Question

Convert given fractions into fractions with equal numerators:
$\left(i\right)$ $\frac{8}{9}$ and $\frac{12}{17}$

Answer 1

Finding $LCM$ of numerators $8$ and $12$

$LCM$ of $8,12:$

$\begin{array}{cc}2\mid & 8,12\\ 2\mid & 4,6\\ 2\mid & 2,3\\ 3\mid & 1,3\\ \mid & 1,1\end{array}$

$LCM$ of $8,12=2\times 2\times 2\times 3=24$

Equalizing the numerators of the given fractions.

As the $LCM$ is $24$, therefore let’s make the numerator $24$ in each fraction as follows:

By multiplying $3$ in numerator and denominator in the $1^{st}$ fraction we get,

$\frac{8}{9}\Rightarrow \frac{8\times 3}{9\times 3}=\frac{24}{27}$

By multiplying $2$ in numerator and denominator in the $2^{nd}$ fraction we get,

$\frac{12}{17}\Rightarrow \frac{12\times 2}{17\times 2}=\frac{24}{34}$


Hence, the given fractions with equal numerators are $\frac{24}{27}$ and $\frac{24}{34}$