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Home >> Equality >> Divide by different number >>

Divide sides of equality with different numbers

 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 the sides of equation i.e. L.H.S. and R.H.S of the equation are divided by different numbers, the equality fails to holds.

Lets understand it with the help of following examples:

Example 1 - Divide L.H.S. by 2 and R.H.S. by 3 of given equation and check what happens to equality

2 + 4 = 3 + 3

Solution - This proceeds as :

Divide L.H.S. by 2 and R.H.S. by 3 of given equation and we get;

(2 + 4) / 2 = (3 + 3) / 3

Solve L.H.S. and we get;

L.H.S. = (2 + 4) / 2
L.H.S. = 3

Solve R.H.S. and we get

R.H.S. = (3 + 3) / 3
R.H.S. = 2

Since L.H.S. in not equals to R.H.S i.e. 2 is not equal to 3

So the given equation 2 + 4 = 3 + 3 fails to hold equality, when we divide L.H.S. by 2 and R.H.S. by 3 of given equation and hence we get that
"When the sides of equation i.e. L.H.S. and R.H.S of the equation are divided by different numbers, the equality fails to holds."

Example 2 - Divide L.H.S. by 5 and R.H.S. by 7 of given equation and check what happens to equality

30 + 5 = 40 - 5

Solution - This proceeds as:

Divide L.H.S. by 5 and R.H.S. by 7 of given equation and we get;

(30 + 5) / 5 = (40 - 5) / 7

Solve L.H.S. and we get;

L.H.S. = (30 + 5) / 5
L.H.S. = 7

Solve R.H.S. and we get

R.H.S. = (40 - 5) / 7
R.H.S. = 5

Since L.H.S. in not equals to R.H.S i.e. 7 is not equal to 5

So the given equation 30 + 5 = 40 - 5 fails to hold equality, when we divide L.H.S. by 5 and R.H.S. by 7 of given equation and hence we get that
"When the sides of equation i.e. L.H.S. and R.H.S of the equation are divided by different numbers, the equality fails to holds."