Which one of the following is true?

MCQ

Which one of the following is true$?$

A
$\frac{1}{2}<\frac{9}{13}<\frac{3}{4}<\frac{12}{17}$
B
$\frac{3}{4}<\frac{9}{13}<\frac{1}{2}<\frac{12}{17}$
C
$\frac{1}{2}<\frac{3}{4}<\frac{9}{13}<\frac{12}{17}$
✓
$\frac{1}{2}<\frac{9}{13}<\frac{12}{17}<\frac{3}{4}$

✓

Answer

Correct option: D.

$\frac{1}{2}<\frac{9}{13}<\frac{12}{17}<\frac{3}{4}$

Consider the fractions $\frac{1}{2},\frac{9}{13},\frac{3}{4}$ and $\frac{12}{17}$
$LCM$ of $2, 4, 13$ and $17 = 884$
Firstly, convert the fractions into equivalent fractions with denominator $884$
$\Rightarrow\frac{1}{2}=\frac{1\times442}{2\times442}=\frac{442}{884}$
$\Rightarrow\frac{9}{13}=\frac{9\times68}{13\times68}=\frac{612}{884}$
$\Rightarrow\frac{3}{4}=\frac{3\times221}{4\times221}=\frac{663}{884}$
$\Rightarrow\frac{12}{17}=\frac{12\times52}{17\times52}=\frac{624}{884}$
Now,
$442<612<624<663$
$\therefore\ \frac{442}{884}<\frac{612}{884}<\frac{624}{884}<\frac{663}{884}$
$\frac{1}{2}<\frac{9}{13}<\frac{12}{17}<\frac{3}{4}$