How to Add or Subtract Decimals

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In mathematics, a decimal can be defined as a number which has two parts: a whole part and a fractional part, and these two parts are separated by a decimal point. The whole part always represents a number greater than one, while the fractional part, i.e., the part after the decimal, always represents a number less than one.

For example, let’s take the number \( 15.74 \). Now here the whole part is represented by \( 15 \), whereas the fractional part \( (\frac{74}{100} \ ) \) is represented by \(74\). Here \( 74 \) can also be denoted as the decimal part, as it lies after the decimal point.

Terminating and Non-Terminating Decimals

Terminating decimals are the one which have an end whereas non-terminating decimals don’t have an end. They are simply recurring digits that go on and on.

For example, \( 3.333333 \) , \( ( \frac{10}{3} \ ) \) is a recurring/non-terminating decimal, whereas \( 2.50\) , \( (\frac{10}{4} \ ) \) is a terminating decimal.

The Concept of Preceding Powers of 10

Now, there’s a very interesting concept linked to decimal numbers. This concept is known as the preceding powers of \( 10\). All decimal numbers are based on this concept. So, as we move from left to right in a decimal number, basically, the place value of every digit gets divided by \( 10\). So, the first digit after a decimal could be represented as \(\frac{1}{10}\) , second as \(\frac{1}{100}\) and so on.
So, from this concept, we can easily find out the expanded form of a decimal.

For example, let’s take the decimal number \(16.457\). The expanded form could be written as: \(10 + 6 + \frac{4}{10} + \frac{5}{100} + \frac{7}{1000}\)
Also, \( 16.457\) can be represented as \(16 \frac{457}{1000} \) in mixed fraction terms.

How to Add or Subtract 2 Decimals

To add or subtract 2 decimals, use the following steps:

First, line up the two numbers as you would do in simple addition or subtraction.
Next add zeroes to the right of decimals to match number of digits (if not same). For example, when performing \( (2.5-2.25) \), convert \( 2.5\) to \( 2.50\).
Then perform simple column addition or subtraction.

Free printable Worksheets

Exercises for Adding and Subtracting Decimals

1) \(\cfrac{-\begin{align}114.334\\62.120\end{align}}{}\)

2) \(\cfrac{-\begin{align}129.743\\34.230\end{align}}{}\)

3) \(\cfrac{+\begin{align}121.373\\31.220\end{align}}{}\)

4) \(\cfrac{+\begin{align}114.648\\31.330\end{align}}{}\)

5) \(\cfrac{+\begin{align}129.494\\56.750\end{align}}{}\)

6) \(\cfrac{+\begin{align}136.978\\42.880\end{align}}{}\)

7) \(\cfrac{-\begin{align}136.712\\16.530\end{align}}{}\)

8) \(123.428 \ + \ \color{red}{\underline{}\underline{}\underline{}} \ = 139.198 \)

9) \(130.666 \ + \ \color{red}{\underline{}\underline{}\underline{}} \ = 205.996 \)

10) \(123.389 \ + \ \color{red}{\underline{}\underline{}\underline{}} \ = 173.919 \)

Answers

1) \(\cfrac{-\begin{align}114.334\\62.120\end{align}}{\color{red}{\quad52.214}}\)

First line up the numbers:\(\cfrac{-\begin{align}114.334\\62.120\end{align}}{}\) , Start with the thousandth place \(4 - 0 = 4\), so \(\cfrac{-\begin{align}114.334\\62.120\end{align}}{ 0.004}\) . Continue with hundredth place. \(3-2=1\) and then the tenth place \(3-1=2\) . \(\cfrac{-\begin{align}114.334\\62.120\end{align}}{0.214}\) . Finally subtract the integer parts \(114 - 62 = 52\), \(\cfrac{-\begin{align}114.334\\62.120\end{align}}{52.214}\).

2) \(\cfrac{-\begin{align}129.743\\34.230\end{align}}{\color{red}{\quad95.513}}\)

First line up the numbers:\(\cfrac{-\begin{align}129.743\\34.230\end{align}}{}\) , Start with the thousandth place \(3 - 0 = 3\), so \(\cfrac{-\begin{align}129.223\\34.730\end{align}}{ 0.003}\) . Continue with hundredth place. \(4-3=1\) and then the tenth place \(7 -2 =5\) . \(\cfrac{-\begin{align}114.334\\62.120\end{align}}{0.513}\) . Finally subtract the integer parts \(129 -34 = 85\), \(\cfrac{-\begin{align}129.743\\34.230\end{align}}{95.513}\).

3) \(\cfrac{+\begin{align}121.373\\31.220\end{align}}{\color{red}{\quad152.593}}\)

First line up the numbers:\(\cfrac{+\begin{align}121.373\\31.220\end{align}}{}\) , Start with the thousandth place \(3 + 0 = 3\), so \(\cfrac{+\begin{align}121.373\\31.220\end{align}}{0.003}\) . Continue with hundredth place \(7+2=9\) and then the tenth place \(3+2=5\) . \(\cfrac{+\begin{align}121.373\\31.220\end{align}}{0.593}\) . Finally subtract the integer parts \(121+31 = 152\), \(\cfrac{+\begin{align}121.373\\31.220\end{align}}{152.593}\).

4) \(\cfrac{+\begin{align}114.648\\31.330\end{align}}{\color{red}{\quad145.978}}\)

First line up the numbers:\(\cfrac{+\begin{align}114.648\\31.330\end{align}}{}\) , Start with the thousandth place \(8+ 0 = 8\), so \(\cfrac{+\begin{align}114.648\\31.330\end{align}}{0.008}\) . Continue with hundredth place \(4+3=7\) and then the tenth place \(6+3=9\) . \(\cfrac{+\begin{align}114.648\\31.330\end{align}}{0.978}\) . Finally subtract the integer parts \(114+31 = 145\), \(\cfrac{+\begin{align}114.648\\31.330\end{align}}{145.978}\).

5) \(\cfrac{+\begin{align}129.494\\56.750\end{align}}{\color{red}{\quad186.244}}\)

6) \(\cfrac{+\begin{align}136.978\\42.880\end{align}}{\color{red}{\quad179.858}}\)

7) \(\cfrac{-\begin{align}136.712\\16.530\end{align}}{\color{red}{\quad120.182}}\)

8) \(123.428 \ + \ \color{red}{\underline{}\underline{}\underline{}} \ = 139.198 \ \ \Rightarrow 139.198 \ - \ 123.428 \ = \ \color{red}{\underline{}\underline{}\underline{}} \)
\(\Rightarrow \cfrac{-\begin{align}139.198\\123.428\end{align}}{\color{red}{\quad15.770}}\)

9) \(130.666 \ + \ \color{red}{\underline{}\underline{}\underline{}} \ = 205.996 \ \ \Rightarrow 205.996 \ - \ 130.666 \ = \ \color{red}{\underline{}\underline{}\underline{}} \)
\(\Rightarrow \cfrac{-\begin{align}205.996\\130.666\end{align}}{\color{red}{\quad75.330}}\)

10) \(123.389 \ + \ \color{red}{\underline{}\underline{}\underline{}} \ = 173.919 \ \ \Rightarrow 173.919 \ - \ 123.389 \ = \ \color{red}{\underline{}\underline{}\underline{}} \)
\(\Rightarrow\cfrac{-\begin{align}173.919\\123.389\end{align}}{\color{red}{\quad50.530}}\)

How to Add or Subtract Decimals