Question

Mark the correct alternative in each of the following:

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

Answer 1

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.

$$\begin{gathered} \frac{1}{2}=\frac{1\times 442}{2\times 442}=\frac{442}{884} \\ \frac{9}{13}=\frac{9\times 68}{13\times 68}=\frac{612}{884} \\ \frac{3}{4}=\frac{3\times 221}{4\times 221}=\frac{663}{884} \\ \frac{12}{17}=\frac{12\times 52}{17\times 52}=\frac{624}{884} \end{gathered}$$

Now,

442 < 612 < 624 < 663

$$\begin{gathered} \therefore \frac{442}{884}<\frac{612}{884}<\frac{624}{884}<\frac{663}{884} \\ \Rightarrow \frac{1}{2}<\frac{9}{13}<\frac{12}{17}<\frac{3}{4} \end{gathered}$$

Hence, the correct answer is option (d).