Question

Which of the following are pairs of equivalent rational numbers?

(i) $\frac{-13}{7},\frac{39}{-21}$
(ii) $\frac{3}{-8},\frac{-6}{16}$
(iii) $\frac{9}{4},\frac{-36}{-16}$
(iv) $\frac{7}{15},\frac{-28}{60}$
(v) $\frac{3}{12},\frac{-1}{4}$
(vi) $\frac{2}{3},\frac{3}{2}$

Answer 1

(i) $\frac{-13}{7},\frac{39}{-21}$
We have:
(−13)×(−21) = 273

And 7×39=273

$\begin{array}{l}(-\text{13})\times (-\text{21})=\text{7}\times \text{39}\\ \text{or}\frac{-\text{13}}{7}=\frac{\text{39}}{-21}\\ \text{Hence,}\frac{-\text{13}}{7}\mathrm{and}\frac{\text{39}}{21}\text{are equivalent rational numbers.}\end{array}$

(ii) $\frac{3}{-8},\frac{-6}{16}$
We have:

3×16=48

And (−8) ×(−6) =48

∴ 3×16 =(−8)×(−6)
$\frac{3}{-8}=\frac{-6}{16}$

(iii)$\frac{9}{4},\frac{-36}{-16}$

We have:

9×(−16)= −144

And 4×(-36)= −144

9×(−16) = 4×(−36)

$\frac{9}{4}=\frac{-36}{-16}$
Therefore, they are equivalent rational numbers.

(iv)$\frac{7}{15},\frac{-28}{60}$

We have:

7×60 =420
And 15×(-28)= −420

∴ 7×60 ≠15×(−28)
Therefore, the rational numbers are not equivalent.

(v) $\frac{3}{12},\frac{-1}{4}$

We have:
3 ×4=12
And 12×(−1)= −12
12 ≠ −12
Therefore, the rational numbers are not equivalent.

(vi) $\frac{2}{3},\frac{3}{2}$

We have:

2×2=4

And 3×3=9

2×2≠3×3

Therefore, the rational numbers are not equivalent.