A rational number between $-\frac{2}{3}$ and $\frac{1}{2}$ is

A)  $-\frac{1}{6}$

B)  $-\frac{1}{12}$

C)  $-\frac{5}{6}$

D)  $\frac{5}{6}$

Given: $-\frac{2}{3}$ and $\frac{1}{2}$

To find: A rational number between $-\frac{2}{3}$ and $\frac{1}{2}$

Solution:

To find a rational number between $-\frac{2}{3}$ and $\frac{1}{2}$ first we need to convert these numbers having equal denominator.

So, LCM of 3 and 2 is 6.

Now,

$-\frac{2}{3} \ =\ -\frac{2}{3} \ \times \ \frac{2}{2} \ =\ -\frac{4}{6}$

$\frac{1}{2} \ =\ \frac{1}{2} \ \times \ \frac{3}{3} \ =\ \frac{3}{6}$

Rational numbers between $-\frac{2}{3}$ and $\frac{1}{2}$ are: 

$-\frac{3}{6} ,\ -\frac{2}{6} ,\ -\frac{1}{6} ,\ 0,\ \frac{1}{6} \ and\ \frac{2}{6}$

So, answer is option (A)  $-\frac{1}{6}$.

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Updated on: 10-Oct-2022

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