Question

Mark the correct alternative in each of the following:

Which of the following is correct?

(a) $\frac{2}{3}<\frac{3}{5}<\frac{11}{15}$ (b) $\frac{3}{5}<\frac{2}{3}<\frac{11}{15}$ (c) $\frac{11}{15}<\frac{3}{5}<\frac{2}{3}$ (d) $\frac{3}{5}<\frac{11}{15}<\frac{2}{3}$

Answer 1

Consider the fractions $\frac{2}{3}$, $\frac{3}{5}$ and $\frac{11}{15}$.

LCM of 3, 5 and 15 = 15

Firstly, convert the fractions into equivalent fractions with denominator 15.

$$\begin{gathered} \frac{2}{3}=\frac{2\times 5}{3\times 5}=\frac{10}{15} \\ \frac{3}{5}=\frac{3\times 3}{5\times 3}=\frac{9}{15} \end{gathered}$$

Now,

9 < 10 < 11

$$\begin{gathered} \therefore \frac{9}{15}<\frac{10}{15}<\frac{11}{15} \\ \Rightarrow \frac{3}{5}<\frac{2}{3}<\frac{11}{15} \end{gathered}$$

Hence, the correct answer is option (b).