Express the following ratios in their simplest form.
A. 20cm to 48cm=
B. 28:252=
C. 50km:80km=
D. 500g:2kg=
E. 14 days to 3 weeks=
A. The simplest form of the ratio 20cm to 48cm is 5:12.
B. The simplest form of the ratio 28:252 is 1:9.
C. The simplest form of the ratio 50km:80km is 5:8.
D. The simplest form of the ratio 500g:2kg is 1:4.
E. The simplest form of the ratio 14 days to 3 weeks is 2:3.
A. To express the ratio 20cm to 48cm in its simplest form, we need to divide both numbers by their greatest common divisor (GCD).
The GCD of 20 and 48 is 4.
Dividing both numbers by 4, we get:
20cm ÷ 4 = 5cm
48cm ÷ 4 = 12cm
Therefore, the simplest form of the ratio 20cm to 48cm is 5cm to 12cm.
B. To express the ratio 28:252 in its simplest form, we again need to find the GCD of these two numbers.
The GCD of 28 and 252 is 28.
Dividing both numbers by 28, we get:
28 ÷ 28 = 1
252 ÷ 28 = 9
Therefore, the simplest form of the ratio 28:252 is 1:9.
C. To express the ratio 50km:80km in its simplest form, we need to find the GCD of 50 and 80.
The GCD of 50 and 80 is 10.
Dividing both numbers by 10, we get:
50km ÷ 10 = 5km
80km ÷ 10 = 8km
Therefore, the simplest form of the ratio 50km:80km is 5km:8km.
D. To express the ratio 500g:2kg in its simplest form, we need to convert both quantities to the same unit.
Since 1 kilogram (kg) is equal to 1000 grams (g), we can convert 2kg to grams by multiplying by 1000.
2kg * 1000g/kg = 2000g
Now we have the ratio 500g:2000g.
Next, we can simplify this ratio by dividing both numbers by their GCD.
The GCD of 500 and 2000 is 500.
Dividing both numbers by 500, we get:
500g ÷ 500 = 1g
2000g ÷ 500 = 4g
Therefore, the simplest form of the ratio 500g:2kg is 1g:4g.
E. To express the ratio 14 days to 3 weeks in its simplest form, we first need to convert both quantities to the same unit.
Since there are 7 days in a week, we can convert 3 weeks to days by multiplying by 7.
3 weeks * 7 days/week = 21 days
Now we have the ratio 14 days:21 days.
Next, we can simplify this ratio by dividing both numbers by their GCD.
The GCD of 14 and 21 is 7.
Dividing both numbers by 7, we get:
14 days ÷ 7 = 2 days
21 days ÷ 7 = 3 days
Therefore, the simplest form of the ratio 14 days to 3 weeks is 2 days:3 days.