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# 3.3: Combining Decimals- Addition and Subtraction with Decimals

• • David Arnold
• Retired Professor (Mathematics) at College of the Redwoods
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Addition of decimal numbers is quite similar to addition of whole numbers. For example, suppose that we are asked to add 2.34 and 5.25. We could change these decimal numbers to mixed fractions and add.

\begin{aligned} 2.34 + 5.25 & = 2 \frac{34}{100} + 5 \frac{25}{100} \\ & = 7 \frac{59}{100} \end{aligned}\nonumber

However, we can also line the decimal numbers on their decimal points and add vertically, as follows.

$\begin{array}{r} 2.34 \\ + 5.25 \\ \hline 7.59 \end{array}\nonumber$

Note that this alignment procedure produces the same result, “seven and fifty nine hundredths.” This motivates the following procedure for adding decimal numbers.

To add decimal numbers, proceed as follows:

1. Place the numbers to be added in vertical format, aligning the decimal points.
2. Add the numbers as if they were whole numbers.
3. Place the decimal point in the answer in the same column as the decimal points above it.

Example 1

Solution

Place the numbers in vertical format, aligning on their decimal points. Add, then place the decimal point in the answer in the same column as the decimal points that appear above the answer.

$\begin{array}{r} 3.125 \\ +4.814 \\ \hline 7.939 \end{array}\nonumber$

Thus, 3.125 + 4.814 = 7.939.

Exercise

5.893

Example 2

Jane has $4.35 in her purse. Jim has$5.62 in his wallet. If they sum their money, what is the total?

Solution

Arrange the numbers in vertical format, aligning decimal points, then add.

$\begin{array}{r} \ 4.35 \\ + \ 5.62 \\ \hline \ 9.97 \end{array}\nonumber$

Exercise

Alice has $8.63 in her purse and Joanna has$2.29. If they combine sum their money, what is the total?