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Equivalent Fractions

Fractions are a part of a whole. Fractions are represented as $\frac{a}{b}$, where a and b both are integers. Fractions which are not in the simple form can be reduced to their simplest forms. Equivalent fractions are those which when simplified have the same value.

If we have a pizza and we cut it into two equal parts, then each part of pizza is one half of the whole and if we cut the pizza into four equal parts, then two parts of pizza represents the same amount as one half of the pizza. This means $\frac{2}{4}$ is equal to $\frac{1}{2}$.

For example, $\frac{3}{12}$ can be reduced as $\frac{1}{4}$, since 3 is the common factor of both numerator and denominator. Here, $\frac{3}{12}$ and $\frac{1}{4}$ are called as equivalent fractions.

Each fraction has infinite number of equivalent fractions. Equivalent fractions have same value, even though they may look different. 
We can make equivalent fractions by multiplying or dividing both top and bottom by the same number.

$\frac{2}{4}$ = $\frac{2 \times 2}{4 \times 2}$ = $\frac{4}{8}$  (Multiplying and dividing by 2)

$\frac{2}{4}$ = $\frac{2 \times 10}{4 \times 10}$ = $\frac{20}{40}$ (Multiplying and dividing by 10)
  
$\frac{2}{4}$ = $\frac{\frac{2}{2}}{\frac{4}{2}}$ = $\frac{1}{2}$ (Multiplying and dividing by $\frac{1}{2}$)

Here, $\frac{2}{4} = \frac{4}{8}=\frac{20}{40} = \frac{1}{2}$ all are equivalent fractions. Simple form and value of each fraction is $\frac{1}{2}$.

Value of all equivalent fractions is equal to its simplest form.
Let us consider one more example.

$\frac{1}{3}$ is the simple fraction which cannot be reduced further.

$\frac{1 \times 2}{3 \times2}$ = $\frac{2}{6}$ is an equivalent fraction of $\frac{1}{3}$. Value of $\frac{2}{6}$ is $\frac{1}{3}$.

$\frac{1 \times 3}{3 \times 3}$ = $\frac{3}{9}$ is an equivalent fraction of $\frac{1}{3}$. Value of this fraction is $\frac{1}{3}$.

$\frac{1 \times 100}{3 \times 100}$ = $\frac{100}{300}$ is an equivalent fraction of $\frac{1}{3}$. Value is $\frac{1}{3}$.

We can get infinite equivalent fractions of $\frac{1}{3}$ by multiplying the same number to both numerator and denominator. 
We divide fraction, when we have to find its simplified form or when we have to find the value of a fraction. We can express value of a fraction in decimal form also.

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