Question

Which of the following fractions lie between $\frac{3}{8}$ and $\frac{7}{8}$ on the number line?

• A. $\frac{1}{4}$
• B. $\frac{9}{8}$
• C. $\frac{20}{16}$
• D. $\frac{1}{2}$

Answer 1

The correct option is D

$\frac{1}{2}$

Converting the given fractions into equivalent fractions with denominator 8, we have

​$\frac{1\times 4}{2\times 4}=\frac{4}{8}$

$\frac{1\times 2}{4\times 2}=\frac{2}{8}$

​$\frac{9\times 1}{8\times 1}=\frac{9}{8}$

​$\frac{20÷2}{16÷2}=\frac{10}{8}$

Since $3<4<8$, we have $\frac{3}{8}<\frac{4}{8}<\frac{7}{8}$
i.e., $\frac{3}{8}<\frac{1}{2}<\frac{7}{8}$

Thus, $\frac{1}{2}$ lies between $\frac{3}{8}$ and $\frac{7}{8}$.