DECIMAL ADDITION

About "Decimal addition"

Decimal addition :

The process of adding and subtracting decimals are similar to adding and subtracting whole numbers.

The place value is important. It is important to arrange the digits one below the other according to the place values. 

While adding 7235 with 47, we have to arrange the numbers as

aaaaaaaaaaaaaaaaaaa7 2 3 5 aaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaa+        4 7 aaaaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaa-----------aaaaaaaaaaaaaaaaaaaaaaaaaa   aaaaaaaaaaaaaaaaa-----------

Not asaaaaaaaaaaaaa7 2 3 5 aaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaa+  4 7 aaaaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaa-----------aaaaaaaaaaaaaaaaaaaaaaaaaa   aaaaaaaaaaaaaaaaa-----------

Decimal addition

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 as we arrange in whole numbers. Then 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. 

Apart from the stuff "Decimal addition", let us look at how to subtract decimals. 

Subtraction of 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 as we arrange in whole numbers. Then subtract them.  

Subtract 0.75 from 2

Not asaaaaaaaaaaaaaaaaa2 . 0 0 aaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaa--  0 . 7 5 aaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaa-----------aaaaaaaaaaaaaaaaaaaa   aaaaaaaaaaaaaaaaaaaaaaa1 . 2 5  aaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaa-----------

In the above addition of decimals, 2 is taken as 2.00, as the second decimal number has two digits on the right side of the decimal point. 

Addition and subtraction of decimals - Practice problems

Questions : 

Simplify the following decimals :

1)  0.36 + 0. 589

2)  1.26 + 1.369

3)  3.286 - 0.689

4)  0.55 - 0.25

5) 3.25 + 2.856

Solution : 

1)  0.949

2)  2.629

3)  2.597

4)  0.30

5)  6.106

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

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