.94 ≈ 7

9. Example 1b Estimate using compatible numbers.
Choose a compatible number for the mixed number.
Multiply.

10. Exit Problems Estimate each product or quotient using compatible
numbers.
–31.82 ÷ (–3.19)
11.4 ÷ (–1.78)

11. Communication Prompt
How are compatible numbers helpful when dividing two
rational numbers?