Travis was practicing for the long jump. His first jump was feet. After practicing for a month, he was able to add feet to his record. About how many feet is Travis able to jump? Estimate the distance.

In this concept, you will learn how to estimate the sums and differences of fractions and mixed numbers.

### Estimating Mixed Numbers and Fractions

A **sum** is the answer in addition problem. You can also estimate the sum of fractions. To estimate a sum of two fractions, round the fractions to the nearest half. Here is an addition problem.

First, round each fraction to the nearest half.

Let’s start with . is rounded to .

. For a whole divided into 8 parts,is rounded 0.

Then, rewrite the problem and find the sum.

The estimate sum is

.When estimating the sum of mixed numbers, round to the nearest whole number instead of the nearest half. Here is an addition problem involving mixed numbers.

First, round each mixed number to the nearest whole number.

will either round down to 3 or up to 4. Look at the fraction part of the mixed number.

is greater than . Round up to 4.will either round down to 2 or up to 3. One-ninth is a very small fraction and less than

. Round down to 2.

Then, rewrite the problem and find the sum.

The estimate sum is 6.

When talking about a **difference**, you are talking about subtraction. Estimating the difference of fractions and mixed numbers is similar to estimating sums. Round each fraction or mixed number and then subtract to find the estimate.

First, round each fraction to the nearest half.

For a whole divided into 5 parts, one-half is between

and . is rounded to 1.For a whole divided into 7 parts, is one-half is between

and . is rounded to .

Then, rewrite the problem and subtract.

The estimate difference is .

### Examples

#### Example 1

Earlier, you were given a problem about Travis practicing the long jump.

Travis started at feet and was able to add

feet to his long jump record. Round the numbers and add the numbers to find an estimate of his current long jump record.

First, round the mixed numbers to the nearest whole number.

Then, rewrite the problem and add.

Travis can now jump approximately 11 feet.

#### Example 2

Estimate the difference:

.

First, round each mixed number to the nearest whole number. Look at the fraction part of each mixed number.

is greater than

. rounds up to 7.is less than

. rounds down to 2.Then, rewrite the problem and subtract.

The estimate sum is 5.

#### Example 3

Estimate the sum: .

First, round each fraction to the nearest half.

Then, rewrite the problem and add.

The estimate sum is .

#### Example 4

Estimate the sum: .

First, round each fraction to the nearest half.

Then, rewrite the problem and add.

The estimate sum is .

#### Example 5

Estimate the difference: .

First, round the mixed numbers to the nearest whole number.

Then, rewrite the problem and find the difference.

The estimate difference is .

### Review

Estimate the following sums.

Estimate each difference.

### Review (Answers)

To see the Review answers, open this PDF file and look for section 6.3.