Question

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

Answer 1

Find the rational numbers between the given numbers:

Given numbers, $-\frac{4}{5}$ and $-\frac{2}{3}$

Rational numbers are numbers which can be represented in $\frac{p}{q}$ form, where $p,q\text{are intergers and}q\ne 0$.

Since denominators of both fractions are different, we have to convert them into like terms.

Take LCM of $5$ and $3$, we get, $-\frac{12}{15}$and $-\frac{10}{15}$

Multiply both fractions by $\frac{6}{6}$ we get $-\frac{72}{90}$ and $-\frac{60}{90}$

So, the required rational numbers are $-\frac{71}{90},-\frac{70}{90},-\frac{69}{90},-\frac{68}{90},-\frac{67}{90}$

Hence, the rational numbers between $\mathbf{-}\frac{\mathbf{4}}{\mathbf{5}}$and $\mathbf{-}\frac{\mathbf{2}}{\mathbf{3}}$ are $\mathbf{-}\frac{\mathbf{71}}{\mathbf{90}}\mathbf{,}\mathbf{}\mathbf{-}\frac{\mathbf{70}}{\mathbf{90}}\mathbf{,}\mathbf{}\mathbf{-}\frac{\mathbf{69}}{\mathbf{90}}\mathbf{,}\mathbf{}\mathbf{-}\frac{\mathbf{68}}{\mathbf{90}}\mathbf{,}\mathbf{}\mathbf{-}\frac{\mathbf{67}}{\mathbf{90}}$.