Question

Which of the following represents a set of 4 rational numbers between $\frac{1}{2}$ and $\frac{1}{3}$ ?

• A. $\frac{11}{30}$,$\frac{22}{30}$,$\frac{33}{30}$,$\frac{40}{30}$
• B. $\frac{11}{30}$,$\frac{12}{30}$,$\frac{13}{30}$,$\frac{14}{30}$
• C. $\frac{1}{30}$,$\frac{2}{30}$,$\frac{3}{30}$,$\frac{4}{30}$
• D. $\frac{1}{30}$,$\frac{11}{30}$,$\frac{10}{30}$,$\frac{12}{30}$

Answer 1

The correct option is B

$\frac{11}{30}$,$\frac{12}{30}$,$\frac{13}{30}$,$\frac{14}{30}$

Difference of $\frac{1}{2}$ and $\frac{1}{3}$ = $\frac{1}{2}-\frac{1}{3}=\frac{1}{6}$
Dividing $\frac{1}{6}$ in 5 parts gives $(\frac{1}{6}÷5)=\frac{1}{30}$
Therefore 4 rational numbers will be
$\frac{1}{3}+\frac{1}{30}=\frac{11}{30}\frac{1}{3}+\frac{1}{30}+\frac{1}{30}=\frac{12}{30}\frac{1}{3}+\frac{1}{30}+\frac{1}{30}+\frac{1}{30}=\frac{13}{30}\frac{1}{3}+\frac{1}{30}+\frac{1}{30}+\frac{1}{30}+\frac{1}{30}=\frac{14}{30}$

So, $\frac{11}{30},\frac{12}{30},\frac{13}{30},\frac{14}{30}$ lies in between $\frac{1}{2}$ and $\frac{1}{3}$.