Question

Find the ratios of the following in their simplest form.
(i) 25 minutes to 55 minutes
() 45 seconds to 30 minutes
(11)4 m. 20 cm to 8 m. 40 cm
v) 5 litres to 0.75 litre
(v) 4 weeks to 4 days
(vi) 5 dozen to 2 scores (1 score=20iitems​

Answer 1

Answer:

1. 25/55=5/11=5:11
2. 45/30=9/6=3/2=3:2
3. 420/840=1/2=1:2

Answer 2

Answer: i) The simplest form of the ratio of 25 minutes to 55 minutes is 5:11.

ii) The simplest form of the ratio of 45 seconds to 30 minutes is 1:40.

iii) The simplest form of the ratio of 4 m. 20 cm to 8 m. 40 cm is 21:42, which can be further simplified to 1:2.

iv) The simplest form of the ratio of 5 liters to 0.75 liter is 2:3.

v) The simplest form of the ratio of 4 weeks to 4 days is 7:1.

vi) The simplest form of the ratio of 5 dozen to 2 scores is 3:2.

(i) 25 minutes to 55 minutes

To find the ratio of 25 minutes to 55 minutes in its simplest form, we need to divide both numbers by their greatest common factor (GCF). The GCF of 25 and 55 is 5. Therefore, we get:

25 minutes ÷ 5 = 5 minutes

55 minutes ÷ 5 = 11 minutes

So the simplest form of the ratio of 25 minutes to 55 minutes is 5:11.

(ii) 45 seconds to 30 minutes

To find the ratio of 45 seconds to 30 minutes in its simplest form, we need to convert both quantities to the same unit (either seconds or minutes). Since we want the ratio to be in minutes, we need to convert 45 seconds to minutes. We can do this by dividing 45 by 60:

45 seconds ÷ 60 = 0.75 minutes

Now we can compare 0.75 minutes to 30 minutes. To simplify the ratio, we can divide both numbers by their GCF, which is 0.75:

0.75 minutes ÷ 0.75 = 1 minute

30 minutes ÷ 0.75 = 40 minutes

So the simplest form of the ratio of 45 seconds to 30 minutes is 1:40.

(iii) 4 m. 20 cm to 8 m. 40 cm

To find the ratio of 4 m. 20 cm to 8 m. 40 cm in its simplest form, we need to convert both quantities to the same unit (either meters or centimeters). Since both quantities are already in meters and centimeters, respectively, we can just add the centimeters to the meters to get:

4 m. 20 cm = 4.20 m

8 m. 40 cm = 8.40 m

Now we can simplify the ratio by dividing both numbers by their GCF, which is 0.20:

4.20 m ÷ 0.20 = 21

8.40 m ÷ 0.20 = 42

So the simplest form of the ratio of 4 m. 20 cm to 8 m. 40 cm is 21:42, which can be further simplified to 1:2.

(iv) 5 litres to 0.75 litre

To find the ratio of 5 litres to 0.75 litre in its simplest form, we need to convert both quantities to the same unit (either liters or milliliters). Since we want the ratio to be in liters, we can convert 0.75 liter to milliliters by multiplying it by 1000:

0.75 liter × 1000 = 750 milliliters

Now we can compare 5 liters to 750 milliliters. To simplify the ratio, we can divide both numbers by their GCF, which is 250:

5 liters ÷ 250 = 0.02 liters

750 milliliters ÷ 250 = 3 liters

So the simplest form of the ratio of 5 liters to 0.75 liter is 2:3.

(v) 4 weeks to 4 days

To find the ratio of 4 weeks to 4 days in its simplest form, we need to convert both quantities to the same unit (either weeks or days). Since we want the ratio to be in days, we can convert 4 weeks to days by multiplying it by 7:

4 weeks × 7 = 28 days

Now we can compare 28 days to 4 days. To simplify the ratio, we can divide both numbers by their GCF, which is 4:

28 days ÷ 4 = 7 days

4 days ÷ 4 = 1 day

So the simplest form of the ratio of 4 weeks to 4 days is 7:1.

(vi) 5 dozen to 2 scores (1 score=20 items)

To find the ratio of 5 dozen to 2 scores in its simplest form, we need to convert both quantities to the same unit (either dozens or items). Since we want the ratio to be in items, we can convert 5 dozen to items by multiplying it by 12:

5 dozen × 12 = 60 items

We can also convert 2 scores to items by multiplying it by 20:

2 scores × 20 = 40 items

Now we can compare 60 items to 40 items. To simplify the ratio, we can divide both numbers by their GCF, which is 20:

60 items ÷ 20 = 3 items

40 items ÷ 20 = 2 items

So the simplest form of the ratio of 5 dozen to 2 scores is 3:2.

Learn more about the greatest common factor here

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