Question

List five rational number between $-\frac{3}{4}$ and $-\frac{1}{5}.$

Answer 1

Find rational numbers between given numbers

Given numbers, $-\frac{3}{4}$and $-\frac{1}{5}$

Rational numbers are numbers that can be represented in $\raisebox{1ex}{$p$}\!\left/ \!\raisebox{-1ex}{$q$}\right.$ form, where $q\ne 0$.

LCM of $4$ and $5$ is $4\times 5=20$ (Since the numbers are relatively prime).

Making the denominator same as LCM for the given numbers we get,

$\frac{-3\times 5}{4\times 5}=\frac{-15}{20}$ and $\frac{-1\times 4}{5\times 4}=\frac{-4}{20}$

Thus,

Five rational numbers between $-\frac{3}{4}$and $-\frac{1}{5}$ are $-\frac{14}{20},-\frac{13}{20},-\frac{12}{20},-\frac{11}{20},-\frac{10}{20}.$

Hence, $-\frac{14}{20},-\frac{13}{20},-\frac{12}{20},-\frac{11}{20},-\frac{10}{20}$ are the five rational numbers between $-\frac{3}{4}$and $-\frac{1}{5}.$