PPT: Ratio and Proportion

 Page 1


Ratio and Proportion
Page 2


Ratio and Proportion
What Are Ratios?
Definition
A ratio is a comparison between 
two or more quantities expressed 
as a fraction or using the colon 
notation.
Expression
If two quantities are a and b, their 
ratio can be written as:
a : b = 
b
a
Key Point
Ratios are dimensionless - they 
have no units and represent relative 
sizes only.
Page 3


Ratio and Proportion
What Are Ratios?
Definition
A ratio is a comparison between 
two or more quantities expressed 
as a fraction or using the colon 
notation.
Expression
If two quantities are a and b, their 
ratio can be written as:
a : b = 
b
a
Key Point
Ratios are dimensionless - they 
have no units and represent relative 
sizes only.
Types of Ratios
Simple Ratio
Comparison of two quantities
Example: 3:4 or 5:7
 
b
a
Compound Ratio
Product of two or more simple 
ratios
Example: (2:3) × (4:5) = 8:15
 ×
b
a
 =
d
c
 
b d
a c
Continued Ratio
Comparison of three or more 
quantities
Example: 2:3:5 or 4:6:9:12
a : b : c : d
CAT loves ratios - EduRev prepares you for every type.
Page 4


Ratio and Proportion
What Are Ratios?
Definition
A ratio is a comparison between 
two or more quantities expressed 
as a fraction or using the colon 
notation.
Expression
If two quantities are a and b, their 
ratio can be written as:
a : b = 
b
a
Key Point
Ratios are dimensionless - they 
have no units and represent relative 
sizes only.
Types of Ratios
Simple Ratio
Comparison of two quantities
Example: 3:4 or 5:7
 
b
a
Compound Ratio
Product of two or more simple 
ratios
Example: (2:3) × (4:5) = 8:15
 ×
b
a
 =
d
c
 
b d
a c
Continued Ratio
Comparison of three or more 
quantities
Example: 2:3:5 or 4:6:9:12
a : b : c : d
CAT loves ratios - EduRev prepares you for every type.
Properties of Ratios
Multiplication & Division
Both terms of a ratio can be multiplied or divided by the 
same non-zero number without changing its value.
Memory Trick: "Same operation on both 
sides keeps ratio alive!"
Equivalence
Two ratios a:b and c:d are equivalent if their cross 
products are equal.
a:b = c:d if ad = bc
Reciprocal
If a:b = c:d, then their reciprocals are also equivalent:
b:a = d:c
Cross Multiplication
For equivalent ratios a:b = c:d, the product of the means 
equals the product of the extremes:
a × d = b × c
Page 5


Ratio and Proportion
What Are Ratios?
Definition
A ratio is a comparison between 
two or more quantities expressed 
as a fraction or using the colon 
notation.
Expression
If two quantities are a and b, their 
ratio can be written as:
a : b = 
b
a
Key Point
Ratios are dimensionless - they 
have no units and represent relative 
sizes only.
Types of Ratios
Simple Ratio
Comparison of two quantities
Example: 3:4 or 5:7
 
b
a
Compound Ratio
Product of two or more simple 
ratios
Example: (2:3) × (4:5) = 8:15
 ×
b
a
 =
d
c
 
b d
a c
Continued Ratio
Comparison of three or more 
quantities
Example: 2:3:5 or 4:6:9:12
a : b : c : d
CAT loves ratios - EduRev prepares you for every type.
Properties of Ratios
Multiplication & Division
Both terms of a ratio can be multiplied or divided by the 
same non-zero number without changing its value.
Memory Trick: "Same operation on both 
sides keeps ratio alive!"
Equivalence
Two ratios a:b and c:d are equivalent if their cross 
products are equal.
a:b = c:d if ad = bc
Reciprocal
If a:b = c:d, then their reciprocals are also equivalent:
b:a = d:c
Cross Multiplication
For equivalent ratios a:b = c:d, the product of the means 
equals the product of the extremes:
a × d = b × c
Understanding Proportions
Definition
A proportion states that two ratios are equal. When four 
quantities a, b, c, d are in proportion:
a : b = c : d o r =
b
a
d
c
Terms in Proportion
Extremes: First and fourth terms (a and d)
Means: Second and third terms (b and c)
Key Rule: Product of extremes = Product of means
a × d = b × c