Properties of Equality

Properties of equality are one of the major concepts in basic mathematics. Before realizing the properties of equality, let’s have a revision of the basic operations of mathematics – addition, subtraction, multiplication and division. Addition refers to combination of objects resulting larger number. Subtraction refers to reducing a part from a collection. Multiplication means scaling one number by another and division is that which includes a dividend, quotient, divisor and remainder. For example: Mother bought food for kids of Rs.500, nestle products for babies for Rs. 200 and some angry bird toys India for John for Rs.150. She paid total of 500 + 200 + 150 = Rs. 850 (addition). She bought three angry bird toys India for John and later gave one to Tina from the collection. John after that has 3-1 = 2 angry bird toys (subtraction). John said he will allow his five friends to play twice with the angry bird toys. Al together they played 5x2 = 10 times (multiplication). Mother bought 6 nestle products for two babies equally. Each baby has 6/2 = 3 nestle products (division).

Properties of equality are applied to all these four mathematical operations. There are eight properties of equality.
1. Reflexive Property: This refers to x=x. For example: 2=2, 3=3, 4=4 or I am equal t myself.
2. Symmetric Property: This refers to x =y, y =x. For example Cerelac food for Rs. 250 and Gerber food for Rs.150 = total food for kids costing Rs. 400.
3. Transitive Property: This refers to x=y, y=z, then x=z. For example: Ana’s weight is equal to Tina’s weight and Tina’s weight is equal to Peter’s weight. Therefore, Ana’s weight is equal to Peter’s weight.
4. Addition Property: If x=y, then x+ z = y+ z. For example: Ana’s weight is equal to Tina’s weight. Then, Ana’s weight + 3 kg = Tina’s weight + 3 kg.
5. Subtraction Property: If x= y, then x-z = y – z. For example: Ana’s weight – 2 kg = Tina’s weight – 2 kg.
6. Multiplication Property: If x= y, then x * z = y * z. For example: Ana’s weight * 2 kg = Tina’s weight * 2 kg.
7. Division Property: If x= y, then x/z = y/z. For example: Ana’s weight / 2 kg = Tina’s weight / 2 kg.
8. Substitution Property: If x = y, then y can be substituted for x in any mathematical expression.
These are the properties of equality.