# Equivalent

## Equivalent

Synonym for “has the same value as” or “is equal to.”

This word is used in many different expressions and contexts where we compare two quantities or two representations. Because of this, “written forms” can be equivalent if they translate the same reality; “surfaces” can be equivalent if they have the same area; expressions can be equivalent if they state the same thing in different ways or if they have the same logical value; etc.

### Examples

• The written forms $$0,5$$, $$\dfrac{1}{2}$$ and $$50 \%$$ are different ways of writing the same real number: $$0,5$$ is the decimal form, $$\dfrac{1}{2}$$ is the fractional form, and $$50 \%$$ is the representation of the equivalent fraction $$\dfrac{50}{100}$$ in the form of a percentage.
• The sequences of operations $$5\times \left( 7-2\right)$$ and $$\left( 5\times 7\right) -\left( 5\times 2\right)$$ are equivalent because they give the same result (the same value). We could also write $$5\times \left( 7-2\right)=\left( 5\times 7\right) -\left( 5\times 2\right)$$
• The equations $$5x=40$$ and $$2x = 16$$ are equivalent because they have the same solution set, which is $${8}$$.