Question

Mark (✓) against the correct answer
Which one of the following is the correct statement?

(a) $\frac{2}{3}<\frac{3}{5}<\frac{14}{15}$
(b) $\frac{3}{5}<\frac{2}{3}<\frac{14}{15}$
(c) $\frac{14}{15}<\frac{3}{5}<\frac{2}{3}$
(d) none of these

Answer 1

(b) $\frac{3}{5}<\frac{2}{3}<\frac{14}{15}$

The given fractions are $\frac{3}{5},\frac{2}{3}\mathrm{and}\frac{14}{15}.$

LCM of 5, 3 and 15 = 15

Now, we have:

$\frac{2}{3}\times \frac{5}{5}=\frac{10}{15}$, $\frac{3}{5}\times \frac{3}{3}=\frac{9}{15}$ and $\frac{14}{15}\times \frac{1}{1}=\frac{14}{15}$

Clearly, $\frac{9}{15}<\frac{10}{15}<\frac{14}{15}$

∴ $\frac{3}{5}<\frac{2}{3}<\frac{14}{15}$