What is a ratio ?
A ratio is a comparison made by dividing the size of two or more quantities of the same type.
The measurements of quantities should be in the same units.
To express the given ratio in a simplest form, we follow the below steps.
Problem 1 :
a) 2 : 4 b) 56 : 14 c) 15 : 25 d) 0.4 : 0.5 e) 0.2 : 0.6 |
f) 0.03 : 0.15 g) 1/5 : 4/5 h) 5/4 : 1/4 i) 1/3 : 2 j) 3 : 1/2 |
Solution :
a) = 2 : 4 HCF(2, 4) is 2. = (2/2) : (4/2) S.F = 1 : 2 |
f) = 0.03 : 0.15 = (0.03×100) : (0.15×100) = 3 : 15 HCF(3, 15) is 3. = 3/3 : 15/3 S. F = 1 : 5 |
b) = 56 : 14 HCF(56, 14) is 14. = (56/14) : (14/14) S. F = 4 : 1 |
g) = 1/5 : 4/5 = (1/5×5) : (4/5×5) S.F = 1 : 4 |
c) = 15 : 25 HCF(15, 25) is 5. = (15/5) : (25/5) S. F = 3 : 5 |
h) = 5/4 : 1/4 = (5/4×4) : (1/4×4) S. F = 5 : 1 |
d) = 0.4 : 0.5 = (0.4×10) : (0.5×10) S. F = 4 : 5 |
i) = 1/3 : 2 = (1/3×3) : (2×3) S. F = 1 : 6 |
e) = 0.2 : 0.6 = (0.2×10) : (0.6×10) = 2 : 6 HCF(2, 6) is 2. = (2/2) : (6/2) S. F = 1 : 3 |
j) = 3 : 1/2 = (3×2) : (1/2×2) S. F = 6 : 1 |
Problem 2 :
34 mm to 1 cm
Solution :
Since the given measurements are in different units, first make their units the same.
10 mm = 1 cm
34 mm = 34/10 cm
= 34/10 : 1
= (34/10×10) : (1×10)
= 34 : 10
HCF(34, 10) is 2.
= (34/2) : (10/2)
Simplest Form = 17 : 5
Problem 3 :
2 m to 125 cm
Solution :
Since the given measurements are in different units, first make their units the same.
1 m = 100 cm
2 m = 200 cm
= 200 : 125
HCF(200, 125) is 25.
= (200/25) : (125/25)
Simplest Form = 8 : 5
Problem 4 :
24 seconds to 1 1/2 min
Solution :
= 24 seconds to 1 1/2 min
Converting mixed fraction into improper fraction.
= 24 seconds to 3/2 min
Now, we need to change their units to be the same.
1 min = 60 sec
3/2 min = 3/2 × 60 = 90 sec
= 24 : 90
HCF(24, 90) is 6.
= (24/6) : (90/6)
Simplest Form = 4 : 15
Problem 5 :
2 L to 750 ml
Solution :
= 2 L to 750 ml
Now, we need to change their units to be the same.
1 L = 1000 ml
2 L = 2000 ml
= 2000 : 750
HCF(2000, 750) is 250.
= (2000/250) : (750/250)
Simplest Form = 8 : 3
Problem 6 :
1 week to 3 days
Solution :
= 1 week to 3 days
1 week = 7 days
Simplest Form = 7 : 3
Problem 7 :
4 weeks to 1 year
Solution :
= 4 weeks to 1 year
1 year = 52 weeks
= 4 : 52
HCF(4, 48) is 4.
= (4/4) : (52/4)
Simplest Form = 1 : 13
Problem 8 :
250 g to 1 kg
Solution :
= 250 g to 1 kg
1 kg = 1000 g
= 250 : 1000
= (250/250) : (1000/250)
Simplest Form = 1 : 4
Problem 9 :
1.5 kg to 125 g
Solution :
= 1.5 kg to 125 g
1 kg = 1000 g
1.5 kg = 1500 g
= 1500 : 125
= (1500/125) : (125/125)
S.F = 12 : 1
Problem 10 :
3 min to 45 seconds
Solution :
= 3 min to 45 seconds
1 min = 60 sec
3 min = 3 × 60 = 180 sec
= 180 : 45
= (180/45) : (45/45)
S. F = 4 : 1
Problem 11 :
Express in simplest form the ratio of shaded area: unshaded area
Shaded area : Unshaded area = 5 : 2 | |
Shaded area : Unshaded area = 4 : 1 | |
Shaded area : Unshaded area = 2 : 2 = 1 : 1 | |
Shaded area : Unshaded area = 1 : 8 |
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