Question

Question 68.
$\frac{12}{75}$ ___ $\frac{32}{200}$

Answer 1

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The given fractions are $\frac{12}{75}$ and $\frac{32}{200}$.
In order to compare fractions with different denominators, we will convert them to like fractions, that is fractions having the same denominator.
LCM of 75 and 200 is calculated below.

$\begin{array}{cc}2& 75,200\\ 2& 75,100\\ 2& 75,50\\ 3& 75,25\\ 5& 25,25\\ 5& 5,5\\ & 1,1\end{array}$
$\therefore$ LCM of 75 and 200 = $2\times 2\times 2\times 3\times 5\times 5=600$
Now, converting each of the given fractions to equivalent fractions with denominator 600.

$\frac{12}{75}=\frac{12\times 8}{75\times 8}=\frac{96}{600}$ and $\frac{32}{200}=\frac{32\times 3}{200\times 3}=\frac{96}{600}$
Clearly, $\frac{96}{600}=\frac{96}{600}$
$\therefore$ $\frac{12}{75}=\frac{32}{200}$