Question

Find each of the following ratios in the simplest form:
(i) 24 to 56
(ii) 84 paise to Rs 3
(iii) 4 kg to 750 g
(iv) 1.8 kg to 6 kg
(v) 48 minutes to 1 hour
(vi) 2.4 km to 900 m

Answer 1

(i) 24:56 = 24 = 24 ​÷ 8 = 3
56 56 ​÷ 8 7
As the H.C.F. of 3 and 7 is 1, the simplest form of 24:56 is 3:7.

(ii) 84 paise to Rs 3 = Rs 0.84 to R. 3 = 0.84 = 0.84​ ÷ 3 = 0.28 = 28 = 28 ​÷ 4 = 7
3 3 ​÷ 3 1 100 100 ​÷ 4 25
As the H.C.F. of 7 and 25 is 1, the simplest form of 0.84:3 is 7:25.

(iii) 4 kg:750 g = 4000 g:750 g = 4000 ​÷ 250 = 16
750 ​÷ 250 3
As the H.C.F. of 16 and 3 is 1, the simplest form of 4000:750 is 16:3.

(iv) 1.8 kg:6 kg = 1.8 = 18 = 18 ​÷ 6 = 3
6 60 60 ​÷ 6 10
As the H.C.F. of 3 and 10 is 1, the simplest form of 1.8:6 is 3:1.

(v) 48 minutes to 1 hour = 48 minutes to 60 minutes = 48:60 = 48 ​÷ 12 = 4
60 ​÷ 12 5
As the H.C.F. of 4 and 5 is 1, the simplest form of 48:60 is 4:5.

(vi) 2.4 km to 900 m = 2400m:900m = 2400 = 24 = 24 ​÷ 3 = 8
900 9 9 ​÷ 3 3
As the H.C.F. of 8 and 3 is 1, the simplest form of 2400:900 is 8:3.