Write each of these ratios in its simplest form.
b) 15:21
c) 72:45
d) 24cm:36cm
e) 350g:2kg
f) 42p:£1.36
g) 2.9:8.7
h) 3/5:9/10
b) 5:7
c) 8:5
d) 2:3
e) 7:40
f) 5:16
g) 1:3
h) 2:3
b) To simplify the ratio 15:21, we can divide both numbers by their greatest common divisor, which is 3. Dividing 15 by 3 gives us 5, and dividing 21 by 3 gives us 7. Therefore, the simplified ratio is 5:7.
c) To simplify the ratio 72:45, we can divide both numbers by their greatest common divisor, which is 9. Dividing 72 by 9 gives us 8, and dividing 45 by 9 gives us 5. Therefore, the simplified ratio is 8:5.
d) To simplify the ratio 24cm:36cm, we can divide both numbers by their greatest common divisor, which is 12. Dividing 24 by 12 gives us 2, and dividing 36 by 12 gives us 3. Therefore, the simplified ratio is 2:3.
e) To simplify the ratio 350g:2kg, we need to convert the units to the same type. Since there are 1000 grams in 1 kilogram, we can convert 2kg to 2000g. Now the ratio is 350g:2000g. We can divide both numbers by their greatest common divisor, which is 50. Dividing 350 by 50 gives us 7, and dividing 2000 by 50 gives us 40. Therefore, the simplified ratio is 7:40.
f) To simplify the ratio 42p:£1.36, we need to convert the units to the same type. Since there are 100 pence in 1 pound, we can convert £1.36 to 136p. Now the ratio is 42p:136p. We can divide both numbers by their greatest common divisor, which is 2. Dividing 42 by 2 gives us 21, and dividing 136 by 2 gives us 68. Therefore, the simplified ratio is 21:68.
g) To simplify the ratio 2.9:8.7, we can multiply both numbers by 10 to remove the decimal point. This gives us 29:87. We can divide both numbers by their greatest common divisor, which is 29. Dividing 29 by 29 gives us 1, and dividing 87 by 29 gives us 3. Therefore, the simplified ratio is 1:3.
h) To simplify the ratio 3/5:9/10, we can multiply both the numerator and denominator of the first fraction by 2 to get 6/10. Now the ratio is 6/10:9/10. Since the denominators are the same, we can combine the numerators to get 6+9=15. The denominator remains 10. Therefore, the simplified ratio is 15/10, which can be further simplified to 3/2.