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# Equivalent Fractions

Equivalent fractions are the types of fractions in which the values of the numerator and denominator remains the same. Equivalent Fractions is one of the important concepts within the study of fractions. This page tries to give you an understanding over the whole equivalent fractions concepts. The page flow goes this way, first a brief description is given for equivalent fractions and then providing examples on equivalent fractions and further making you learn how to do equivalent fractions. Thus grab a quality learning here.

Before we get into understanding equivalent fractions, its important to know the basic operations in fractions like, adding, subtracting, multiplying, how to reduce and how to convert fractions. While learning about equivalent fractions online one must be careful in finding the following points. This helps you identify the equal fractions.
Whole numbers must be in the numerator and denominator
To check whether the given fractions are equivalent, we can divide or multiply the numerator and denominator with the same number.
Please don't add or subtract any numbers from the numerator and denominator to get the fractions which are equivalent.

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## What are Equivalent Fractions?

Equivalent fractions are fractions that have the equal value or which represent the same part of an object. If an apple is cut into two pieces, each piece is also one-half of the apple. If an apple is cut into 6 pieces, then that three pieces denote the same amount of apple that $\frac{1}{2}$ did. We say that $\frac{1}{2}$ is equivalent to $\frac{3}{6}$. Equivalent means equal in value. Fraction can look different but they can have same value and hence equivalent. These fractions have the value same,

Example:
$\frac{1}{2}$=$\frac{3}{6}$=$\frac{6}{12}$

## Equivalent Fractions Definition

The equivalent fractions are fractions that are equal to the each other. We can use cross multiplication to decide to whether two fractions are equivalent. The fractions that explain the same amount are called equivalent fractions.

The equivalent fractions of the same value or equivalent means equal in value. Fraction can look different but be equivalent. These fractions are really the same,

Example: $\frac{2}{3}$ = $\frac{8}{12}$ = $\frac{32}{48}$

## Equivalent Fractions Chart

The common denominator is add and subtract fraction each fraction must have a common denominator they must be same thing. In fraction we must find a number that all the denominators will divide evenly into, Example look at the fraction $\frac{1}{2}$ and $\frac{1}{3}$

The denominators for these fractions are 2 and 3. A number that 2 and 3 will divide into evenly is 6. We can express both of these fractions as sixths, and so give them both a common denominator.

 Basic Fraction Equivalent Fraction $\frac{1}{6}$ $\frac{2}{32}$,$\frac{3}{48}$,$\frac{4}{64}$,$\frac{5}{80}$,$\frac{6}{96}$,$\frac{7}{112}$,$\frac{8}{128}$,$\frac{9}{144}$ $\frac{1}{12}$ $\frac{2}{24}$,$\frac{3}{36}$,$\frac{4}{48}$,$\frac{5}{60}$,$\frac{6}{72}$,$\frac{7}{84}$,$\frac{8}{96}$,$\frac{9}{108}$ $\frac{1}{10}$ $\frac{2}{20}$,$\frac{3}{30}$,$\frac{4}{40}$,$\frac{5}{50}$,$\frac{6}{60}$,$\frac{7}{70}$,$\frac{8}{80}$,$\frac{9}{90}$ $\frac{1}{8}$ $\frac{2}{16}$,$\frac{3}{24}$,$\frac{4}{32}$,$\frac{5}{40}$,$\frac{6}{48}$,$\frac{7}{56}$,$\frac{8}{64}$,$\frac{9}{72}$ $\frac{1}{7}$ $\frac{2}{14}$,$\frac{3}{21}$,$\frac{4}{28}$,$\frac{5}{35}$,$\frac{6}{42}$,$\frac{7}{49}$,$\frac{8}{56}$,$\frac{9}{63}$ $\frac{1}{6}$ $\frac{2}{12}$,$\frac{3}{18}$,$\frac{4}{24}$,$\frac{5}{30}$,$\frac{6}{36}$,$\frac{7}{42}$,$\frac{8}{48}$,$\frac{9}{54}$ $\frac{1}{5}$ $\frac{2}{10}$,$\frac{3}{15}$,$\frac{4}{20}$,$\frac{5}{25}$,$\frac{6}{30}$,$\frac{7}{35}$,$\frac{8}{40}$,$\frac{9}{45}$ $\frac{1}{4}$ $\frac{2}{8}$,$\frac{3}{12}$,$\frac{4}{16}$,$\frac{5}{20}$,$\frac{6}{24}$,$\frac{7}{28}$,$\frac{8}{32}$,$\frac{9}{36}$ $\frac{1}{3}$ $\frac{2}{6}$,$\frac{3}{9}$,$\frac{4}{12}$,$\frac{5}{15}$,$\frac{6}{18}$,$\frac{7}{21}$,$\frac{8}{24}$,$\frac{9}{27}$ $\frac{1}{2}$ $\frac{2}{4}$,$\frac{3}{6}$,$\frac{4}{8}$,$\frac{5}{10}$,$\frac{6}{12}$,$\frac{7}{14}$,$\frac{8}{16}$,$\frac{9}{18}$

## How to do Equivalent Fractions

Its an easy task to identify the equivalent fractions on checking numerator and denominator value. Below see some solved examples on how to find equivalent fractions.

### Solved Examples

Question 1: Find three equivalent fraction of $\frac{2}{3}$.
Solution:

The numerator is 2 and denominator is 3

Multiply the numerator and denominator with 2.So, $\frac{2}{3}$ = $\frac{4}{6}$

Multiply the numerator and denominator with 3.So, $\frac{2}{3}$ = $\frac{6}{9}$

Multiply the numerator and denominator with 4.So, $\frac{2}{3}$ = $\frac{8}{12}$

Three equivalent fraction of $\frac{2}{3}$ is $\frac{4}{6}$, $\frac{6}{9}$. $\frac{8}{12}$.

Question 2: $\frac{3}{7}$ =$\frac{9}{?}$
Solution:

We know the numerators of the two fractions. They are 3 and 9.

Relation between them 3 times 3 is 9. So, multiply the denominator also with 3.

So 7 x 3 = 21. $\frac{3}{7}$ is equivalent to $\frac{9}{21}$.

So the unknown is $\frac{9}{21}$

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