Multiply both 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 multiplied with different numbers, the equality fails to holds. Let's understand it with the help of following examples: Example 1 - Multiply L.H.S. by 2 and R.H.S. by 3 of given equation and check what happens to equality 2 X 10 = 5 X 4 Solution - This proceeds as : Multiply L.H.S. by 2 and R.H.S. by 3 of given equation and we get; 2 X 10 X 2 = 5 X 4 X 3 Solve L.H.S. and we get; L.H.S. = 2 X 10 X 2 L.H.S. = 40 Solve R.H.S. and we get R.H.S. = 5 X 4 X 3 R.H.S. = 60 Since L.H.S. in not equals to R.H.S i.e. 40 is not equal to 60 So the given equation 2 X 10 = 5 X 4 fails to hold equality, when we multiply 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 multiplied with different numbers, the equality fails to holds." Example 2 - Multiply L.H.S. by 5 and R.H.S. by 7 of given equation and check what happens to equality 5 + 2 = 6 + 1 Solution - This proceeds as: Multiply L.H.S. by 5 and R.H.S. by 7 of given equation and we get; (5 + 2) X 5 = (6 + 1) X 7 Solve L.H.S. and we get; L.H.S. = (5 + 2) X 5 L.H.S. = 35 Solve R.H.S. and we get R.H.S. = (6 + 1) X 7 R.H.S. = 49 Since L.H.S. in not equals to R.H.S i.e. 35 is not equal to 49 So the given equation 5 + 2 = 6 + 1 fails to hold equality, when we multiply 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 multiplied with different numbers, the equality fails to holds."