Fractions and Decimals Lesson 8 Fractions and Decimals Estimating Sums and Differences

Warm-up Round 542 to the nearest ten. Round 1,389 to the nearest hundred. Find the value of 34 + 28. Find the value of 23 – 15.

Estimating Sums and Differences Target: Estimate sums and differences of expressions with fractions and mixed numbers.

Estimating Sums or Differences Using Fractions Round to 0, ½ or 1, whichever is closest. If the numerator is very small compared to the denominator, estimate as 0. If the numerator is about half of the denominator, estimate as ½. If the numerator is nearly as big as the denominator, estimate as 1. Add or subtract.

Example 1 Hayden had about of a box of pencils. Trevor had about of a box. Kelsey had about of a box and Asha had about of a box. About how many boxes of pencils do they have altogether? Add the estimated amounts. They have about 2 boxes of pencils altogether. Hayden Trevor Kelsey Asha The numerator is very small compared to the denominator. The numerators are about half of their denominators. The numerator is nearly as big as the denominator.

Example 2 Asha Found that instead of of a box of pencils, she had of a box. About how much less does she have than she originally thought? Write the problem. Round to 0, or 1. Subtract. Asha has about half a box less than she thought she had.

Estimating Sums or Differences Using Mixed Numbers Round to the nearest whole number. Add or subtract.

Example 3 Estimate the value of . Write the problem. Round to the nearest whole number. Add.

Example 4 According to the Guinness Book of World Records, the world’s tallest man, Robert Pershing Wadlow, was feet tall. The world’s shortest woman, Zhu Haizhen, was feet tall. Approximately how much taller was the tallest man than the shortest woman? Write the problem. Round. Subtract.

Exit Problems Estimate the value of each expression.

Communication Prompt What are some situations where estimating with fractions or mixed numbers would be useful?