Question

Mark the correct alternative in each of the following:

Which is the smallest of the following fractions?

(a) $\frac{4}{9}$ (b) $\frac{2}{5}$ (c) $\frac{3}{7}$ (d) $\frac{1}{4}$

Answer 1

Consider the fractions $\frac{4}{9}$, $\frac{2}{5}$, $\frac{3}{7}$ and $\frac{1}{4}$.

LCM of 4, 5, 7 and 9 = 1260

Firstly, convert the fractions into equivalent fractions with denominator 1260.

$$\begin{gathered} \frac{4}{9}=\frac{4\times 140}{9\times 140}=\frac{560}{1260} \\ \frac{2}{5}=\frac{2\times 252}{5\times 252}=\frac{504}{1260} \\ \frac{3}{7}=\frac{3\times 180}{7\times 180}=\frac{540}{1260} \\ \frac{1}{4}=\frac{1\times 315}{4\times 315}=\frac{315}{1260} \end{gathered}$$

Now,

315 < 504 < 540 < 560

$$\begin{gathered} \therefore \frac{315}{1260}<\frac{504}{1260}<\frac{540}{1260}<\frac{560}{1260} \\ \Rightarrow \frac{1}{4}<\frac{2}{5}<\frac{3}{7}<\frac{4}{9} \end{gathered}$$

Thus, the smallest fraction is $\frac{1}{4}$.

Hence, the correct answer is option (d).