# 2.2: Estimate Sums and Differences Using Front-End Estimation

Difficulty Level: At Grade Created by: CK-12
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Practice Front-End Estimation

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#### Example 2

Estimate the following sum.

\begin{align*}4.01 + 6.27 + 18.12 + 11.30\end{align*}

First, look only at the whole numbers and add the digits in the ones places.

\begin{align*}4+6+18+11=39\end{align*}

Next, look at the decimals and round them to the nearest whole number.

0.01 is approximately 0.

0.27 is approximately 0.3.

0.12 is approximately 0.1.

0.30 is approximately 0.3.

So \begin{align*}0.3+0.1+0.3=0.7\end{align*}.

Then, add the two together.

\begin{align*}39+0.7=39.7\end{align*}

The answer is 39.7.

#### Example 3

Estimate the following sum

\begin{align*}3.43+6.14+4.51\end{align*}

First, add the digits in the ones places.

\begin{align*}3+6+4=13\end{align*}

Next, let’s look at the decimals. You want to make these decimals easier to add.

0.43 is approximately 0.4

0.14 is approximately 0.1

0.51 is approximately 0.5

\begin{align*}0.4+0.1+.5=1\end{align*}.

Then, add the two together.

\begin{align*}13+1=14\end{align*}

The answer is 14.

#### Example 4

\begin{align*}8.238-4.596\end{align*}

First, add the digits in the ones places: \begin{align*}8-4=4\end{align*}

Next, let’s look at the decimals. You want to make these decimals easier to subtract.

0.238 is approximately 0.2

0.596 is approximately 0.6

\begin{align*}0.2-0.6=-0.4\end{align*}

Then, add the two together.

\begin{align*}4+(-0.4)=3.6\end{align*}

The answer is 3.6.

#### Example 5

\begin{align*}4.53+6.32+7.02+3.45\end{align*}

First, add the digits in the ones places: \begin{align*}4+6+7+3=20\end{align*}

Next, let’s look at the decimals. You want to make these decimals easier to add.

0.53 is approximately 0.5

0.32 is approximately 0.3

0.02 is approximately 0

0.45 is approximately 0.4

\begin{align*}0.5+0.3+0.4=1.2\end{align*}.

Then, add the two together.

\begin{align*}20+1.2=21.2\end{align*}

The answer is 21.2.

### Review

Find each estimate by using front-end estimation.

1. \begin{align*}45.67 + 3.04 = \underline{\;\;\;\;\;\;\;\;\;\;}\end{align*}
2. \begin{align*}55.10 + 5.6 = \underline{\;\;\;\;\;\;\;\;\;\;}\end{align*}
3. \begin{align*}88.99 - 2.10 = \underline{\;\;\;\;\;\;\;\;\;\;}\end{align*}
4. \begin{align*}80.09 - 12.78 = \underline{\;\;\;\;\;\;\;\;\;\;}\end{align*}
5. \begin{align*}34.75 - 3.05 = \underline{\;\;\;\;\;\;\;\;\;\;}\end{align*}
6. \begin{align*}5.67 + 3.87 = \underline{\;\;\;\;\;\;\;\;\;\;}\end{align*}
7. \begin{align*}235.56 - 120.45 = \underline{\;\;\;\;\;\;\;\;\;\;}\end{align*}
8. \begin{align*}17.8 + 12.3 + 5.3 = \underline{\;\;\;\;\;\;\;\;\;\;}\end{align*}
9. \begin{align*}33.1 + 11.4 + 2.8 = \underline{\;\;\;\;\;\;\;\;\;\;}\end{align*}
10. \begin{align*}18.11 + 25.4 + 2.1 = \underline{\;\;\;\;\;\;\;\;\;\;}\end{align*}
11. \begin{align*}34.1 - 10.123= \underline{\;\;\;\;\;\;\;\;\;\;}\end{align*}
12. \begin{align*}301.1 - 10.2345 = \underline{\;\;\;\;\;\;\;\;\;\;}\end{align*}
13. \begin{align*}12.234 + 15.1004 = \underline{\;\;\;\;\;\;\;\;\;\;}\end{align*}
14. \begin{align*}2.00987 + 5.0123 + 8.118 = \underline{\;\;\;\;\;\;\;\;\;\;}\end{align*}
15. \begin{align*}3.0045 - 1.0008 = \underline{\;\;\;\;\;\;\;\;\;\;}\end{align*}

To see the Review answers, open this PDF file and look for section 2.2.

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