# OPERATIONS WITH DECIMALS

## About "Operations with decimals"

Operations with decimals :

We can not imagine the subject Math without the term "Decimal". Because, we solve many problems with it. So, we must be aware of the operations which we often do with decimals.

Let us explore the following operations with decimals.

(i) Addition

(ii) Subtraction

(iii) Multiplication

(iv) Division

## Adding decimals

Let us see, how to add the decimals 0.24 and 0.15.

Observe the figure given below. 0.24 and 0.15 are shaded in two different colors. Now the sum of 0.24 and 0.15 is 0.39

That is,

3 tenths and 9 hundredths

Method 1 : Therefore,

0.24 + 0.15  =  0.39

Method 2 :

Not asaaaaaaaaaaaaaaaaa0 . 2 4 aaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaa+  0 . 1 5  aaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaa-----------aaaaaaaaaaaaaaaaaaaa   aaaaaaaaaaaaaaaaaaaaaaa0 . 3 9  aaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaa-----------

Therefore,

0.24 + 0.15  =  0.39

Note :

In both the methods, arrange the decimal numbers according to the place values and add them.

Add : 0.75 and 0.5

Not asaaaaaaaaaaaaaaaaa0 . 7 5 aaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaa+  0 . 2 0  aaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaa-----------aaaaaaaaaaaaaaaaaaaa   aaaaaaaaaaaaaaaaaaaaaaa0 . 9 5  aaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaa-----------

In the above addition of decimals, 0.2 is taken as 0.20, as the first decimal number has two digits on the right side of the decimal point.

## Subtracting decimals

Let us see, how to subtract 0.14 from 0.25

Method 1 : Therefore,

0.25 - 0.14  =  0.11

Method 2 :

Not asaaaaaaaaaaaaaaaaa0 . 2 5 aaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaa-  0 . 1 4  aaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaa-----------aaaaaaaaaaaaaaaaaaaa   aaaaaaaaaaaaaaaaaaaaaaa0 . 1 1  aaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaa-----------

Therefore,

0.25 - 0.14  =  0.11

Note :

In both the methods, arrange the decimal numbers according to the place values and subtract them.

## Multiplying decimals

Let us see, how to multiply 1.5 and 4.3

Multiplying 15 and 43, we get 645.

Both, in 1.5 and 4.3, there is 1 digit to the right of the decimal point. So, count 2 digits from the right and put a decimal point.

So, we get 1.5 x 4.3  =  6.45

While multiplying 1.43 and 2.1, you will first multiply 143 and 21. For placing the decimal in the product obtained, you will count 2 + 1 = 3 digits starting from the right most digit.

Thus 1.43 × 2.1 = 3.003.

## Dividing decimals

Dividing decimals by whole numbers :

Method 1 :

Find 4.2 ÷ 3

Solution :

Write the decimal number 4.2 as a fraction with multiples of 10.

Since there is only one digit after the decimal in 4.2, we can write 4.2 as 42/10.

(If there are two digits after the decimal, we have to take 100 as denominator)

Now, we have to divide 42/10 by 3 as given below.

4.2 ÷ 3  =  42/10 ÷ 3

4.2 ÷ 3  =  42/10 x 1/3

4.2 ÷ 3  =  14/10

4.2 ÷ 3  =  1.4

Method 2 :

Find 18.5 ÷ 5

Solution :

First, let us find 185 ÷ 5. We get 37

There is one digit to the right of the decimal point in 18.5.

Place the decimal point in 37 such that there would be one digit to its right.

Then, we will get 3.7

Dividing decimals by another decimal :

Find 17.6 ÷ 0.4

Solution :

First, let us write both the decimals 17.6 and 0.4 as 176/10 and 4/10.

Now, we can divide 176/10 by 4/10 as given below.

17.6 ÷ 0.4  =  176/10 ÷ 4/10

17.6 ÷ 0.4  =  176/10 x 10/4

17.6 ÷ 0.4  =  44

After having gone through the stuff given above, we hope that the students would have understood "Operations with decimals".

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