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Finding Equivalent Fractions

Equivalent fractions are the fractions which have same value. Equivalent fractions may appear different, but they give same value when simplified. If numerator and denominator of a fraction are multiplied by same number, then the resulting fraction is said to be equivalent to previous one.

For example: If an apple pie is divided into two parts, then each part is $\frac{1}{2}$. If it is divided into four parts and 2 are chosen then we say that it is $\frac{2}{4}$.

Similarly, when pie is cut into 8 parts, out of then four parts are chosen, it means the fraction is represented as $\frac{4}{8}$. This can be shown in figure below:
Equivalent Fractions
So, we can write that,
$\frac{1}{2}$$\frac{2}{4}$$\frac{4}{8}$ = .....


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Examples

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Finding Equivalent Fractions

(1) Multiplying numerator and denominator by same number: If we multiply numerator and denominator of a fraction by a same number, the value of the fraction does not change and we can get equivalent fraction.
Thus, we can write -
Equivalent Fraction

Example: 
Find two fractions equivalent to $\frac{2}{3}$.

Solution: Multiply and divide $\frac{2}{3}$ by 2,

$\frac{2}{3}$ = $\frac{2 \times 2}{3 \times 2}$ = $\frac{4}{6}$

Multiply and divide $\frac{4}{6}$ by 2,

$\frac{4}{6}$ = $\frac{4 \times 2}{6 \times 2}$ = $\frac{8}{12}$

Therefore, $\frac{2}{3}$ = $\frac{4}{6}$ = $\frac{8}{12}$

(2) Dividing numerator and denominator by same number: If we divide the numerator and denominator of a fraction by a same number, then value of fraction remains unchanged. In this way, we obtain equivalent fraction:
Equivalent Fractions

Example:
 Find two fractions equivalent to $\frac{25}{125}$.

Solution: Dividing numerator and denominator by 5,

$\frac{25}{125}$ = $\frac{25\div 5}{125\div 5}$ = $\frac{5}{25}$

Dividing numerator and denominator of $\frac{5}{25}$ by 5,

$\frac{5}{25}$ = $\frac{5\div 5}{25\div 5}$ = $\frac{1}{5}$

Therefore, $\frac{25}{125}$ = $\frac{5}{25}$ = $\frac{1}{5}$

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