## Equivalent Fractions

#### Introduction

Equivalent fractions are fractions that are equal. In order to determine if one fraction is equal or equivalent to another, both fractions must first be simplified if needed.

#### Terms

**- Fractions are used when using numbers to express parts of whole.**

**- a fraction expressed in its lowest terms.**

## Lesson

To determine if a fraction is equivalent to another, we need to compare the two fractions in their simplest form. So if we are given $rac{1}{4}$ and $rac{2}{8}$, we can see that $rac{1}{4}$ is in its simplest form, but $rac{2}{8}$ can be further reduced to $rac{1}{4}$ by dividing the top and bottom by 2.

$dfrac{2}{8} div dfrac{2}{2} = dfrac{1}{4}$

Therefore $rac{1}{4}$ and $rac{2}{8}$ are equivalent fractions.

Similarly, if we are given $rac{5}{10}$ and $rac{21}{30}$, we first simplify both fractions.

$dfrac{5}{10} div dfrac{5}{5} = dfrac{1}{2}$

$dfrac{21}{30} div dfrac{3}{3} = dfrac{7}{10}$

We can now see that $rac{5}{10}$ is NOT equivalent to $rac{21}{30}$, because $rac{1}{2}$ is not equivalent to $rac{7}{10}$

To find the equivalent of a fraction when we are given either the numerator or denominator is similar to expressing a fraction in higher terms. If we are told to solve the following problem:

$dfrac{3}{10} = dfrac{15}{?}$

we can determine that in order for the new numerator to equal 15, the original numerator must be multiplied by 5. So we multiply the denominator by 5 as well, and get the answer

$dfrac{3}{10} = dfrac{15}{50}$