Question

Find six rational numbers between $\dfrac{3}{5}$ and $\dfrac{4}{5}$ ?

Answer 1

Hint: Here in this question we have been asked to find six rational numbers between $\dfrac{3}{5}$ and $\dfrac{4}{5}$. To answer this question we will multiply the numerator and denominator of both the given numbers by $7$ and then consider any six rational numbers between them.

Complete step by step answer:
Now considering from the question we have been asked to find six rational numbers between $\dfrac{3}{5}$ and $\dfrac{4}{5}$
To answer this question we will multiply the numerator and denominator of both the given numbers by $7$ and then consider the six rational numbers between them.
From the basic concepts we know that the rational number is defined as a number in the form of $\dfrac{p}{q}$ where $p$ and $q$ are integers and $q\ne 0$ .
From the basic concepts of rational numbers we know that when both numerator and denominator are multiplied by a same number then the value of it does not change, only the representation changes. These rational numbers are known as equivalent rational numbers.
Now we will obtain the equivalent rational numbers of $\dfrac{3}{5}$ and $\dfrac{4}{5}$ by multiplying their numerator and denominator by $7$ . Now we will have $\dfrac{21}{35}$ and $\dfrac{28}{35}$.
We need to find six rational numbers between $\dfrac{21}{35}$ and $\dfrac{28}{35}$. We can say that the rational numbers between them are given as $\dfrac{22}{35},\dfrac{23}{35},\dfrac{24}{35},\dfrac{25}{35},\dfrac{26}{35},\dfrac{27}{35}$ .
Hence we can conclude that the six rational numbers between $\dfrac{3}{5}$ and $\dfrac{4}{5}$are given as $\dfrac{22}{35},\dfrac{23}{35},\dfrac{24}{35},\dfrac{25}{35},\dfrac{26}{35},\dfrac{27}{35}$ .

Note: In the process of answering questions of this type we should carefully apply the concepts that we have learnt. Similarly we can find the rational numbers between any two numbers for example we can say that the five rational numbers between $\dfrac{3}{5}$ and $\dfrac{4}{5}$are given as $\dfrac{19}{30},\dfrac{20}{30},\dfrac{21}{30},\dfrac{22}{30},\dfrac{23}{30}$ .