Question

Which of the following form an equivalent pair of rational numbers?

(a) \(\frac{120}{45} \,and \,\frac{160}{6}\)

(b) \(\frac{55}{6} \,and \,\frac{220}{12}\)

(c) \(\frac{-8}{13} \,and \,\frac{16}{26}\)

(d) \(\frac{-230}{300} \,and \,\frac{-46}{60}\)

This question was addressed to me by my school teacher while I was bunking the class.

This question is from Representation of Numbers on Number Line topic in portion Rational Numbers of Mathematics – Class 8

Answer 1

Right option is (d) \(\frac{-230}{300} \,and \,\frac{-46}{60}\)

Explanation: When the rational numbers in their reduced form give equal fractions those numbers are called equivalent pair of rational numbers.

Here, we have 4 pairs of rational numbers in fractional form.

\(\frac{120}{45} \,and \,\frac{160}{6}\) when reduced we get 8/3 and 80/3

\(\frac{55}{6} \,and \,\frac{220}{12}\) when reduced we get 55/6 and 55/3

\(\frac{-8}{13} \,and \,\frac{16}{26}\)  when reduced we get (-8)/13 and 8/13

\(\frac{-230}{300} \,and \,\frac{-46}{60}\) when reduced we get \(\frac{-23}{30} \,and \,\frac{-23}{30}\). Here we see that both the numbers are equal and hence this pair is equivalent pair.