Question

Which of the following fractions lie between 2 and 3 on number line?

• A. $\frac{13}{3}$
• B. $\frac{9}{4}$
• C. $\frac{8}{3}$
• D. $\frac{1}{3}$

Answer 1

Answer: (B), (C)

The correct options are
B $\frac{9}{4}$
C $\frac{8}{3}$

Let us convert the given fractions into mixed fractions.

1. $\frac{13}{3}=\frac{12+1}{3}=4+\frac{1}{3}$

$⟹\frac{13}{3}$ lies between 4 and 5.

2. $\frac{9}{4}=\frac{8+1}{4}=2+\frac{1}{4}.$

$⟹\frac{9}{4}$ lies between 2 and 3.

3. $\frac{8}{3}=\frac{6+2}{3}=2+\frac{2}{3}.$
$⟹\frac{8}{3}$ lies between 2 and 3.

4. $0<\frac{1}{3}<1.$ Thus, $\frac{1}{3}$ lies between 0 and 1.