Question

Find two rational numbers between \[\dfrac{{ - 2}}{9}\] and \[\dfrac{5}{9}\].

Answer 1

Hint: There are two rational numbers given as rational numbers in the form of \[\dfrac{p}{q}\]. To find the rational numbers lying between them equating their denominators. As we equate them, the value of denominators should be equal, so we will be able to conduct the number of rational numbers lying between. Let us discuss how two rational numbers can be found that are lying between the given numbers.

Complete step-by-step answer:
 The rational numbers are those which are in the form of \[\dfrac{p}{q}\] where \[q \ne 0\].
In rational numbers, the value of \[p\] is equal to zero but the value of \[q\] doesn’t equal to zero.
There is a condition on rational numbers that \[q \ne 0\].
Let’s discuss more…..
If we have to find the rational number lies between two number, then firstly, take the L.C.M of the denominator make sure the value of the denominator is same like \[\dfrac{2}{5}\], \[\dfrac{6}{5}\]. In that case, the rational numbers lying between them can be found.
We have given the number \[\dfrac{{ - 2}}{9}\] and \[\dfrac{5}{9}\]; in \[\dfrac{{ - 2}}{9}\], the numerator is \[2\] and the denominator is \[9\].
In \[\dfrac{5}{9}\], the numerator is \[5\] and the denominator is \[9\].
So, these is no need to take L.C.M of both the numbers \[\dfrac{{ - 2}}{9}\] and \[\dfrac{5}{9}\] as we can say that the two numbers lying between \[\dfrac{{ - 2}}{9}\] and \[\dfrac{5}{9}\] are:
\[\dfrac{1}{9}\] and \[\dfrac{2}{9}\]
Both \[\dfrac{1}{9}\] and \[\dfrac{2}{9}\] are positive numbers.
As \[\dfrac{1}{9}\] and \[\dfrac{2}{9}\] lie between \[\dfrac{{ - 2}}{9}\] and \[\dfrac{5}{9}\], it can be written as:
\[\dfrac{{ - 2}}{9},\dfrac{1}{9},\dfrac{2}{9},\dfrac{5}{9}\]
In that way, we can find the rational numbers.

Note: In the given question, rational numbers are \[\dfrac{{ - 2}}{9},\dfrac{5}{9}\]; we concluded that there are two rational numbers lying between them i.e., \[\dfrac{1}{9},\dfrac{2}{9}\]. There are many rational numbers lying between any two numbers. Rational numbers are used for buying and selling products using money.