Find ten rational numbers between $\frac{-2}{5}$ and $\frac{1}{2}$.


Given: 

Given rational numbers are $\frac{-2}{5}$ and $\frac{1}{2}$.

To do:  

We have to find ten rational numbers between $\frac{-2}{5}$ and $\frac{1}{2}$.

Solution:

LCM of 5 and 2 is 10.

$\frac{-2}{5}=\frac{-2\times2}{5\times2}$

$=\frac{-4}{10}$

$\frac{1}{2}=\frac{1\times5}{2\times5}$

$=\frac{5}{10}$

As we need 10 rational numbers between $\frac{-4}{10}$ and $\frac{5}{10}$, multiply both the fractions by $\frac{2}{2}$.

This implies,

$\frac{-4}{10}=\frac{-4}{10}\times\frac{2}{2}$

$=\frac{-8}{20}$

$\frac{5}{10}=\frac{5}{10}\times\frac{2}{2}$

$=\frac{10}{20}$

Therefore,

Ten rational numbers between $\frac{-2}{5}$ and $\frac{1}{2}$ are $\frac{-7}{20}, \frac{-6}{20}, ........,\frac{1}{20}, \frac{2}{20}$. 

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Updated on: 10-Oct-2022

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