Question

Find the six rational numbers between \[2\]and\[3\].

Answer 1

Hint: We know that the definition of a Rational Number can be made by dividing two integers. To insert rational numbers between any two rational numbers, we make the denominators of the two rational numbers the same. The above way we can easily insert any number of rational numbers between any two rational numbers. There are infinite rational numbers between \[2\]and\[3\].

Complete answer:
Firstly, we need to insert six rational numbers between \[2\]and\[3\].
Let, starting number or \[2 = a\]
Ending number or \[3 = b\]
And, the number of rational numbers to find \[ = n = 6\]
Now, as stated in the predefined mathematical process, we have to do the following mathematical calculations,
\[n = 6\]
\[n + 1 = 6 + 1 = 7\]
Now, to make the denominators same in the given two rational numbers, we multiply and divide the numbers with the same number, like the denominators of both the numbers will be the same.
Now, we can write the \[a\] and \[b\] in the following manner also,
\[a = 2 \times \dfrac{7}{7} = \dfrac{{14}}{7}\]
\[b = 3 \times \dfrac{7}{7} = \dfrac{{21}}{7}\]
Now, \[2\]can be written as \[\dfrac{{14}}{7}\]and \[3\]can be written as\[\dfrac{{21}}{7}\].
Now, \[a\] and \[b\] are in rational forms, we just need to write the in-between rational numbers of \[a\] and\[b\].
Rational numbers \[ = \dfrac{{15}}{7},\dfrac{{16}}{7},\dfrac{{17}}{7},\dfrac{{18}}{7},\dfrac{{19}}{7},\dfrac{{20}}{7}\]
Hence, the correct answer of the six rational numbers between \[2\] and \[3\] is \[\dfrac{{15}}{7},\dfrac{{16}}{7},\dfrac{{17}}{7},\dfrac{{18}}{7},\dfrac{{19}}{7},\dfrac{{20}}{7}\].

Note:
A rational number is in the form of \[\dfrac{p}{q}\] , where \[p\] and \[q\] are integers and\[q \ne 0\]. The set of rational numbers includes all the integers which can be written as a quotient with the integers as the numerator and \[1\] as the denominator. We multiply and divide a rational number with new number because it does not make any change in the existing number. These rational numbers are also known as an equivalent rational numbers.