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Home >> Equality >> Subtract same number >>

Subtract same number from 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 subtracted from 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 - Subtract 5 from both the sides of given equation and check what happens to equality
4 + 2 = 2 X 3

Solution - This proceeds as :
Subtract 5 from both sides of given equation and we get;
4 + 2 – 5 = 2 X 3 - 5

Solve L.H.S. and we get;
L.H.S. = 4 + 2 – 5
Now solve as per BODMAS rule and we get;
L.H.S.= 1

Solve R.H.S. and we get
R.H.S. = 2 X 3 - 5
Now solve as per BODMAS rule and we get;
R.H.S.= 1

Since L.H.S. = R.H.S i.e. 1 = 1

So the given equation 4 + 2 = 2 X 3, is said to be in equality even after subtracting 5 from both the sides and hence we get
“When same number is subtracted both the sides of equation, equality still holds true.”


Example 2 - Subtract 9 from both the sides of given equation and check what happens to equality
26 + 10 = 30 + 6

Solution - This proceeds as :
Subtract 9 from both sides of given equation and we get;
26 + 10 -9 = 30 + 6 - 9

Solve L.H.S. and we get;
L.H.S. = 26 + 10 -9
Now solves as per BODMAS rule and we get;
L.H.S. = 27

Solve R.H.S. and we get
R.H.S. = 30 + 6 - 9
Now solves as per BODMAS rule and we get;
R.H.S.= 27

Since L.H.S. = R.H.S i.e. 27 = 27

So the given equation 26 + 10 = 30 + 6, is said to be in equality even after subtracting 9 from both the sides and hence we get
“When same number is subtracted both the sides of equation, equality still holds true.”

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