Question

Find five rational numbers between $$\dfrac{-3}{5}$$ and $$\dfrac{-1}{2}$$.

Answer 1

Hint: In this question it is given that we have to find five rational numbers between $$\dfrac{-3}{5}$$ and $$\dfrac{-1}{2}$$. So to find the solution we need to first equate the denominators with their LCM. After that we can easily find the rational number by changing the numerator.

Complete step-by-step solution:
First of all we will find the LCM of 5 and 2, i.e, LCM(5,2)=10.
Now we make the denominator 10, so the given numbers,
 $$\dfrac{-3}{5}$$ and $$\dfrac{-1}{2}$$
=$$\dfrac{-3\times 2}{5\times 2}$$ and $$\dfrac{-1\times 5}{2\times 5}$$
=$$\dfrac{-6}{10}$$ and $$\dfrac{-5}{10}$$...........(1)
So there is no rational number in between $$\dfrac{-6}{10}$$ and $$\dfrac{-5}{10}$$.
So to find 5 rational numbers, we have to multiply the numerator and denominator by 6(=5+1).
So from (1) we can write,
$$\dfrac{-6\times 6}{10\times 6}$$ and $$\dfrac{-5\times 6}{10\times 6}$$
=$$\dfrac{-36}{60}$$ and $$\dfrac{-30}{60}$$
So the five rational numbers are-$$\dfrac{-35}{60} ,\dfrac{-34}{60} ,\dfrac{-33}{60} ,\dfrac{-32}{60} ,\dfrac{-31}{60}$$
So we have got our required answer.

Note: To solve this type of question you need to know that if any number can be written in the form of $$\dfrac{p}{q}$$ where $q\neq 0$ and p,q are integer, then the number is called rational number. And to find the rational number in between any two numbers, you have to equate their denominators and then choose a rational number by taking any numerator in between the obtained numerator.