Multiply both sides of equality with same number

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 both the sides of equation i.e. L.H.S. and R.H.S of the equation are multiplied with same number, the equality still holds true. Let's understand it with the help of following examples: Example 1 - Multiply both the sides of given equation with 10 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; 4 X 3 X 10 = 2 X 6 X 10 Solve L.H.S. and we get; L.H.S. = 4 X 3 X 10 L.H.S. = 120 Solve R.H.S. and we get R.H.S. = 2 X 6 X 10 R.H.S. = 120 Since L.H.S. = R.H.S i.e. 120 = 120 So the given equation 4 X 3 = 2 X 6, is said to be in equality even after multiplying both sides by 10 and hence we get "When both the sides of equation i.e. L.H.S. and R.H.S of the equation are multiplied with same number, the equality still holds true." Example 2 - Multiply both the sides of given equation with 2 and check what happens to equality 3 + 3 = 5 + 1 Solution - This proceeds as : Add 5 to both sides of given equation and we get; (3 + 3) X 2 = (5 + 1) X 2 Solve L.H.S. and we get; L.H.S. = (3 + 3) X 2 L.H.S. = 12 Solve R.H.S. and we get R.H.S. = (5 + 1) X 2 R.H.S. = 12 Since L.H.S. = R.H.S i.e. 12 = 12 So the given equation 3 + 3 = 5 + 1, is said to be in equality even after multiplying both sides by 2 and hence we get "When both the sides of equation i.e. L.H.S. and R.H.S of the equation are multiplied with same number, the equality still holds true."