Table of Contents

Last modified on July 19th, 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.**

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:

Here,

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 July 19th, 2024