Question

Convert given fractions into fractions with equal numerators:
$\left(ii\right)$ $\frac{6}{13},\frac{15}{23}$ and $\frac{12}{17}$

Answer 1

Finding $LCM$ of numerators $6,15$ and $12$:

$LCM$ of $6,15,12$

$\begin{array}{cc}2\mid & 15,6,12\\ 2\mid & 15,3,6\\ 3\mid & 15,3,3\\ 5\mid & 5,1,1\\ \mid & 1,1,1\end{array}$

$LCM$ of $6,15,12=2\times 2\times 3\times 5=60$

Equalizing the numerators of the given fractions.

By multiplying $10$ in numerator and denominator in the $1^{st}$ fraction we get,

$\frac{6}{13}\Rightarrow \frac{6\times 10}{13\times 10}=\frac{60}{130}$

By multiplying $4$ in numerator and denominator in the $2^{nd}$ fraction we get,

$\frac{15}{23}\Rightarrow \frac{15\times 4}{23\times 4}=\frac{60}{92}$

By multiplying $5$ in numerator and denominator in the $3^{rd}$ fraction we get,

$\frac{12}{17}\Rightarrow \frac{12\times 5}{17\times 5}=\frac{60}{85}$

Hence, the given fractions with equal numerators are $\frac{60}{130},\frac{60}{92}$ and $\frac{60}{85}$