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

Warm-Up Find the value of each expression. 4.7 + 5.08 10 – 3.58

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

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

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.

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 – 4 + 3 = –1 – 4.23 + 2.8 ≈ –1

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 + 0.5 = 1.5 0.94 – (–0.43) ≈ 1.5

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

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

Exit Problems Estimate the value of each expression. 3.21 + 6.3 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?

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