# Addition and Subtraction of Decimals

Go back to  'Decimals'

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}

Important Notes
1. The value of a decimal does not change on placing a zero after the decimal digits.
2. The decimal for the answer in the addition or subtraction of decimal numbers is the maximum of the decimals of the individual numbers.
3. Even though the time and angle measure is represented in decimal format, they cannot be added or subtracted as decimals.

## How do You Add and Subtract Decimals and Whole Numbers?

For adding or subtracting a decimal and whole number, the whole number is changed into a decimal number. This is done by placing a decimal after the whole number and then writing the required number of zeroes after the decimal point.

The whole number 5 is written in decimal form as 5.0

Let us add the number 15 to 12.56. Here the number 15 is changed to 15.00

\begin{align} 15.00 + 12.56 &= 15 + 0.00 + 12 + 0.56 \\ &=15 + 12 + 0.00 + 0.56 \\&=17 + 0.56 \\&= 27.56 \end{align}

\begin{align} 15.00 \\+ 12.56 \\ \hline \\ 27.56 \\ \hline \end{align}

Challenging Question

Find the sum of the fractions after converting them into decimals.  $\dfrac{1}{2} +\dfrac{1}{4} + \dfrac{1}{8} + \dfrac{1}{16} +\dfrac{1}{32} + \dfrac{1}{64}$

## Solved Examples

 Example 1

James has been asked by his teacher to add .2 + .22 + .222 + .2222.  How can we help James with his addition of these decimal numbers?

Solution

The numbers are altered by placing a few zeros after the decimals, such that each of the numbers has an equal number of decimals.

\begin{align}0.2 = 0.2000 \\0.22 = 0.2200 \\0.222 = 0.2220 \\ 0.2222 = 0.2222 \end{align}

\begin{align}.2000 \\ .2200\\.2220 \\+.2222 \\ \hline \\ 0.8642 \\ \hline\end{align}

 $$\therefore \text{The sum is } 0.8642$$
 Example 2

Diya is trying to simplify 11.89 – 14.32 + 20.87. Can you help Diya in simplifying the given numbers?

Solution

Let us first add the numbers 11.89, 20.87, and then subtract 14.32 from the result.

\begin{align} 11.89\\+20.87 \\ \hline \\ 32.76 \\ \hline\end{align}

\begin{align} 32.76 \\-14.32 \\ \hline \\ 18.44 \\ \hline\end{align}

 $$\therefore \text{The answer is } 18.44$$
 Example 3

Find the answer for 987.62 + 0.08 + 43.5

Solution

The number of decimals in each of the numbers to be added should be equal.

43.5 is changed to 43.50 and now we have equal number of decimal digits in all the numbers.

\begin{align} 987.62\\ 0.08& \\+ 43.50 \\ \hline \\ 1031.20 \\ \hline\end{align}

 $$\therefore \text{The answer is } 1031.20$$
 Example 4

Find the value for 328.7 + 443.035

Solution

Before adding the numbers the number of decimals in each of the numbers, needs to be equal.

328.7 is changed to 328.700. Now, both the numbers 328.700 and 443.035 have an equal number of decimals.

\begin{align} 328.700 \\+ 443.035 \\ \hline \\ 771.735\\ \hline\end{align}

 $$\therefore \text{The value is } 771.735$$
 Example 5

Solution

The number 7847 is written in decimal form as 7847.00. Now the subtraction can be performed in the following step.

\begin{align} 7847.00 \\– 78.47 \\ \hline \\ 7768.53\\ \hline\end{align}

### 5. How do you add a decimal and whole number?

To add a decimal and a whole number, the whole number should be changed to a decimal. Let us add 5 and 3.236.

Here we change 5 to 5.000 and we have  5.000 + 3.326 = 8.326

### 6. How do you multiply two decimals?

On multiplying two decimal numbers the number of decimal add up in the resultant answer.  $0.2 \times 0.04 = 0.008$

### 7. How do you divide one decimal with another decimal number?

The process of division of two decimal numbers is the same as the normal division.  Here the number of decimal places in the answer is a subtraction of the decimal places of the individual numbers.  $\dfrac{0.008}{0.2} = 0.04$

More Important Topics
Numbers
Algebra
Geometry
Measurement
Money
Data
Trigonometry
Calculus