Understanding Properties of Equality

There are a variety of properties of equality in mathematics. They include addition, subtraction, multiplication, division, reflexive, symmetric, transitive, substitution, and zero product. The Addition Property of Equality is if a = b and c = d then a + c = b + d. An example of this property is where if a= 2, b = 2, c = 3, and d = 3, then 2 + 3 = 2 + 3 which results in 5 = 5. The resulting values on both sides of the equal sign are equal. The Subtraction Property of Equality is if a = b and c = d then a – c = b – d. An example of this property is where if a= 2, b = 2, c = 3, and d = 3, then 2 - 3 = 2 - 3 which is equal to -1 = -1. The results on each side of the equal sign are the same value.

Similarly, equality properties also apply to multiplication and division. The Multiplication Property of Equality is if a = b and c = d then ac = bd. For example, if a = 3, b = 3, c = 4, and d = 4, then 3 * 4 = 3 * 4 which results in 12 = 12 . Values on each side of the equal sign are the same. In the case of the property of equality for division, the divisor can never be equal to zero for any value divided by zero is 'undefined. The Division Property of Equality is if a = b then a/c = b/c provided that c is not equal to 0. Dividing a number by 0 is undefined. An example of this property is if a = 2, b = 2, and c = 4 then 2/4 = 2/4 which results in .5 = .5. Both values of each side of the equal sign are equal.

Other properties of equality include the Reflexive, Symmetric, Transitive, Substitution and Zero properties. The Reflexive Property of Equality is where a = a. A value is always equal to itself. The Symmetric Property of Equality is where if a+b = b+a then b+a = a+b. For example, if a = 5 and b = 6 then 6 + 5 = 5 + 6 or 11 = 11. Values on both sides of the equal sign are the same. The Symmetric property can also be applied to multiplication.  For example,  2 * 3 = 3 * 2. The Transitive Property of Equality is if a = b, and b = c, then a = c. For example, if a = 3, b = 3, and c = 3 then a = c because both values are the same value of ‘3’.
The Substitution Property of Equality is if a = b then either can be substituted for the other. The value of ‘3’ assigned to ‘a’ can also be assigned to ‘b’. The Zero Property of Equality is if ab = 0, then a = 0, b = 0, or both. One value, either for ‘a’ or ‘b’ (or both) is zero and zero times a number results in zero.