Question

Mark the correct alternative in each of the following:

Which one of the following is the correct statement?

(a) $\frac{3}{4}<\frac{2}{3}<\frac{12}{15}$ (b) $\frac{2}{3}<\frac{3}{4}<\frac{12}{15}$ (c) $\frac{2}{3}<\frac{12}{15}<\frac{3}{4}$ (d) $\frac{12}{15}<\frac{2}{3}<\frac{3}{4}$

Answer 1

Consider the fractions $\frac{3}{4}$, $\frac{2}{3}$ and $\frac{12}{15}$.

LCM of 4, 3 and 15 = 60

Firstly, convert the fractions into equivalent fractions with denominator 60.

$$\begin{gathered} \frac{3}{4}=\frac{3\times 15}{4\times 15}=\frac{45}{60} \\ \frac{2}{3}=\frac{2\times 20}{3\times 20}=\frac{40}{60} \\ \frac{12}{15}=\frac{12\times 4}{15\times 4}=\frac{48}{60} \end{gathered}$$

Now,

40 < 45 < 48

$$\begin{gathered} \therefore \frac{40}{60}<\frac{45}{60}<\frac{48}{60} \\ \Rightarrow \frac{2}{3}<\frac{3}{4}<\frac{12}{15} \end{gathered}$$

Hence, the correct answer is option (b).