Question

Find three rational numbers between $ 5 $ and $ - 2 $ .

Answer 1

Hint: In this question we have to find the rational numbers between two numbers. But the given numbers are whole numbers, so first we have to convert them in the rational form. So, find the LCM of the denominator of the number then multiplying the LCM with the rational form we get the numbers in the rational form. Now we can easily find the rational numbers between these two numbers.

Complete step-by-step answer:
Given:
The numbers given are $ 5 $ and $ - 2 $ .
We can write these two numbers in the form as given below,
 $ \dfrac{5}{1} $ and $ \dfrac{{ - 2}}{1} $
Denominators for the both numbers are the same so the LCM of both would also be the same.
Taking the LCM of the denominator of the both numbers we have get,
 $ \Rightarrow LCM\left( {1,1} \right) = 1 $
So, now we have to multiply the given numbers with a number which will result in the denominator of the result of the product of the numbers equal to the LCM of the denominator of both numbers that we have calculated.
 $ \Rightarrow \dfrac{{ - 2}}{1} \times \dfrac{1}{1} = \dfrac{{ - 2}}{1} $
And,
 $ \dfrac{5}{1} \times \dfrac{1}{1} = \dfrac{5}{1} $
So, numbers $ \dfrac{{ - 2}}{1} $ and $ \dfrac{5}{1} $ are the rational forms of the given numbers $ - 2 $ and $ 5 $ respectively.
Now writing the rational numbers between $ \dfrac{{ - 2}}{1} $ and $ \dfrac{5}{1} $ in the ascending order we have,
 $ \dfrac{{ - 1}}{1},0,\dfrac{1}{1},\dfrac{2}{1},\dfrac{3}{1},\dfrac{4}{1} $
There are a total of $ 5 $ rational numbers between the given numbers $ - 2 $ and $ 5 $ .
Therefore, the three rational numbers between $ 5 $ and $ - 2 $ are $ \dfrac{{ - 1}}{1},\dfrac{1}{1}{\rm{ and }}\dfrac{2}{1} $ .

Note: It should be noted that when writing the rational numbers between two numbers the value of the denominator for all the numbers should be the same, because the value of the denominator of all numbers is the LCM of the denominators of the two numbers.