Simplify the following ratios. 450 g : 2 1 4 kg : 3 . 6 kg

Given, To find the simplest form of the ratio of 450 g : 2 1 4 kg : 3 . 6 kg Two or more quantities can be compared only if they are in the same unit. We know that, 1000 g = 1 kg 450 g = 450 1000 = 9 20 kg 2 1 4 kg = 8 + 1 4 = 9 4 kg Also, 3 . 6 kg = 36 10 = 18 5 kg So the ratio is 9 20 : 9 4 : 18 5 Now, we need to convert 9 20 : 9 4 : 18 5 into simple ratio. Multiply each term with the L.C.M. of its consequents. The L.C.M. of 20 , 4 , 5 is 20 . ⇒ 9 20 : 9 4 : 18 5 = 9 20 × 20 : 9 4 × 20 : 18 5 × 20 ⇒ 9 20 : 9 4 : 18 5 = 9 : 45 : 72 or 1 : 5 : 8 Thus, the simplest form of the given ratio is 1 : 5 : 8

Simplify the following ratios. 45 min : 900 sec : 1 2 hour

Given, To find the simplest form of the ratio of 45 min : 900 sec : 1 2 hour Two or more quantities can be compared only if they are in the same unit. We know that, 60 sec = 1 min and 60 min = 1 hour 900 sec = 900 60 = 15 min 1 2 hour = 1 2 × 60 = 30 min So the ratio is 45 min : 15 min : 30 min Now, we need to convert 45 : 15 : 30 into simple ratio. Divide each term with the HCF of three terms. The HCF of 45 , 15 , 30 is 15 . ⇒ 45 : 15 : 30 = 45 15 : 15 15 : 30 15 ⇒ 45 : 15 : 30 = 3 : 1 : 2 Thus, the simplest form of the given ratio is 3 : 1 : 2