Express the following ratios in their simplest forms. Work them out.
A. 20cm to 48cm=
B. 28:252=
C. 50km:80km=
D. 500g:2kg=
E. 14 days to 3 weeks=
A. To simplify the ratio 20cm to 48cm, we divide both numbers by their greatest common divisor, which is 4:
20cm ÷ 4 = 5cm
48cm ÷ 4 = 12cm
Therefore, the simplified ratio is 5cm to 12cm.
B. Again, we simplify the ratio 28:252 by dividing both numbers by their greatest common divisor, which is 28:
28 ÷ 28 = 1
252 ÷ 28 = 9
So, the simplified ratio is 1:9.
C. To simplify the ratio 50km:80km, we divide both numbers by their greatest common divisor, which is 10:
50km ÷ 10 = 5km
80km ÷ 10 = 8km
Hence, the simplified ratio is 5km to 8km.
D. The ratio 500g:2kg can be simplified by converting 2kg to grams, since both numbers are in the same unit:
2kg = 2,000g
Now, the ratio becomes 500g:2,000g.
To simplify this ratio, we divide both numbers by their greatest common divisor, which is 500:
500g ÷ 500 = 1g
2,000g ÷ 500 = 4g
Therefore, the simplified ratio is 1g to 4g.
E. To simplify the ratio 14 days to 3 weeks, we convert weeks to days since both numbers are in the same unit:
1 week = 7 days
Thus, 3 weeks equals 3*7 = 21 days.
Now, the ratio becomes 14 days:21 days.
To simplify this ratio, we divide both numbers by their greatest common divisor, which is 7:
14 days ÷ 7 = 2 days
21 days ÷ 7 = 3 days
Hence, the simplified ratio is 2 days to 3 days.
A. To simplify the ratio 20cm to 48cm, we need to find the greatest common divisor (GCD) of these two numbers. The GCD of 20 and 48 is 4. Divide both numbers by 4 to simplify the ratio:
20cm ÷ 4 : 48cm ÷ 4 = 5cm : 12cm
So, the simplest form of the ratio 20cm to 48cm is 5cm to 12cm.
B. To simplify the ratio 28:252, we again find the GCD of these two numbers, which is 28. Divide both numbers by 28:
28 ÷ 28 : 252 ÷ 28 = 1 : 9
Therefore, the simplest form of the ratio 28:252 is 1:9.
C. The ratio 50km:80km can be simplified by finding the GCD of 50 and 80, which is 10. Divide both numbers by 10:
50km ÷ 10 : 80km ÷ 10 = 5km : 8km
So, the simplest form of the ratio 50km:80km is 5km:8km.
D. To simplify the ratio 500g:2kg, we need to convert one of the units to match the other. Since there are 1000 grams in a kilogram, we can convert 2kg to grams:
2kg = 2 × 1000g = 2000g
Now we have the ratio 500g:2000g. Notice that we can divide both numbers by 500:
500g ÷ 500 : 2000g ÷ 500 = 1g : 4g
Thus, the simplest form of the ratio 500g:2kg is 1g:4g.
E. To simplify the ratio 14 days to 3 weeks, we need to express both quantities in the same unit of time. Since there are 7 days in a week, we can convert 3 weeks to days:
3 weeks = 3 × 7 days = 21 days
Now the ratio becomes 14 days to 21 days. Notice that we can divide both numbers by 7:
14 days ÷ 7 : 21 days ÷ 7 = 2 days : 3 days
Hence, the simplest form of the ratio 14 days to 3 weeks is 2 days to 3 days.