# Ex.1.2 Q4 Rational Numbers Solution - NCERT Maths Class 8

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## Question

Find ten rational numbers between \begin{align}\frac{{ - 2}}{5}\end{align} and \begin{align}\frac{1}{2}\end{align}

Video Solution
Rational Numbers
Ex 1.2 | Question 4

## Text Solution

What is known?

Rational numbers.

What is unknown?

The rational numbers between given rational numbers.

Reasoning:

We can find infinitely many rational numbers between any two given rational numbers by taking the mean of the two rational numbers.

Another method: We can make the denominator same for the two given rational numbers.

Steps:

\begin{align}\frac{{ - 2}}{5} = \frac{{ - 2 \times 2}}{{5 \times 2}} = \frac{{ - 4}}{{10}}\end{align}  [multiplying both numerator and denominator by $$2$$]

\begin{align}\frac{1}{2} = \frac{{1 \times 5}}{{2 \times 5}} = \frac{5}{{10}}\end{align} [multiplying both numerator and denominator by $$5$$]

[Multiplying both numerators and denominators by the same number]

Now, there are $$9$$ rational numbers between \begin{align}\frac{{ - 4}}{{10}}\end{align} and \begin{align}\frac{5}{{10}}\end{align}, but we need $$10$$ numbers. So, we should again multiply both numerator and denominator by $$2$$ in the two rational numbers \begin{align}\frac{{ - 4}}{{10}}\end{align} and \begin{align}\frac{5}{{10}}\end{align}

\begin{align}\frac{{ - 4 \times 2}}{{10 \times 2}} = \frac{{ - 8}}{{20}}\end{align}and \begin{align}\frac{5}{{10}} \times \frac{2}{2} = \frac{{10}}{{20}}\end{align}

The ten rational numbers between \begin{align}\frac{{ - 2}}{5}\end{align} and \begin{align}\frac{1}{2}\end{align} which can be taken as.

\begin{align}&\frac{- 7}{20},\;\;\frac{- 6}{20},\;\;\frac{- 5}{20}, \;\;\frac{- 4}{20},\;\;\frac{- 3}{20},\;\; \\ & \frac{- 2}{20},\;\;\frac{1}{20},\;\;0,\;\;\frac{1}{20} \;\; \text{and} \;\; \frac{2}{20}\end{align}

[There are many more such rational numbers.]

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