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Home >> Equality >> Add same number >>

Add same number to both the sides of equality

Add same number Add different number Subtract same number Subtract different number Multiply with same number
Multiply with different numbers Divide by same number Divide by different number

Explanation: When same number is added to both the sides of equation i.e. L.H.S. and R.H.S of the equation, the equality still holds true.

Let’s understand it with the help of following examples:

Example 1 - Add 5 to both the sides of given equation and check what happens to equality
4 X 3 = 2 X 6
Solution - This proceeds as :
Add 5 to both sides of given equation and we get;
5 + 4 X 3 = 5 + 2 X 6

Solve L.H.S. and we get;
L.H.S. = 5 + 4 X 3
Now solve as per BODMAS rule and we get;
L.H.S. = 17

Solve R.H.S. and we get
R.H.S. = 5 + 2 X 6
Now solve as per BODMAS rule and we get;
R.H.S. = 17

Since L.H.S. = R.H.S i.e. 17 = 17

So the given equation 4 X 3 = 2 X 6, is said to be in equality even after adding 5 to both the sides and hence we get

“When same number is added to both the sides of equation, equality still holds true.”


Example 2 - Add 10 to both the sides of given equation and check what happens to equality
15 + 1 = 20 - 4
Solution - This proceeds as :
Add 10 to both sides of given equation and we get;
15 + 1 + 10 = 20 – 4 +10

Solve L.H.S. and we get;
L.H.S. = 15 + 1 + 10
L.H.S. = 26

Solve R.H.S. and we get
R.H.S. = 20 – 4 +10
Now solve as per BODMAS rule and we get;
= 26
Since L.H.S. = R.H.S i.e. 26 = 26

So the given equation 15 + 1 = 20 - 4, is said to be in equality even after adding 10 to both the sides and hence we get

“When same number is added to both the sides of equation, equality still holds true.”

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