# Addition and Subtraction of Decimals

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Counting numbers was easy. But it became difficult once the numbers changed to decimals, isn't it? We will try making it simple. Did you know, we can add and subtract decimals also, with the help of our ten fingers?

In this mini-lesson, we shall explore the world of decimals, by finding answers to questions like how to add or subtract decimals, how to add or subtract decimals of varying lengths, and other similar questions related to decimals.

## Lesson Plan

 1 How to Add or Subtract Decimals? 2 Important Notes 3 Challenging Questions 4 Solved Examples on Addition and Subtraction of Decimals 5 Interactive Questions on Addition and Subtraction of Decimals

## How to Add or Subtract Decimals?

The operations of addition or subtraction of decimals are the same as the normal numbers.

But, the place values of the digits in the numbers should be rightly matched. This addition of decimals can be understood with the help of a simple example: $12.5 + 4.9$

We can separate the decimals from the whole numbers.   \begin{align}12.5 + 4.9 &=12 + 0.5 + 4 + 0.9 \\&= 12 + 4 + 0.5 + 0.9 \\ &= 16 + 1.4 \\&= 16 + 1 + 0.4 \\&= 17.4 \end{align}

Here, the addition of $$0.5 + 0.9$$ is the same as the addition $$5 + 9 = 14$$. And the decimal is placed in the answer $$1.4$$

\begin{align}12.5& \\ +4.9 \\ \hline \\ 17.4 \\ \hline \end{align}

### Subtraction of Decimals For the operation of subtraction in decimals the rule of rule of carry over is followed as in the normal whole numbers.

Let us understand this with an example: $14.5 - 8.7$

Here, we segregate the decimals and whole numbers and separately conduct the operation of subtraction.

\begin{align} 14.5 - 8.7 &= 14 + 0.5 -(8 + 0.7) \\&= 14 + 0.5 - 8 - 0.7 \\ &=14 - 8 + 0.5 - 0.7 \\ &= 6 -0.2 \\ &= 5 + 1.0 - 0.2 \\ &= 5 + 0.8 \\ &= 5.8\end{align}

Here the number 1 is taken from 6, to help for further subtraction.

Also the subtraction $$1 .0 - 0.2$$ is same as the subtraction $$10 - 2 = 8$$. And a decimal is placed in the answer $$0.8$$

\begin{align} 14.5\\ - 8.7\\ \hline\\5.8 \\ \hline \end{align}

## How to Add or Subtract Decimals of Varying Lengths?

The operation of addition and subtraction can be conveniently performed, even with decimals of varying lengths.

The decimal digits in each of the numbers should be made equal.

To understand this, let us add the decimal numbers 24, 32.1, 0.08, 0.5, and 4.003

Here each of the numbers needs to have an equal number of decimal digits.

For this, we change the numbers as 24.000, 32.100, 0.080, 0.500, and 4.003

\begin{align}24.000+ 32.100+ 0.080+0.500+ 4.003 &= 24 + 32 + 4 + 0.000 + 0.100 + 0.080 + 0.500 + 0.003 \\&=60 + 0.683 \\&=60.683 \end{align}

\begin{align}24.000\\ 32.100\\ 0.080\\0.500\\+ 4.003 \\ \hline \\60.683 \\\hline \end{align}

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Numbers
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