Question

The part of the number line between the points denoted by the numbers $\frac{1}{3}$ and $\frac{1}{2}$ is divided into four equal parts as shown below. The numbers denoted by A,B and C are _______.

• A. $\frac{1}{3},\frac{1}{4},\frac{1}{5}$
• B. $\frac{3}{8},\frac{5}{12},\frac{11}{24}$
• C. $\frac{9}{24},\frac{10}{24},\frac{11}{24}$
• D. $\frac{9}{12},\frac{10}{12},\frac{11}{12}$

Answer 1

Answer: (B), (C)

The correct options are
B

$\frac{3}{8},\frac{5}{12},\frac{11}{24}$

C

$\frac{9}{24},\frac{10}{24},\frac{11}{24}$

$\frac{1}{3}=\frac{2}{6}$ and $\frac{1}{2}=\frac{3}{6}$

We need 3 numbers between $\frac{2}{6}$ and $\frac{3}{6}$.

Multiply both $\frac{2}{6}$ and $\frac{3}{6}$ with (3 + 1) i.e. 4

$\Rightarrow \frac{2}{6}=\frac{8}{24}$ and $\frac{3}{6}=\frac{12}{24}$

Now, numbers between $\frac{8}{24}$ and $\frac{12}{24}$ are

$\frac{9}{24},\frac{10}{24},\frac{11}{24}$

$\therefore$ A, B, C are $\frac{9}{24},\frac{10}{24},\frac{11}{24}$ respectively, i.e. $\frac{3}{8},\frac{5}{12},\frac{11}{24}$