Table of Contents
Last modified on June 28th, 2024
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.
Here are some more equivalent fractions.
| Unit Fraction | Equivalent Fractions |
|---|---|
| ${\dfrac{1}{4}}$ | ${\dfrac{2}{8}}$, ${\dfrac{3}{12}}$, ${\dfrac{4}{16}}$, ${\dfrac{5}{20}}$, … |
| ${\dfrac{1}{5}}$ | ${\dfrac{2}{10}}$, ${\dfrac{3}{15}}$, ${\dfrac{4}{20}}$, ${\dfrac{5}{25}}$, … |
| ${\dfrac{1}{6}}$ | ${\dfrac{2}{12}}$, ${\dfrac{3}{18}}$, ${\dfrac{4}{24}}$, ${\dfrac{5}{30}}$, … |
| ${\dfrac{1}{7}}$ | ${\dfrac{2}{14}}$, ${\dfrac{3}{21}}$, ${\dfrac{4}{28}}$, ${\dfrac{5}{35}}$, … |
| ${\dfrac{1}{8}}$ | ${\dfrac{2}{16}}$, ${\dfrac{3}{24}}$, ${\dfrac{4}{32}}$, ${\dfrac{5}{40}}$, … |
| ${\dfrac{1}{9}}$ | ${\dfrac{2}{18}}$, ${\dfrac{3}{27}}$, ${\dfrac{4}{36}}$, ${\dfrac{5}{45}}$, … |
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 ${\dfrac{2}{10}}$
${\dfrac{1}{5}}$ is equivalent to ${\dfrac{2}{10}}$
${\dfrac{1}{5}}$ is equivalent to ${\dfrac{2}{10}}$
To get equivalent fractions, we multiply or divide the numerator and denominator of a given fraction 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 ${\dfrac{3}{4}}$.
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 ${\dfrac{30}{20}}$.
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:
${\dfrac{5\times 2}{3\times 2}}$ = ${\dfrac{10}{6}}$
${\dfrac{5\times 3}{3\times 3}}$ = ${\dfrac{15}{9}}$
${\dfrac{5\times 4}{3\times 4}}$ = ${\dfrac{20}{12}}$
${\dfrac{5\times 5}{3\times 5}}$ = ${\dfrac{25}{15}}$
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.
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.
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
Verify whether the fractions ${\dfrac{12}{18}}$ and ${\dfrac{16}{24}}$ are equivalent.
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 ${\dfrac{2}{3}}$
Here,Â
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 ${\dfrac{2}{3}}$
Last modified on June 28th, 2024