Ratio and Proportion
What is Ratio and Proportion?
A comparison of two quantities by division, expressed as a:b or a/b.
Key formula / rule: Product of Extremes and Means
Key points
- Understand the concept of ratio and proportion.
- Solve problems involving comparison of quantities.
- Apply ratio and proportion to solve real-world problems.
- Identify and use properties of proportion.
Common exam trap
Confusing the order of terms in a ratio.
Definitions
- Term
Ratio
- Meaning
A comparison of two quantities by division, expressed as a:b or a/b.
- Term
Proportion
- Meaning
An equation stating that two ratios are equal, e.g., a:b = c:d.
- Term
Terms of Proportion
- Meaning
In a proportion a:b = c:d, a and d are called extremes, while b and c are called means.
- Term
Continued Proportion
- Meaning
When the means of two equal ratios are the same, e.g., a:b = b:c.
Learning objectives
Understand the concept of ratio and proportion.
Solve problems involving comparison of quantities.
Apply ratio and proportion to solve real-world problems.
Identify and use properties of proportion.
Formulae
- Name
Product of Extremes and Means
- Note
This is the fundamental property of proportion.
- Expression
If a:b = c:d, then a × d = b × c
- Name
Continued Proportion
- Note
Here, b is the mean proportional between a and c.
- Expression
If a:b = b:c, then b² = ac
Prerequisites
Basic Arithmetic (Addition, Subtraction, Multiplication, Division)
Fractions and Decimals
Simplification of Fractions
Common mistakes
Confusing the order of terms in a ratio.
Incorrectly applying the product of extremes and means rule.
Failing to simplify ratios before comparison.
Misinterpreting the relationship in a proportion.
Keywords
Ratio
Proportion
Comparison
Means
Extremes
Continued Proportion
Direct Proportion
Inverse Proportion
Practice preview
If 15 men can complete a work in 20 days, how many days will 20 men take to complete the same work?…
medium
If A:B = 2:3 and B:C = 4:5, then A:B:C is?…
medium
Divide Rs. 1200 between A and B in the ratio 3:5.…
easy