Question

Reduce each of the following ratios to their lowest terms:

(i) 1 hour 20 min: 2 hours

(ii) 4 weeks: 49 days

(iii) 3 years 4 months: 5 years 5 months

(iv) 2 m 40 cm: 1 m 44 cm

Answer 1

(i) 1 hour 20 min: 2 hours

We know that,

1 hour = 60 minutes

Hence, we can convert hour into minutes as:

1 hour = 1 × 60 minutes = 60 minutes

2 hours = 2 × 60 minutes = 120 minutes

So, the above expression can be written as follows:

(60 + 20) minutes / 120 minutes = 80 / 120

On further calculation, we get

= 2 / 3

= 2: 3

∴ The ratio of 1 hour 20 minutes: 2 hours will be 2: 3

(ii) 4 weeks: 49 days

We know that,

1 week = 7 days

Hence, we can convert weeks into days as given below

4 weeks = 4 × 7 days

= 28 days

So, the above expression can be written as follows:

28 days / 49 days = 4 / 7

We get

= 4: 7

∴ The ratio of 4 weeks: 49 days will be 4: 7

(iii) 3 years 4 months: 5 years 5 months

We know that,

1 year = 12 months

Hence, we can convert years into months as follows:

3 years = 3 × 12 months

= 36 months

5 years = 5 × 12 months

= 60 months

So, the above expression can be written as follows:

(36 + 4) months / (60 + 5) months = 40 / 65

On further calculation, we get

= 8 / 13

= 8: 13

∴ The ratio of 3 years 4 months: 5 years 5 months will be 8: 13

(iv) 2 m 40 cm: 1 m 44 cm

We know that,

1 metre = 100 cm

So, we can convert meter into centimetre as follows:

2 metre = 2 × 100 centimetres

= 200 centimetres

1 metre = 1 × 100 centimetre

= 100 centimetres

So, the above expression can be written as follows:

(200 + 40) centimetres / (100 + 44) centimetres = 240 / 144

On calculating further, we get

= 20 / 12

= 5 / 3

= 5: 3

∴ The ratio of 2 m 40 cm: 1 m 44 cm will be 5: 3