Question

Find any two rational numbers between $ \left( { - \dfrac{5}{7}} \right) $ and $ \left( { - \dfrac{2}{7}} \right) $ .

Answer 1

Hint: Here, we have to find two rational numbers between $ \left( { - \dfrac{5}{7}} \right) $ and $ \left( { - \dfrac{2}{7}} \right) $ . For that we need to multiply and divide both these numbers by any same number. Here we have multiplied and divided by 10. Now, the denominators will be the same so we can compare the numerators and find two numbers between these numbers.

Complete step-by-step answer:
In this question, we are given two rational numbers and we need to find two more rational numbers between them.
The given rational numbers are: $ \left( { - \dfrac{5}{7}} \right) $ and $ \left( { - \dfrac{2}{7}} \right) $ .
So, we need to find two rational numbers that lie between $ \left( { - \dfrac{5}{7}} \right) $ and $ \left( { - \dfrac{2}{7}} \right) $ . That means the 2 rational numbers must be greater than $ \left( { - \dfrac{5}{7}} \right) $ and less than $ \left( { - \dfrac{2}{7}} \right) $ .
Steps for finding rational numbers between two rational numbers:
Step 1:
Write the two given rational numbers.
 $ \left( { - \dfrac{5}{7}} \right) $ $ \left( { - \dfrac{2}{7}} \right) $
Step 2:
Multiply and divide both the rational numbers with any same number. Here, we are going to multiply and divide these numbers with 10. Therefore,
 $ \Rightarrow - \dfrac{5}{7} \times \dfrac{{10}}{{10}} = - \dfrac{{50}}{{70}} $
 $ \Rightarrow - \dfrac{2}{7} \times \dfrac{{10}}{{10}} = - \dfrac{{20}}{{70}} $
Step 3:
Now, we have 2 rational numbers with the same denominator. So, we can compare the numerators.
Now, there are many numbers between -50 and -20. Two of them would be -49 and -48.
Therefore, two rational numbers between $ \left( { - \dfrac{{50}}{{70}}} \right) $ and $ \left( { - \dfrac{{20}}{{70}}} \right) $ will be $ \left( { - \dfrac{{49}}{{70}}} \right) $ and $ \left( { - \dfrac{{48}}{{70}}} \right) $ .

Note: Here, we can see that the denominators are already the same and so we can also find the two rational numbers between them without multiplying and dividing them with any number.
The numbers are: $ \left( { - \dfrac{5}{7}} \right) $ and $ \left( { - \dfrac{2}{7}} \right) $
The numerators are -5 and -2 and we need to find numbers between these two numbers. Let us draw a number line for this.

Here, we can see that -4 and -3 lie between -5 and -2.
Therefore, two rational numbers between $ \left( { - \dfrac{5}{7}} \right) $ and $ \left( { - \dfrac{2}{7}} \right) $ are $ \left( { - \dfrac{4}{7}} \right) $ and $ \left( { - \dfrac{3}{7}} \right) $ .