Question

Write five equivalent rational numbers to
(i) \[\dfrac{5}{2}\]
(ii) \[-\dfrac{7}{9}\]
(iii) \[-\dfrac{3}{7}\]

Answer 1

Hint: We will use the concept of rational numbers to solve this question. A rational number, can be defined as any number which can be represented in the form of \[\dfrac{p}{q}\] where q is greater than 0. To find five rational numbers to a given number we will multiply the numerator and denominator of the given number consecutively for 5 times starting with integer 2 till integer 6.

Complete step-by-step answer:
Before proceeding with the question we should understand the concept of rational numbers.
Rational numbers are represented in \[\dfrac{p}{q}\] form where q is not equal to zero. Any fraction with non-zero denominators is a rational number. Hence, we can say that ‘0’ is also a rational number, as we can represent it in many forms such as 0/1, 0/2, 0/3, etc. But, 1/0, 2/0, 3/0, etc. are not rational. Also, we can say that any fraction fit under the category of rational numbers, where denominator and numerator are integers and the denominator is not equal to zero.
So here we have to calculate the five rational numbers of a fraction. Hence we will first multiply 2 in both numerator and denominator, then 3 in both numerator and denominator, similarly 4 in both numerator and denominator, likewise 5 in both numerator and denominator and at last 6 in both numerator and denominator.
(i) Five rational number to \[\dfrac{5}{2}\] are \[\dfrac{5\times 2}{2\times 2}=\dfrac{10}{4}\], \[\dfrac{5\times 3}{2\times 3}=\dfrac{15}{6}\], \[\dfrac{5\times 4}{2\times 4}=\dfrac{20}{8}\], \[\dfrac{5\times 5}{2\times 5}=\dfrac{25}{10}\] and \[\dfrac{5\times 6}{2\times 6}=\dfrac{30}{12}\].
(ii) Five rational number to \[-\dfrac{7}{9}\] are \[-\dfrac{7\times 2}{9\times 2}=-\dfrac{14}{18}\], \[-\dfrac{7\times 3}{9\times 3}=-\dfrac{21}{27}\], \[-\dfrac{7\times 4}{9\times 4}=-\dfrac{28}{36}\], \[-\dfrac{7\times 5}{9\times 5}=-\dfrac{35}{45}\] and \[-\dfrac{7\times 6}{9\times 6}=-\dfrac{42}{54}\].
(iii) Five rational number to \[-\dfrac{3}{7}\] are \[-\dfrac{3\times 2}{7\times 2}=-\dfrac{6}{14}\], \[-\dfrac{3\times 3}{7\times 3}=-\dfrac{9}{21}\], \[-\dfrac{3\times 4}{7\times 4}=-\dfrac{12}{28}\], \[-\dfrac{3\times 5}{7\times 5}=-\dfrac{15}{35}\] and \[-\dfrac{3\times 6}{7\times 6}=-\dfrac{18}{42}\].

Note: Remembering the definition of rational numbers is the key here. Also in a hurry we can make a mistake of multiplying 4 in both numerator and denominator after 2 while missing 3. Also in subpart (ii) and (iii) we can forget to write minus signs in a hurry so we need to be careful while doing this step.