Question

Find five rational numbers between $\frac{1}{2}$ and $\frac{1}{3}$.

Answer 1

Compute the required rational numbers:

A Rational number can be defined as, any number which can be expressed in the form of $\frac{p}{q}$ where $q\ne 0$.

• On multiplying the numerator and denominator of $\frac{1}{2}$ by $3$, we get, $\frac{3}{6}$and,

on further multiplying the numerator and denominator by $6$, we get, $\frac{3\times 6}{6\times 6}=\frac{18}{36}$.

• On multiplying the numerator and denominator of $\frac{1}{3}$ by $2$, we get, $\frac{2}{6}$and,

on further multiplying the numerator and denominator by $6$, we get, $\frac{2\times 6}{6\times 6}=\frac{12}{36}$.

Therefore, the rational numbers between $\frac{1}{2}$ and $\frac{1}{3}$ are the rational numbers between $\frac{12}{36}$ and $\frac{18}{36}$ i.e. $\frac{13}{36}$, $\frac{14}{36}$, $\frac{15}{36}$, $\frac{16}{36}$ and $\frac{17}{36}$.

Hence, the five rational numbers between $\frac{1}{2}$ and $\frac{1}{3}$ are $\frac{13}{36}$, $\frac{14}{36}$, $\frac{15}{36}$, $\frac{16}{36}$ and $\frac{17}{36}$.