# Equivalent fractions with tenths and hundredths

## In a nutshell

The is no limit to the way a fraction can be expressed. Different looking fractions can represent the same value even if the numerators and denominators involved are multiples of tens or hundreds apart.

## Vocabulary reminder

The word **equivalent** means **equal in value**. So if two fractions are equivalent, they represent the same value.

##### Example 1

*The following fractions are equivalent:*

*$\dfrac3{10}$ and $\dfrac{60}{200}$*

## Showing equivalence

### Using common denominators

One way to check whether two fractions are equivalent is to make the denominators the same before comparing numerators.

##### Example 2

*Are the following fractions equivalent?*

*$\dfrac4{10}$ and $\dfrac{90}{300}$*

*To make both denominators the same, pick a common denominator. Here you can use $300$:*

*$\dfrac4{10}=\dfrac{4\times30}{10\times30}=\dfrac{120}{300}$*

*Now compare numerators. *

*As $90$ and $120$ are not equal, $\dfrac4{10}$ and $\dfrac{90}{300}$ **are not equivalent fractions**.*

### Simplifying fractions

Alternatively, simplifying fully will also tell you if two fractions are equivalent.

##### Example 3

*Consider again the fractions:*

*$\dfrac3{10}$ and $\dfrac{60}{200}$*

*Their equivalence can be shown by fully simplifying each fraction. The first fraction is already fully simplified since there are no factors (other than $1$) in common between the numerator and the denominator. The second fraction can be simplified. This can be done in steps: first divide the numerator and denominator by $2$ and then by $10$:*

*$\dfrac{60}{200}=\dfrac{\cancel{60}^{\space\space30}}{\cancel{200}^{\space\space100}}=\dfrac{\cancel{30}^{\space\space3}}{\cancel{100}^{\space\space10}}=\dfrac3{10}$*

* As $\dfrac{60}{200}=\dfrac3{10}$, **they are equivalent fractions**.*