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# 2.2: Estimate Decimal 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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Have you ever tried to figure out a restaurant bill? Take a look at this situation.

Carmen and her friend went out for lunch. When they received the bill, they saw the following figures written down.

\begin{align*}1.09,1.09,6.26,7.35,3.50,4.25\end{align*}

Carmen wants to add this up quickly in her head so that she can estimate the bill.

Do you know how she can do this? In this Concept, you will learn how to use front-end estimation in situations just like this one.

### Guidance

Did you know that you can estimate decimal sums and differences using front-end estimation? Let's take a look at front-end estimation. What is it?

Front-end estimation is a particular way of rounding numbers to estimate sums and differences. To use front-end estimation, add or subtract only the numbers in the greatest place value.

Take a look at this estimation problem.

Estimate the sum using front-end estimation: \begin{align*}4.8+3.2+7.2\end{align*}

First add the digits in the ones places: \begin{align*}4+3+7=14\end{align*}. So 14 is a good first estimate.

Now look at the digits in the tenths places: \begin{align*}8+2+2=12\end{align*}. Since there are more than 10 tenths, adjust your first estimate. Add 1 one for a more accurate estimate.

\begin{align*}14+1=15\end{align*}

A good estimate for the sum is 15. This is our answer.

Here is a problem using subtraction. We can use front-end estimation for this one too.

Estimate the difference using front-end estimation: \begin{align*}9.52-3.39\end{align*}

First subtract the digits in the ones places: \begin{align*}9-3=6\end{align*}. So 6 is a good first estimate.

Now look at the digits in the tenths places. Since the difference of 5 and 3 is 2, it will not affect your first estimate.

A good estimate for the difference is 6. This is our answer.

Use front-end estimation to find each sum or difference.

#### Example A

\begin{align*}3.4 + 6.1 + 4.5\end{align*}

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

#### Example B

\begin{align*}8.2 - 4.5\end{align*}

Solution:\begin{align*}8 - 4 = 4\end{align*}

#### Example C

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

Solution:\begin{align*}4 + 6 + 7 + 3 = 20\end{align*}

Now let's go back to the dilemma from the beginning of the Concept.

Here is the list of costs that was on Carmen's bill.

\begin{align*}1.09,1.09,6.26,7.35,3.50,4.25\end{align*}

We use front-end estimation by taking the first value from each price. Then we add.

\begin{align*}1 + 1 + 6 + 7 + 3 + 4 = 22\end{align*}

The estimated cost of lunch is \begin{align*}22.00\end{align*}.

### Vocabulary

Decimal
a part of a whole. The numbers to the left of the decimal point represent whole quantities. The numbers to the right of the decimal point represent parts.
Estimate
to find an approximate answer that is reasonable or makes sense given the problem.
Front-End Estimation
a method of estimating where you only add the digits in the greatest place value

### Guided Practice

Here is one for you to try on your own.

Estimate the following sum.

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

Solution

To complete this task using front-end estimation, we take the leading value from each number.

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

\begin{align*}39\end{align*}

Our estimate is \begin{align*}39\end{align*}.

### Practice

Directions: 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*}

### Notes/Highlights Having trouble? Report an issue.

Color Highlighted Text Notes

### Vocabulary Language: English

Decimal

In common use, a decimal refers to part of a whole number. The numbers to the left of a decimal point represent whole numbers, and each number to the right of a decimal point represents a fractional part of a power of one-tenth. For instance: The decimal value 1.24 indicates 1 whole unit, 2 tenths, and 4 hundredths (commonly described as 24 hundredths).

Front-End Estimation

Front-end estimation is a method of estimating where you only add the digits in the greatest place value.

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