State whether the following ratios are equivalent or not?
(a) 2 : 3 and 4 : 5
(b) 1 : 3 and 2 : 6
(a) Given ratios = 2 : 3 and 4 : 5
or 2/3 and 4/5
LCM of 3 and 5 = 15
⇒ 2/3 = (2 × 5)/(3 × 5) = 10/15
⇒ 4/5 = (4 × 3)/(5 × 3) = 12/15
Here, 10/15 ≠ 12/15
Hence 2 : 3 and 4 : 5 are not equivalent ratios.
(b) Given ratios = 1 : 3 and 2 : 6
or 1/3 and 2/6
LCM of 3 and 6 = 6
⇒ 1/3 = (1 × 2)/(3 × 2) = 2/6
⇒ 2/6 = (2 × 1)/(6 × 1) = 2/6
Here, 2/6 = 2/6
Hence, 1 : 3 and 2 : 6 are equivalent ratios.