Equivalent Fractions

Equivalent fractions are different fractions that represent the same part of a whole having the same value. This equivalence results from multiplying or dividing the numerator and the denominator by the same number.

Examples

Here are some more equivalent fractions.

How To Represent

We can represent equivalent fractions by comparing them on a bar model or number lines.

Let us represent ${\dfrac{1}{5}}$ and its equivalent fraction ${\dfrac{2}{10}}$

Using Bar Model

${\dfrac{1}{5}}$ is equivalent to ${\dfrac{2}{10}}$

Using Number Line

${\dfrac{1}{5}}$ is equivalent to ${\dfrac{2}{10}}$

How To Find

To get equivalent fractions, we multiply or divide the numerator and denominator of a given fraction by the same number.

Multiplying by the Same Number

Let us find the equivalent fractions of ${\dfrac{3}{4}}$ by multiplying both numerator and denominator by the same number.

Here, ${\dfrac{6}{8}}$ and ${\dfrac{12}{16}}$ are equivalent fractions of ${\dfrac{3}{4}}$.

Dividing by the Same Number

Let us find the equivalent fractions of ${\dfrac{30}{20}}$ by dividing both numerator and denominator by the same number.

Here, ${\dfrac{15}{10}}$ and ${\dfrac{3}{2}}$ are equivalent fractions of ${\dfrac{30}{20}}$.

For Mixed Numbers

If the given mixed fraction is ${1\dfrac{2}{3}}$

First, we will convert the mixed number into an improper fraction and then find its equivalent fractions.

${1\dfrac{2}{3}}$ = ${\dfrac{\left( 1\times 3\right) +2}{3}}$ = ${\dfrac{5}{3}}$

Thus, the equivalent fractions of ${\dfrac{5}{3}}$ are:

${\dfrac{5\times 2}{3\times 2}}$ = ${\dfrac{10}{6}}$

${\dfrac{5\times 3}{3\times 3}}$ = ${\dfrac{15}{9}}$

${\dfrac{5\times 4}{3\times 4}}$ = ${\dfrac{20}{12}}$

${\dfrac{5\times 5}{3\times 5}}$ = ${\dfrac{25}{15}}$

How To Determine

Making the Denominators the Same

Let us determine whether ${\dfrac{5}{10}}$ and ${\dfrac{1}{2}}$ are equivalent.

Since ${\dfrac{1}{2}}$ = ${\dfrac{5}{10}}$, the given fractions are equivalent.

Cross Multiplying

Now, by cross-multiplying the fractions ${\dfrac{5}{10}}$ and ${\dfrac{1}{2}}$ fractions, we get

Since both the products are equal, the fractions ${\dfrac{5}{10}}$ and ${\dfrac{1}{2}}$ are equivalent fractions.

Converting to Decimals

Finding their decimal numbers is also a way to verify whether the given fractions are equivalent.

Converting ${\dfrac{5}{10}}$ and ${\dfrac{1}{2}}$ to the decimal form, we get

Solved Examples

Verify whether the fractions ${\dfrac{12}{18}}$ and ${\dfrac{16}{24}}$ are equivalent.

Solution:

In the given fractions, the denominators are 18 and 24
LCM of 18 and 24 are 72
Now, for making the denominators of the given fractions equal, we get
${\dfrac{12\times 4}{18\times 4}}$ = ${\dfrac{48}{72}}$
${\dfrac{16\times 3}{24\times 3}}$ = ${\dfrac{48}{72}}$
Thus the fractions ${\dfrac{12}{18}}$ and ${\dfrac{16}{24}}$ are equivalent.

Is ${\dfrac{8}{12}}$ an equivalent fraction of ${\dfrac{2}{3}}$

Solution:

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On dividing the numerator and the denominator of ${\dfrac{8}{12}}$ by 4, we get
${\dfrac{8\div 4}{12\div 4}}$ = ${\dfrac{2}{3}}$
Thus, ${\dfrac{8}{12}}$ is an equivalent fraction of ${\dfrac{2}{3}}$