Question

Which of the following pairs represent the same rational numbers?
(a). $\dfrac{-7}{21}\text{ and }\dfrac{3}{9}$
(b). $\dfrac{-16}{20}\text{ and }\dfrac{20}{-25}$
(c). $\dfrac{-2}{-3}\text{ and }\dfrac{2}{3}$
(d). $\dfrac{-1}{3}\text{ and }\dfrac{2}{9}$

Answer 1

Hint: For solving this problem, we consider all the options individually and try to simplify both the numerator and denominator to compare the values. If both the values are the same then the pair represents the same rational number.

Complete step-by-step solution -
Rational numbers are those numbers which can be represented in the form of $\dfrac{p}{q}$, where p is the numerator and q is the denominator and $q\ne 0$. p and q may belong to any of the three categories such as natural, whole or integers.
Considering option (a), we simplify $\dfrac{-7}{21}\text{ as }\dfrac{-1}{3}\text{ and }\dfrac{3}{9}\text{ as }\dfrac{1}{3}$. Since the denominator is the same, on comparing both of the values comes out to be different.
Considering option (b), we simplify $\dfrac{-16}{20}\text{ as }\dfrac{-4}{5}\text{ and }\dfrac{20}{-25}\text{ as }\dfrac{-4}{5}$. Since the denominator is the same, on comparing both the values comes out to be the same. So, this is the correct option.
Considering option (c), we simplify $\dfrac{-2}{-3}\text{ as }\dfrac{2}{3}\text{ and }\dfrac{2}{3}\text{ as }\dfrac{2}{3}$. Since the denominator is the same, on comparing both the values comes out to be the same. So, this is the correct option.
Considering option (d), we simplify $\dfrac{-1}{3}\text{ as }\dfrac{-3}{9}\text{ and }\dfrac{2}{9}\text{ as }\dfrac{2}{9}$ . Since the denominator is the same, on comparing both of the values comes out to be different.
Therefore, option (b) and (c) are correct.

Note: Students must be careful while dealing with the sign of the given rational number. The sign could be transferred from denominator to numerator by multiplying both the denominator and numerator with -1. One key step is the simplification of the numbers to the same denominator for comparison of numbers.