Question

Convert given fractions into fractions with equal numerators:
$\left(iii\right)$$\frac{15}{19},\frac{25}{28},\frac{9}{11}$ and $\frac{45}{47}$

Answer 1

Finding $LCM$ of numerators $15,25,9$ and $45:$

$LCM$ of $15,25,9$ and $45:$

$\begin{array}{cc}3\mid & 9,15,25,45\\ 3\mid & 3,5,25,15\\ 5\mid & 1,5,25,5\\ 5\mid & 1,1,5,1\\ \mid & 1,1,1,1\end{array}$

$LCM$ of $15,25,9$ and $45=3\times 3\times 5\times 5=225$

Equalizing the numerators of the given fractions.

As the $LCM$ is $225$, therefore let's make the numerator $225$ in each fraction as fallows:

By multiplying $15$ in numerator and denominator in the $1^{st}$ fraction we get,

$\frac{15}{19}\Rightarrow \frac{15\times 15}{19\times 15}=\frac{225}{285}$

By multiplying $9$ in numerator and denominator in the $2^{nd}$ fraction we get,

$\frac{25}{28}\Rightarrow \frac{25\times 9}{28\times 9}=\frac{225}{252}$

By multiplying $25$ in numerator and denominator in the $3^{rd}$ fraction we get,

$\frac{9}{11}\Rightarrow \frac{9\times 25}{11\times 25}=\frac{225}{275}$

By multiplying $5$ in numerator and denominator in the $4^{th}$ fraction we get,

$\frac{45}{47}\Rightarrow \frac{45\times 5}{47\times 5}=\frac{225}{235}$

Hence, the given fractions with equal numerators are $\frac{225}{285},\frac{225}{252},\frac{225}{275}$ and $\frac{225}{235}$