1. Rational Numbers & Equations
Lesson 16
Rational Numbers & Equations
Estimating Sums and Differences

2. Warm-Up
Find the value of each expression.
10 – 3.58

3. Estimating Sums and Differences
Target:
Estimate sums and differences of rational numbers.

4. Vocabulary
Rational Number: A number that can be written as a fraction of two integers.

7. Estimating Sums and Differences
Decimals
With numbers less than one unit from zero, round to 0, ±0.5 or ±1.
With numbers more than one unit from zero, round to the nearest integer.
Fractions
With fractions less than one unit from zero, round to 0, ± ½ or ±1.
With mixed numbers that are more than one unit from zero, round to the nearest integer.

8. Example 1a – 4.23 → – 4 2.8 → 3 Estimate the value of – 4.23 + 2.8.
Both numbers are more than one and should be rounded to nearest integer.
– 4.23 → – 4
2.8 → 3
– = –1
– ≈ –1

9. Example 1b
Estimate the value of 0.94 – (–0.43).
Both numbers are less than one unit away from zero and should be rounded to the nearest 0.5.
0.94 → 1
– 0.43 → – 0.5
1 – (–0.5) = = 1.5
0.94 – (–0.43) ≈ 1.5

10. Example 2a Estimate the value of .
Each fraction is less than 1 unit from zero so round to the
nearest .

11. Example 2b Estimate the value of .
Each fraction is more than 1 unit from zero so round to the nearest integer.

12. Exit Problems
Estimate the value of each expression.
0.13 – 0.925
Matt bought pounds of apples, pounds of grapes and pounds of potatoes. What was the approximate weight of Matt’s purchases?

13. Communication Prompt
Describe a time when you used estimating in a situation outside of math class.