Question

Find five rational numbers between $\frac{2}{3}$ and $\frac{4}{5}$.

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 $q\ne 0$.

• Given two rational numbers are $\frac{2}{3}$ and $\frac{4}{5}$.
• By multiplying the numerator and denominator of $\frac{2}{3}$ by $15$, we get, $\frac{30}{45}$.
• By multiplying the numerator and denominator of $\frac{4}{5}$ by $9$, we get, $\frac{36}{45}$.
• Therefore, the rational numbers between $\frac{30}{45}$ and $\frac{36}{45}$ are $\frac{31}{45},\frac{32}{45},\frac{33}{45},\frac{34}{45}$ and $\frac{35}{45}$.

Hence, the five rational numbers between $\frac{2}{3}$ and $\frac{4}{5}$ are $\frac{31}{45},\frac{32}{45},\frac{33}{45},\frac{34}{45}$ and $\frac{35}{45}$.