Question

List any five rational numbers that lie between: $\dfrac{-4}{5}\text{ and }\dfrac{-2}{3}.$

Answer 1

Hint:First we will convert fraction into decimal, so that it is easier to understand. Then we just have to find some decimal numbers that lie between the two given numbers and then we will again convert those decimal numbers into fraction and that will be our final answer.

Complete step-by-step answer:
So, let’s start with our method of solving this question as discussed in the hint.
Converting two numbers from fraction to decimal it becomes:
$\dfrac{-4}{5}=-0.80\text{ and }\dfrac{-2}{3}=-0.67$
Now, we just have to find five numbers which lie between -0.67 and -0.80.
Let’s take these five numbers as: $-0.70,-0.72,-0.74,-0.76\text{ and }-\text{0}\text{.78}\text{.}$
Now we are going to convert this decimal numbers to fractions,
The number -0.70 will be equal to $\dfrac{-7}{10}$ .
The number -0.72 will be equal to $\dfrac{-72}{100}=\dfrac{-18}{25}$ .
The number -0.74 will be equal to $\dfrac{-74}{100}=\dfrac{-37}{50}$ .
The number -0.76 will be equal to $\dfrac{-76}{100}=\dfrac{-19}{25}$.
The number -0.78 will be equal to $\dfrac{-78}{100}=\dfrac{-39}{50}$ .
As we have converted all our decimal numbers into fractions which is the required answer of this question.
Hence, the five numbers are: $\dfrac{-7}{10},\dfrac{-18}{25},\dfrac{-37}{50},\dfrac{-19}{25}\text{ and }\dfrac{-39}{50}.$

Note: There are many methods to solve this question, one method is already stated, the second method is to use a number line and then plot the given points in the number line and then we just have to pick random five numbers from the region between the two given numbers. And in this method also we could have picked some other five sets of numbers and one thing that should be kept in mind that there are infinite rational numbers between any two rational numbers.