Mathematical equality

Mathematical equality is the proposition of equivalence between two algebraic expressions connected through the sign = in which both express the same value.

The equality relationship established in such an expression is used to denote that two mathematical objects express the same value.

9 – 1 = 8

Mathematical equality is an expression that is made up of two members. The member on the right, on the left side of the equal sign and the member on the left, on the right side of the equality sign. The solution of the previous statement reveals the approach of equality of expressions. Thus, the member on the left results in a value of eight, equal to the value of the member on the right, which is also eight.

It is said that an expression of equality is false, when the result of one of its members is different from the other. Thus, the following expression turns out to be false.

10x + 2 = 5 * (2x + 5)

As the result of this expression is: 10x + 2 = 10x + 25 that expression turns out to be false.

Also, it is said that an expression of equality turns out to be true when the result of both members of the approach turns out to be of the same value. Thus, the following expression turns out to be true.

10x + 2 = 5 * (2x + 1)

Since the result of this expression is: 10x + 2 = 10x + 5, that expression turns out to be true.

Properties of mathematical equality

  • If both members of the expression are multiplied by the same value, equality is maintained.
  • If we divide both members of the expression by the same value, equality is maintained.
  • If we subtract the same value from both members of expression, equality is maintained.
  • If we add the same value to both members of the expression, equality is maintained.

Finally, it is worth highlighting the importance of not confusing equation with mathematical equality. An equation is articulated by an equality although it may not be fulfilled. Such is the case of systems of equations that have no solution. On the other hand, a mathematical equality can be without being equation. For example:

5 = 5

It is an equality since 5 is equal to 5, but this does not constitute an equation because there are no unknowns.

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