The equality properties can be classified according to the addition, subtraction, multiplication and multiplication of real numbers.

**1. Additive Property of Equality: **If equals are added to equals the wholes are equal.

( or ) When same quantity is added on both sides of an equation, the equality is unaffected.

Let a, b, c be any three real numbers, then a = b => a + c = b + c

**Example**: 5 = 5

=> 5 + 2 = 5 + 2 [ 2 is added on both sides of the equality ]

=> 7 = 7

**2. Subtractive property of Equality: **If equals are subtracted from equals, the results are equal. ( or ) when same quantity is subtracted from both sides of an equation, the equality is unaffected.

Let a, b, c be ay three real numbers, then a = b => a - c = b - c

** ****Example:** 5 = 5

=> 5 - 2 = 5 - 2 [ 2 is subtracted from both sides of the equality ]

=> 3 = 3

**3. ****Multiplicative property of Equality:** If equals are multiplied to equals, the results will be equal.

( or ) when both sides of an equation is multiplied by the same non-zero number, the equality is unaffected.

Let a, b, c be any three real numbers such that c $\ne$ 0. Then a = b => a x c = b x c => ac = bc

**Example:** 5 = 5

=> 5 x 3 = 5 x 3 [ 3 is multiplied on both sides of the equality ]

=> 15 = 15

**4. Division Property of Equality: **If equals are divided by the same non-zero equals, the results will be equal.

( or ) when both sides of an equation is divided by the same non-zero number, the equality is unaffected.

Let a, b and c be any three real numbers such that c = $\ne$ 0, then a = b => $\frac{a}{c}$ = $\frac{b}{c}$,

**Example:** 10 = 10

=> $\frac{10}{2}$ = $\frac{10}{2}$ [ 2 is divided on both sides of the equality ]

=> 5 = 5