Symmetric property of equality

The symmetric property of equality is one of the basic properties of equality in mathematics. Others include the reflexive and transitive properties of equality. The symmetric property of equality states that for two variables, a and b:

if a = b, then b = a

This just means that regardless which side of an equal sign any given variables are on, the two variables (or expressions) are equal. This is used widely throughout mathematics, such as in algebra, in which equations are solved based on the understanding that expressions on either side of any given equation are equal. It is also worth noting that when solving equations in algebra, the result x = 12 is the same as 12 = x. Although both are correct, by convention, the variable is typically written on the left hand side of the equation.


1. If 3 + 4 = 7, then 7 = ?:

7 = 3 + 4 or 7 = 4 + 3

2. If A = l × w, then l × w = ?:

l × w = A or w × l = A

It doesn't matter how the numbers or variables are re-arranged on the same side of the equation, they will remain equal as long as any operations applied to either side are applied to the other side in exactly the same way. It is common to manipulate equations in this manner in algebra. For example, if we added 5 to both sides of the equation in example 1, although the value would change, the expressions would remain equal:

3. If 3 + 4 + 5 = 7 + 5:

7 + 5 = 7 + 5

12 = 12