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# 3.17: Decimal Addition

Difficulty Level: At Grade Created by: CK-12
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Yoshi and his family have decided to have a yard sale. Yoshi's mother has him collect all the money from the customers. Yoshi wants to make sure that he is collecting the right amount from each person.The first person buys one item for $12.25, a second item for$0.50 and a third item for 0.75. Yoshi knows that he needs to add the decimals but isn't sure how to begin. How much money does the first person owe Yoshi? In this concept, you will learn how to add decimals ### Adding Decimals To add decimals, work with the wholes and parts of the numbers separately. Add the parts then add the wholes. The best way to do this is to keep the parts together and keep the wholes together. To do this, simply line up the decimal points in each number that you are adding. Let's look at an example. Add 3.45 + 2.37 = _____ In this problem you have parts and wholes. Let’s rewrite the problem vertically, lining up the decimal points. 3.45+ 2.37\begin{align*}3.45 \\ \underline{+\ 2.37}\end{align*} Next, add the columns vertically and bring the decimal point down into the answer of the problem. 3.45+ 2.375.82\begin{align*}3.45 \\ \underline{+\ 2.37} \\ 5.82\end{align*} The answer is 5.82. Let's look at another example. 5 + 3.45 + 0.56 = _______ In a problem like this, line up the decimal points, but add zeros to help hold places where there aren’t numbers. This helps keep the addition straight. First, line up the problem vertically. 5.003.45+ 0.56\begin{align*}5.00 \\ 3.45 \\ \underline{+\ 0.56} \end{align*} Notice that zeros help hold places where you did not have numbers. Now each number in the problem has the same number of digits. Add the numbers. 5.003.45+ 0.569.01\begin{align*}5.00\\ 3.45 \\ \underline{+\ 0.56} \\ 9.01 \end{align*} The answer is 9.01. ### Examples #### Example 1 Earlier, you were given a problem about Yoshi and the yard sale. Yoshi's first customer wants to buy 3 different things. To ask for the correct total amount, Yoshi needs to add12.25, $0.50 and$0.75.  Can you find the total amount due?

First, line up the numbers vertically.

12.250.50+ 0.75\begin{align*} 12.25\\ 0.50\\ \underline {+ \ 0.75}\end{align*}

Then, add the numbers.

13.50\begin{align*}13.50\end{align*}

The answer is $13.50. Yoshi must collect$13.50 from the customer.

#### Example 2

Add the following numbers.

13.25 + 0.80 + 1.30  = _____

First, line up the numbers vertically.

13.250.80+ 1.30\begin{align*} 13.25\\ 0.80\\ \underline {+ \ 1.30}\end{align*}

Then, add the numbers.

15.35\begin{align*}15.35\end{align*}

The answer is 15.35.

#### Example 3

Add the following decimals.

4.56 + 0.89 + 2.31 = _____

First, line up the numbers vertically.

4.560.89+ 2.31\begin{align*} 4.56\\ 0.89\\ \underline {+ \ 2.31}\end{align*}

Then, add the numbers.

7.76\begin{align*}7.76\end{align*}

The answer is 7.76.

#### Example 4

Add the following decimals.

5.67 + 0.65 + 0.93 =_____

First, line up the numbers vertically.

5.670.65+ 0.93\begin{align*}5.67\\ 0.65\\ \underline {+ \ 0.93}\end{align*}

Then, add the numbers.

7.25\begin{align*}7.25\end{align*}

The answer is 7.25.

#### Example 5

Add the following decimals.

88.92 + 0.57 + 3.12 = _____

First, line up the numbers vertically.

88.920.57+3.12\begin{align*} 88.92 \\ 0.57 \\ \underline{+3.12}\end{align*}

Then, add the numbers.

92.61\begin{align*}92.61\end{align*}

The answer is 92.61.

### Review

Add the following decimals.

1. 4.5 + 6.7 = _____
2. 3.45 + 2.1 = _____
3. 6.78 + 2.11 = _____
4. 5.56 + 3.02 = _____
5. 7.08 + 11.9 = _____
6. 1.24 + 6.5 = _____
7. 3.45 + .56 = _____
8. 87.6 + 98.76 = _____
9. 76.43 + 12.34 = _____
10. 5 + 17.21 = _____
11. 78 + 13.456 = _____
12. .456 + .23 + .97 = _____
13. 1.234 + 4.5 + 6.007 = _____
14. 3.045 + 3.3 + 9 = _____
15. 23 + 4.56 + .0091 = _____

To see the Review answers, open this PDF file and look for section 3.17.

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### Vocabulary Language: English

TermDefinition
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).
Rounding Rounding is reducing the number of non-zero digits in a number while keeping the overall value of the number similar.
Sum The sum is the result after two or more amounts have been added together.
Vertically Vertically means written up and down in columns.

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