Question

Mark the correct alternative in each of the following:

Which of the following statements is true?

(a) $\frac{7}{12}<\frac{4}{21}$ (b) $\frac{7}{12}=\frac{4}{21}$ (c) $\frac{7}{12}>\frac{4}{21}$ (d) None of these

Answer 1

Consider the fractions $\frac{7}{12}$ and $\frac{4}{21}$.

Prime factorisation of 12 = 2 × 2 × 3

Prime factorisation of 21 = 3 × 7

∴ LCM of 12 and 21 = 2 × 2 × 3 × 7 = 84

Firstly, convert the fractions to equivalent fractions with denominator 84.

$$\begin{gathered} \frac{7}{12}=\frac{7\times 7}{12\times 7}=\frac{49}{84} \\ \frac{4}{21}=\frac{4\times 4}{21\times 4}=\frac{16}{84} \end{gathered}$$

Now,

49 > 16

$$\begin{gathered} \therefore \frac{49}{84}>\frac{16}{84} \\ \Rightarrow \frac{7}{12}>\frac{4}{21} \end{gathered}$$

Hence, the correct answer is option (c).