Juan goes to the store and purchases two items. One costs $21.95 and the other costs $14.25. He wants to estimate his total before he gets to the register, but he isn't sure how to estimate the values. What is an estimate of Juan's total?

In this concept, you will learn how to estimate sums and differences of decimals.

### Estimating Sums and Differences

To **estimate** means to find an answer that is close to but not exact. It is a reasonable answer to a problem.

A **sum** is the answer of an addition problem. A **difference** is the answer of a subtraction problem.

The easiest way to estimate a sum or a difference of decimals is to round the decimal. If you round the decimal to the nearest whole number, you can complete the problem using mental math or at least simplify the problem so that finding an answer is easier.

Let's look at an example.

Estimate 15.7 + 4.9 = _____

In this problem, you only want to estimate the sum. You can do that by rounding each decimal to the nearest whole number.

In 15.7, the place being rounded is the 5. Look at the 7 and round up.

15.7 becomes 16

In 4.9, the place being rounded is the 4. Look at the 9 and round up.

4.9 becomes 5

Next, rewrite the problem.

16 + 5 = 21

The answer is that 15.7 + 4.9 is approximately 21.

You can also use rounding when estimating sums of larger numbers.

Let's look at another example.

Estimate 350.12 + 120.78 = _____

Round each number to the nearest whole number to find a reasonable estimate.

350.12 becomes 350

120.78 becomes 121

350 + 121 = 471

The answer is that 350.12 + 120.78 is approximately 471.

Now let's look at estimations with subtraction.

You can work on these problems in the same way, by rounding.

Estimate 45.78 - 22.10 = _____

45.78 rounds to 46

22.10 rounds to 22

46 - 22 = 24

The answer is that 45.78 - 22.10 is approximately 24.

### Examples

#### Example 1

Earlier, you were given a problem about Juan who wants to estimate the total cost of his purchases.

Estimate the sum of $21.95 and $14.25.

First, round each decimal to the nearest whole dollar.

$21.95 becomes $22

$14.25 becomes $14

Next, add the rounded values.

$22 + $14 = $36

Then, write the approximate sum.

$36

The answer is that $21.95 + $14.25 is approximately $36.

#### Example 2

Estimate $588.80 - $310.11 = _____

First, round each decimal to the nearest whole dollar.

$588.80 becomes $589

$310.11 becomes $310

Next, subtract the rounded values.

$589 - $310 = $279

The answer is that $588.80 - $310.11 is approximately $279.

#### Example 3

Estimate 2.67 + 3.88 = _____

First, round each decimal to the nearest whole number.

2.67 becomes 3

3.88 becomes 4

Next, add the rounded values.

3 + 4 = 7

Then, write the approximate sum.

7

The answer is that 2.67 + 3.88 is approximately 7.

#### Example 4

Estimate 56.7 - 22.3 = _____

First, round each decimal to the nearest whole number.

56.7 becomes 57

22.3 becomes 22

Next, subtract the rounded values.

57 - 22 = 35

Then, write the approximate difference.

35

The answer is that 56.7 - 22.3 is approximately 35.

#### Example 5

Estimate $486.89 - $25.22 = _____

First, round each decimal to the nearest whole dollar.

$486.89 becomes $487

$25.22 becomes $25

Next, subtract the rounded values.

$487 - $25 = $462

Then, write the approximate difference.

$462

The answer is that $486.89 - $25.22 is approximately $462.

### Review

Estimate each sum or difference by rounding.

- 56.32 + 23.12 = _____
- 18.76 + 11.23 = _____
- 14.56 + 76.98 = _____
- 11.12 + 54.62 = _____
- 33.24 + 45.32 = _____
- 18.97 + 15.01 = _____
- 22.43 + 11.09 = _____
- 4.52 + 3.21 = _____
- 19.19 + 27.75 = _____
- 87.12 + 88.90 = _____
- 67.19 - 33.12 = _____
- 88.92 - 33.10 = _____
- 76.56 - 3.45 = _____
- 65.72 - 11.12 = _____
- 77.34 - 43.02 = _____
- 88.02 - 11.10 = _____
- 89.32 - 18.03 = _____
- 24.67 - 10.10 = _____
- 37.82 - 14.20 = _____
- 55.88 - 44.22 = _____
- 334.56 - 125.86 = _____
- 456.11 + 112.18 = _____

### Review (Answers)

To see the Review answers, open this PDF file and look for section 3.15.