Question

Find four rational numbers between \[\dfrac{1}{2}\] and \[\dfrac{2}{3}\].

Answer 1

Hint: For solving this question you should know about rational numbers. Rational numbers are the numbers which lie between the two numbers. But here both of these are not in a form of that so we will change it in equivalent fractions. We can determine the equivalent fractions by just calculating the multiplication of the same fraction of with the fraction. Or we can say that by taking the square, cube or so on we can calculate the equivalent fraction, or we can also calculate it by multiplying with the fraction of the same numerator and denominator.

Complete step-by-step solution:
According to the question we have to find the rational numbers between \[\dfrac{1}{2}\] and \[\dfrac{2}{3}\].
Both of these numbers are not in an actual form for that and if we find equivalent fractions then it will be possible.
So, as we can see that the equivalent fractions of a fraction will be equal to the fraction which will be the same in the ratio of original fraction or main fraction.
We can say that we will multiply to our main fraction with various forms of 1 which will modify the numerator and denominator of a fraction.
However, because we are multiplying by 1 which will not change to the fraction.
So, if we see our question then we have to find the rational numbers between \[\dfrac{1}{2}\] and \[\dfrac{2}{3}\].
So, for the rational numbers,
Equivalent fraction of \[\dfrac{1}{2}=\dfrac{3}{6}=\dfrac{30}{60}\]
Equivalent fraction of \[\dfrac{2}{3}=\dfrac{20}{30}=\dfrac{40}{60}\]
So, four rational numbers are:
\[\dfrac{31}{60},\dfrac{32}{60},\dfrac{33}{60},\dfrac{34}{60}\]

Note: For calculating the equivalent fraction we can take both positive and negative numbers but it is mandatory that both are the same numbers with the same sign and this is always in a form of 1. And if we divide by the same fraction then our original fraction will occur. And the rational numbers are between them.