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Fractions can be written as $\frac{p}{q}$, where ‘p’ and ‘q’ are whole Numbers and q ≠ 0. The fractions can be called equivalent when we find that the fractions in their lowest form are equal. If the lowest form of the fractions is not equal, it means that the fractions are not equivalent.
To reduce fractions we need to first find the HCF of the given numerator and the denominator and then we divide the numerator and the denominator by the highest common multiple which we have just calculated. All the Equivalent Fractions, when converted into their lowest form, results in the same fraction. |
Example :
Consider three fractions $\frac{3}{5}$, $\frac{9}{15}$ and $\frac{15}{25}$
$\frac{3}{5}$
The HCF of the numerator and the denominator of $\frac{3}{5}$ is 1
= $\frac{\frac{3}{1}}{\frac{5}{1}}$
= $\frac{3}{5}$
$\frac{9}{15}$
The HCF of the numerator and the denominator of $\frac{9}{15}$ is 3
= $\frac{\frac{9}{3}}{\frac{15}{3}}$
= $\frac{3}{5}$
$\frac{15}{25}$
The HCF of the numerator and the denominator of $\frac{15}{25}$ is 5.
= $\frac{\frac{15}{5}}{\frac{25}{5}}$
= $\frac{3}{5}$
In all the three fractions, we observe that on converting the given fractions into their lowest form by dividing them by their HCF of the numerator and the denominator, we get the same fraction $\frac{3}{5}$ all the times. Thus we conclude that as the resultant fraction is same in all the three fractions so these all the three forms of the fractions are equivalent fractions.