Eduardo has 67 apps on his phone. His older brother Rocco has 79 apps, and their younger sister, Jemima, has just 22 apps. Eduardo’s father asks him how many apps the kids have in total. Eduardo starts to get out his pen and paper to make the calculation, but his dad stops him and asks him to just estimate. How can Eduardo quickly come up with an approximate answer?

In this concept, learn how to estimate sums and differences of whole numbers using rounding.

### Estimating Adding and Subtracting Whole Numbers

To **estimate** means to find an answer that is close to the exact answer. The key with estimation is to only use it in instances that don’t require an exact answer. Estimation means to find an answer that makes sense and works with the problem, but is not necessarily exact.

You can estimate **sums** (the answers to addition problems), and **differences** (the answers to subtraction problems). The first step in estimating a sum or a difference is to **round** the numbers, by changing them to the nearest power of ten, hundred, thousand, etc. Round the numbers first, then use mental math to estimate an answer.

When rounding, follow these rounding rules:

- If the number being rounded is less than 5, round down.
- If the number being rounded is 5 or greater, round up.

For example, to round the number 69 to the nearest ten:

First, to round to the tens place, look at the digit to the right (in this case, the 9).

Next, see that 9 is greater than 5, so round the tens digit up. The 6 becomes a 7.

Finally, to round to the nearest ten, make the ones digit a zero. The answer is 70.

As another example, round the number 130 to the nearest hundred:

First, to round to the hundreds place, consider the value in the tens.

Next, notice that 3 is less than 5, so round down (keep the hundreds digit the same).

Finally, replace the tens and ones digits with zeroes. The rounded value is 100.

To see how rounding can help with estimating, consider this problem:

\begin{align*}58 + 22 = \underline{\;\;\;\;\;\;\;}\end{align*}

To estimate this answer, first round both numbers to the nearest ten.

58 rounds up to 60.

22 rounds down to 20.

Then sum the rounded values: 60 + 20 = 80

The estimated answer is 80.

**Some key things to think about when estimating:**

- The estimate must make sense for the problem.
- The estimate must be reasonable.
- The estimate must be close to the exact answer.
- If none of the above fit the estimate, use exact math for the problem.

### Examples

#### Example 1

Earlier, you were given a problem about Eduardo and his application approximation.

Eduardo needs to estimate the sum of 67, 79 and 22.

First, round the numbers.

67 rounds up to 70

79 rounds up to 80

22 rounds down to 20

Next, use mental math.

70 + 80 + 20

The estimation is 170.

Eduardo can tell his dad that the kids have approximately 170 apps between them.

#### Example 2

Estimate the sum.

\begin{align*}387 + 293 =\underline{\;\;\;\;\;\;\;}\end{align*}

First, to estimate this answer, since these numbers are a little bigger than the last problem, round to the nearest hundred.

387 rounds up to 400.

293 rounds up to 300.

Then sum the estimated values. 400 + 300 = 700

The estimate is 700.

#### Example 3

\begin{align*}17 + 27 =\underline{\;\;\;\;\;\;\;}\end{align*}

First, to round the 17 to the tens place, look at the digit to the right of the tens place.

Next, since the number in the ones place is a 7, which is larger than 5, round the 1 in the tens place up to 2. The first number rounds to 20.

Then, to round the 27 to the tens place, look at the digit to the right of the tens place.

Then, since the number in the ones place is a 7, which is larger than 5, round the 2 in the tens place up to a 3. The second number rounds to 30.

Finally, sum the estimated values. 20 + 30 = 50

The solution is 50.

#### Example 4

\begin{align*}290 + 510 = \underline{\;\;\;\;\;\;\;}\end{align*}

First, to round the 290 to the nearest hundred, look at the digit to the right of the hundreds place, which would be the tens.

Next, since the number in the tens place is a 9, which is larger than 5, round the 2 in the hundreds place up to 3. The first number rounds to 300.

Next, to round the 510 to the hundreds place, look at the digit in the tens place.

Then, since the number in the tens place is a 1, which is smaller than 5, keep the 5 in the hundreds place. The second number rounds to 500.

Finally, sum the estimated values. 300 + 500 = 800

The answer is 800.

#### Example 5

\begin{align*}592 - 411 = \underline{\;\;\;\;\;\;\;}\end{align*}

First, to round the 592 to the hundreds place, look at the digit in the tens place.

Next, since the number in the tens place is a 9, which is larger than 5, round the hundreds place up to 6. The first number rounds to 600.

Then, to round the 411 to the hundreds place, look at the digit to the right of the hundreds place.

Then, since the number in the tens place is a 1, which is smaller than 5, keep the 4 in the hundreds place. The second number rounds to 400.

Finally, subtract the estimated values. 600 - 400 = 200

The answer is 200.

### Review

Estimate the following sums and differences.

- \begin{align*}45 + 62 = \underline{\;\;\;\;\;\;\;}\end{align*}
- \begin{align*}32 + 45 = \underline{\;\;\;\;\;\;\;}\end{align*}
- \begin{align*}21 + 54 = \underline{\;\;\;\;\;\;\;}\end{align*}
- \begin{align*}103 + 87 = \underline{\;\;\;\;\;\;\;}\end{align*}
- \begin{align*}101 + 92 = \underline{\;\;\;\;\;\;\;}\end{align*}
- \begin{align*}342 + 509 = \underline{\;\;\;\;\;\;\;}\end{align*}
- \begin{align*}502 + 307 = \underline{\;\;\;\;\;\;\;}\end{align*}
- \begin{align*}672 + 430 = \underline{\;\;\;\;\;\;\;}\end{align*}
- \begin{align*}201 + 303 = \underline{\;\;\;\;\;\;\;}\end{align*}
- \begin{align*}678 + 407 = \underline{\;\;\;\;\;\;\;}\end{align*}
- \begin{align*}23 - 9 = \underline{\;\;\;\;\;\;\;}\end{align*}
- \begin{align*}46 - 8 = \underline{\;\;\;\;\;\;\;}\end{align*}
- \begin{align*}58 - 12 = \underline{\;\;\;\;\;\;\;}\end{align*}
- \begin{align*}76 - 9 = \underline{\;\;\;\;\;\;\;}\end{align*}
- \begin{align*}204 - 112 = \underline{\;\;\;\;\;\;\;}\end{align*}
- \begin{align*}87 - 65 = \underline{\;\;\;\;\;\;\;}\end{align*}
- \begin{align*}98 - 33 = \underline{\;\;\;\;\;\;\;}\end{align*}
- \begin{align*}354 - 102 = \underline{\;\;\;\;\;\;\;}\end{align*}
- \begin{align*}562 - 112 = \underline{\;\;\;\;\;\;\;}\end{align*}
- \begin{align*}789 - 99 = \underline{\;\;\;\;\;\;\;}\end{align*}

### Review (Answers)

To see the Review answers, open this PDF file and look for section 1.5.