# Rounding and Estimation

Estimating and rounding are very important math skills. It provides a tool for people to judge the reasonableness of answers to math problems and provides a framework for making an educational and informed guess when necessary.

## Estimating Sums

A sum is the answer to an addition problem. It is best to estimate before adding decimals and fractions. You can use an estimate to check the accuracy of the sum when adding decimals or fractions.

1. Find the sum of 24.86 + 15.15.
2. Round each decimal to the nearest whole number.
3. 24.86 is rounded to 25  and  15.15 is rounded to15
4. Add:   25 + 15 = 40 , so the actual sum should be close to 40. Use this to check the actual sum. 24.86+15.15 = 40.01
5. The sum 40.01 is very close to the estimate 40, so the answer is reasonable and probably correct.

## Estimating Differences

A difference is the answer to a subtraction problem. It is best to estimate before subtracting decimals and fractions. You can use an estimate to check the accuracy of the difference when adding decimals or fractions.

### Find the difference of

95.16 – 16.73.

1. Round each decimal to the nearest whole number.
2. 95.16 is rounded to 95 and  16.73 is rounded to 17.
3. Subtract:   95-17 = 78 , so the actual difference should be close to 78.
4. Use this to check the actual difference.
5. 95.16 – 16.73 = 78.43

The difference 78.43 is very close to the estimate 78, so the answer is reasonable and probably correct.

## Use Compatible Numbers

In mathematics, compatible numbers are the numbers that are easy to add, subtract, multiply, or divide mentally. Compatible numbers are close in value to the actual numbers that make estimating the answer and computing problems easier.

500 + 300 = 800

The numbers 500 and 300 are compatible for addition, since the sum of 800 can be easily calculated mentally.

519 + 293 = 812

The numbers 519 and 293 are not compatible for addition, since the sum (812) cannot be easily calculated mentally. To estimate 513 + 299, replace 513 and 299 with the compatible numbers 500 and 300. An estimate of 513 + 299 is found by mentally calculating 500 + 300 = 800.

Example 2 (Subtraction)

19.4 − 3.8 = 15.6

The numbers 19.4 and 3.8 are not compatible for subtraction, since the difference (15.6) cannot be easily calculated mentally. To estimate 19.4 − 3.8, replace 19.4 and 3.8 with the compatible numbers 19 and 4. An estimate of 19.4 − 3.8 is found by mentally calculating 19 − 4 = 15.

Example 3 (Multiplication)

19.4 × 3.8 = 73.72

The numbers 19.4 and 3.8 are not compatible for multiplication since the product (73.72) can’t be easily calculated mentally. To estimate 19.4 × 3.8, replace 19.4 and 3.8 with the compatible numbers 20 and 4. An estimate of 19.4 × 3.8 is found by mentally calculating 20 × 4 = 80.

Example 4 (Division)

721 ÷ 70 = 10.3

The numbers 721 and 70 are not compatible for division, since the quotient (10.3) can’t be easily calculated mentally. To estimate 721 ÷ 70, replace 721 with 700 so that the numbers involved are compatible. An estimate of 721 ÷ 70 is found by mentally calculating 700 ÷ 70 = 10.