Hannah and Allison are going out for lunch. They need to estimate their bill before they go to lunch so they can see if they have enough money or need to go to the ATM. Hannah wants to get a Caesar salad and a pepperoni pizza with a juice. Allison wants a Caesar salad and chicken wrap along with her milk. Based on the menu above, if each of the girls has $10.00, will they need to go to the ATM?

In this concept, you will learn to add and subtract decimals with and without rounding.

### Adding and Subtracting Decimals

A **decimal** is a number that uses a decimal point and place value to show tenths, hundredths, thousandths, and so on. The **decimal point** divides the whole number portion from the fractional portion of the number.

Looking at the number 35.492, the whole number portion is 35, or 3 tens and 5 ones. The fractional portion is 0.492, or 4 tenths, 9 hundredths, and 2 thousandths. Sometimes there are decimals with both wholes and parts, and sometimes, there are decimals with only parts.

You can add and subtract decimals by adding according to place value or by rounding the values before adding them.

Decimals can be added the same way whole numbers can: by lining up the place values. For decimals, this means lining up the decimal points and adding each place value with its common place value. For instance, don’t add hundredths and tens, add hundredths and hundredths, and add tenths and tenths.

Let’s look at an example.

Add

First, line up the addition problem by lining up the place values.

\begin{align*}& \ \ \ 48.08\\
& \underline{+ \ \ 6.215}\\\end{align*}

Next, add each place value, remembering to carry when necessary.

\begin{align*}48.080\\
\underline{+ \;\; 6.215}\\
54.295\end{align*}

The answer is 54.295.

You can also find an approximate sum by estimating. Remember that when you **estimate** you will find an approximate answer, which means it will not be exact. One way of estimating is by rounding.

You can round each value to the nearest whole number. To determine which whole number to round a number to, look at the decimal portion of the number. If the decimal part is less than .5, then round down. If the decimal part is .5 or greater, then round up.

Let’s look at an example.

Round 4.56 to the nearest whole number.

The decimal part (.56) is greater than .5, so 4.56 rounds up to 5.

You can also subtract decimals by using place value or by rounding.

Let’s look at an example.

Complete the subtraction problem .

First, line up the values according to place value so that one can be subtracted from the other.

\begin{align*}56.93\\
\underline{- \;\; 10.14}\\\end{align*}

Next, perform the subtraction.

The answer is 46.79.

You can also find the difference by rounding to the nearest whole number. You need to round each number to the nearest whole number and then find the difference between the two values.

56.93 rounds up to 57

10.14 rounds down to 10

The answer is 47.

Notice that the estimated and actual answers are close.

### Examples

#### Example 1

Earlier, you were given a problem about Hannah and Allison going to lunch.

The girls need to know if they need to stop at the ATM first. Let’s add up the bills for both girls to see if they have enough money for lunch.

Hannah’s order:

Caesar salad……..$1.99

Pepperoni pizza….$5.99

Juice……………..$0.99

Total………..…....$8.97

Allison’s order:

Caesar salad…....$1.99

Chicken wrap…..$6.99

Milk…………....$1.25

Total…………...$10.23

Since each of the girls has only $10.00, Hannah will have enough for her lunch but Allison will have to stop at the ATM first.

Subtract the following decimals with and without estimation:

Let’s estimate the subtraction.

First, round 5.678 up to 6.

Next, round .82 up to 1.

Then, subtract:

The estimated answer is 5.

Now let’s calculate the subtraction.

First, line up the values according to place value so that you can subtract one from the other.

\begin{align*}& \quad \ 5.678\\
& \underline{- \ \ 0.82 \;\;\;}\\\end{align*}

Next, perform the subtraction.

\begin{align*}& \quad \ 5.678\\
& \underline{- \ \ 0.82 \;\;\;}\\
& \quad \ 4.858\end{align*}

The accurate answer is 4.858.

The estimate of 5 is very close to the accurate answer of 4.858.

#### Example 2

Round 2.3 to the nearest whole number.

Remember, with rounding, if the decimal is greater than 0.5, you round up and if less than 0.5, you round down.

0.3 is less than 0.5 so you round down.

The answer is 2

#### Example 3

Estimate by rounding \begin{align*}48.08+7.578\end{align*}

Remember, with rounding, if the decimal is greater than 0.5, you round up and if less than 0.5, you round down.

First, round 48.08 to the nearest whole number. Note that 0.08 is less than 0.5 so you round down.

48.08 now will be 48.

Next, round 7.578 to the nearest whole number. Note that 0.0578 is greater than 0.5 so you round up.

7.578 now will be 8.

Then, complete the addition problem.

The answer is 55.

#### Example 4

Subtract

First, line up the values according to place value so that you can subtract one from the other.

Next, perform the subtraction.

The answer is 43.216.

### Review

Find the exact sum or difference by adding or subtracting the following decimals according to place value.

- \begin{align*}16.27 + 3.45 = \underline{\;\;\;\;\;\;\;\;\;\;}\end{align*}
16.27+3.45=−−−−− - \begin{align*}22.34 + 9.21 = \underline{\;\;\;\;\;\;\;\;\;\;}\end{align*}
22.34+9.21=−−−−− - \begin{align*}34.5 + 1.234 = \underline{\;\;\;\;\;\;\;\;\;\;}\end{align*}
34.5+1.234=−−−−− - \begin{align*}5.6 + 8.9 = \underline{\;\;\;\;\;\;\;\;\;\;}\end{align*}
5.6+8.9=−−−−− - \begin{align*}1.02 + 12.34 = \underline{\;\;\;\;\;\;\;\;\;\;}\end{align*}
1.02+12.34=−−−−− - \begin{align*}67.89 + 23.45 = \underline{\;\;\;\;\;\;\;\;\;\;}\end{align*}
67.89+23.45=−−−−− - \begin{align*}123.4 + 7.89 = \underline{\;\;\;\;\;\;\;\;\;\;}\end{align*}
123.4+7.89=−−−−− - \begin{align*}34.05 + 102.10 = \underline{\;\;\;\;\;\;\;\;\;\;}\end{align*}
34.05+102.10=−−−−− - \begin{align*}34.56 - 11.23 = \underline{\;\;\;\;\;\;\;\;\;\;}\end{align*}
34.56−11.23=−−−−− - \begin{align*}67.09 - 2.34 = \underline{\;\;\;\;\;\;\;\;\;\;}\end{align*}
67.09−2.34=−−−−− - \begin{align*}88.9 - 13.24 = \underline{\;\;\;\;\;\;\;\;\;\;}\end{align*}
88.9−13.24=−−−−− - \begin{align*}234.5 - 16.7 = \underline{\;\;\;\;\;\;\;\;\;\;}\end{align*}
234.5−16.7=−−−−− - \begin{align*}708.90 - 45.67 = \underline{\;\;\;\;\;\;\;\;\;\;}\end{align*}
708.90−45.67=−−−−− - \begin{align*}27.56 - 1.20 = \underline{\;\;\;\;\;\;\;\;\;\;}\end{align*}
27.56−1.20=−−−−− - \begin{align*}327.66 - 301.20 = \underline{\;\;\;\;\;\;\;\;\;\;}\end{align*}
327.66−301.20=−−−−− - \begin{align*}540.26 - 18.50 = \underline{\;\;\;\;\;\;\;\;\;\;}\end{align*}
540.26−18.50=−−−−−

### Review (Answers)

To see the Review answers, open this PDF file and look for section 2.1.