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## Add and subtract decimals by lining up the decimal points.

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### Introduction

When Kelsey arrived for her shift at the ice cream stand, she was surprised to find out that the cash register was broken. “You can just figure out each total and the customer’s change,” Ms. Nelson said to Kelsey with a smile. Kelsey grimaced as she got out a pad of paper and pencil. She knew that she was going to need to do some quick addition and subtraction to make this whole day work. Very soon her first customer arrived. This customer ordered a small cone for \$2.30 and gave Kelsey exact change. “Maybe this won’t be so tough after all,” Kelsey thought. Then her luck ended. A woman arrived and ordered a small cone with sprinkles, caramel, and an extra scoop of ice cream. Kelsey quickly jotted the following numbers down on a piece of paper.

[Figure1]

While Kelsey was working to figure out the sum, let's take a few minutes to learn how to add decimals.

### Guided Learning

In the last two Concepts you learned how to estimate the sums and differences of problems with decimals. Remember, an estimate only works when we don’t need an exact answer.

Let’s think about Kelsey. She can’t use an estimation to solve her problem. She needs to know the exact cost of the ice cream cone. In this case, Kelsey can't use estimation. She will need to know how to add decimals.

To add decimals, we are going to be working with the wholes and parts of the numbers separately.

How can we do this?

The best way to do this is to keep the parts together and keep the wholes together.

To do this, we simply line up the decimal points in each number that we are adding.

Add 4.35 + 3.27 = _____

In this problem we have parts and wholes. Let’s rewrite the problem vertically, lining up the decimal points.

4.35+ 3.27\begin{align*}4.35 \\ \underline{+\ 3.27}\end{align*}Next, we can add the columns vertically and bring the decimal point down into the answer of the problem.

4.35+ 3.277.62\begin{align*}4.35 \\ \underline{+\ 3.27} \\ 7.62\end{align*}

What happens when you have decimals with different numbers of digits in them?

When we have a problem like this, we still line up the decimal points, but we add zeros to help hold places where there aren’t numbers. This helps us to keep our addition straight.

7 + 4.35 + .86 = _____

First, we line up the problem vertically.

7.004.35+ 0.86\begin{align*}7.00 \\ 4.35 \\ \underline{+\ 0.86} \end{align*}

Notice that we added in zeros to help hold places where we did not have numbers. Now each number in the problem has the same number of digits. We can add them with ease.

7.004.35+ 0.8612.18\begin{align*}7.00\\ 4.35 \\ \underline{+\ 0.86} \\ 12.18 \end{align*}

Now it is time for you to try a few on your own. Add the following decimals.

#### Example A

5.46 + .98 + 3.21 = _____

Solution:

#### Example B

6.57 + .56 + .39 =_____

Solution:

#### Example C

98.82 + .75 + 2.13 = _____

Solution:

Now that you have learned how to add decimals, let's go back and help Kelsey with her dilemma.

First, we need to figure out the cost of the ice cream cone. Here are the numbers that Julie wrote down.

2.30 + .15 + .25 + .75 = _____

Next, we need to line up the numbers vertically.

2.30.15.25+ .85\begin{align*}2.30 \\ .15 \\ .25 \\ \underline{+\ .85} \\ \end{align*}

The cost of the ice cream cone: ____________

Here is one for you to try on your own. Be sure to line up the digits vertically before adding.

6.45+.87+2.401\begin{align*}6.45 + .87 + 2.401\end{align*} = _____

### Video Review

Here is a video for review.

### Practice Set

1. 5.7 + 4.6 = _____

2. 2.15 + 3.3 = _____

3. 6.28 + 7.11 = _____

4. 2.16 + 3.72 = _____

5. 7.10 + 21.9 = _____

6. 6.24 + 6.3 = _____

7. 4.43 + .65 = _____

8. 97.2 + 58.06 = _____

9. 36.73 + 32.14 = _____

10. 5 + 7.21 = _____

11. 87 + 13.45 = _____

12. .406 + .73 + .17 = _____

13. 1.204 + 3.5 + 3.005 = _____

14. 6.045 + 2.3 + 10 = _____

15. 13 + 2.46 + .0081 = _____

Solve the word problems. Include labels.

16.  Eric is connecting three
fire hoses to make one longer hose.
The first hose is 25.25 feet long, the
second hose is 15.755 feet long, and the
third hose is 35.5 feet long. Find
the total length once the fire hoses are connected.

17.

Olivia has three favorite songs on her first CD. Her first favorite song is
5.43 minutes long. The second favorite song on her CD is 8.67 minutes long.

The CD has 56.34 minutes of music.
How much of the total time on the CD is taken by her two favorite songs?

### Review

• An estimate only works when we don’t need an exact answer.
• When adding decimals work with the wholes and parts of the numbers separately.

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

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