Question

Which of the following pairs represent equivalent rational numbers ? 

(i) 7/12 and 28/48 

(ii) –2/-3 and –16/24

Answer 1

(i) 7/12 and 28/48

Now, first rational number is 7/12 and it is already in the standard form because there is no common factor in 7 and 12 other than 1. 

So, 7/12 is in its standard form ......(a)

Now, Consider 28/48

28 = 2 × 2 × 7 

48 = 2 × 2 × 2 × 2 × 3 

HCF = 2 × 2 = 4

Now, to reduce the rational numbers to its standard form, we divide the numerator and denominator by their HCF. First we take HCF of 28 and 48: 

Now, 28/48 = (28 ÷ 4)/(48 ÷ 4) = 7/12 .......(b)

From (a) and (b), we can say that the rational numbers 7/12 and 28/48 are equivalent.

(ii) -2/-3 and -16/24

First we multiply the numerator and denominator of –2/–3 by (–1), we get

-2/-3 = (-2) x (-1)/ (-3) x (-1) = 2/3  .....(a)

Now it is in its standard form.

Now, Consider 16/24

HCF of 16 and 24 is 2 × 2 × 2 = 8 

16 = 2 × 2 × 2 × 2 

24 = 2 × 2 × 2 × 3 

HCF = 2 × 2 × 2 = 8

So, -16/24 = (-16 ÷ 8)/(24 ÷ 8) = -2/3  .......(b)

From (a) and (b), we can say that the rational numbers -2/3-3 and -16/24 are not equivalent.