Question

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

• A. True
• B. False
• 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

False

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 $\frac{1}{3}$.