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
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
(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
(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
