Question

Mark the correct alternative in each of the following:

Which of the following fractions is greater than $\frac{3}{4}$ and less than $\frac{5}{6}$?

(a) $\frac{2}{3}$ (b) $\frac{1}{2}$ (c) $\frac{4}{5}$ (d) $\frac{9}{10}$

Answer 1

Consider the fractions $\frac{3}{4},\frac{5}{6},\frac{2}{3},\frac{1}{2},\frac{4}{5}$ and $\frac{9}{10}$.

LCM of 2, 3, 4, 5, 6 and 10 = 60

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

$$\begin{gathered} \frac{3}{4}=\frac{3\times 15}{4\times 15}=\frac{45}{60} \\ \frac{5}{6}=\frac{5\times 10}{6\times 10}=\frac{50}{60} \\ \frac{2}{3}=\frac{2\times 20}{3\times 20}=\frac{40}{60} \\ \frac{1}{2}=\frac{1\times 30}{2\times 30}=\frac{30}{60} \\ \frac{4}{5}=\frac{4\times 12}{5\times 12}=\frac{48}{60} \\ \frac{9}{10}=\frac{9\times 6}{10\times 6}=\frac{54}{60} \end{gathered}$$

Now,

30 < 40 < 45 < 48 < 50 < 54

$$\begin{gathered} \therefore \frac{30}{60}<\frac{40}{60}<\frac{45}{60}<\frac{48}{60}<\frac{50}{60}<\frac{54}{60} \\ \Rightarrow \frac{1}{2}<\frac{2}{3}<\frac{3}{4}<\frac{4}{5}<\frac{5}{6}<\frac{9}{10} \end{gathered}$$

Thus, the fraction $\frac{4}{5}$ is greater than $\frac{3}{4}$ and less than $\frac{5}{6}$.

Hence, the correct answer is option (c).