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Home >> Equality >> Subtract different number >>

Subtract different number from 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 different numbers are subtracted from the sides of equation i.e. L.H.S. and R.H.S of the equation, the equality fails to hold.

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

Example 1 - Subtract 3 from L.H.S. and 5 from R.H.S. of given equation and check what happens to equality
2 X 10 = 5 X 4

Solution - This proceeds as :
Subtract 3 from L.H.S. & 5 from R.H.S. of given equation and we get;
2 X 10 – 3 = 5 X 4 - 5

Solve L.H.S. and we get;
L.H.S. = 2 X 10 – 3
Now solves as per BODMAS rule and we get;
L.H.S. = 17

Solve R.H.S. and we get
R.H.S. = 5 X 4 - 5
Now solves as per BODMAS rule and we get;
R.H.S.= 15

Since L.H.S. in not equals to R.H.S i.e. 17 is not equal to 15

So the given equation 2 X 10 = 5 X 4 fails to hold equality, when we subtract 3 from L.H.S. and 5 from R.H.S. of given equation and hence we get that
“When different numbers are subtracted from the sides of equation i.e. L.H.S. and R.H.S of the equation, the equality fails to hold.”


Example 2 - Subtract 6 from L.H.S. and 8 from R.H.S. of given equation and check what happens to equality
50 - 20 = 20 + 10

Solution - This proceeds as :
Subtract 6 from L.H.S. & 8 from R.H.S. of given equation and we get;
50 - 20 – 6 = 20 + 10 - 8

Solve L.H.S. and we get;
L.H.S. = 50 - 20 – 6
Now solves as per BODMAS rule and we get;
L.H.S. = 24

Solve R.H.S. and we get
R.H.S. = 20 + 10 - 8
Now solves as per BODMAS rule and we get;
R.H.S.= 22

Since L.H.S. in not equals to R.H.S i.e. 24 is not equal to 22

So the given equation 50 - 20 – 6 = 20 + 10 - 8 fails to hold equality, when we subtract 6 from L.H.S. and 8 from R.H.S. of given equation and hence we get that
“When different numbers are subtracted from the sides of equation i.e. L.H.S. and R.H.S of the equation, the equality fails to hold.”
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