Chapter 7 of 16
Concept Maps
Ratio and Proportion — Concept Maps
Maharashtra Board · Class 9 · Mathematics
3 concept maps of Ratio and Proportion for Maharashtra Board Class 9 Mathematics, each also written out as a text outline.
58 questions10 formulas & key relations5 concepts
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3 Concept Maps
Ratio and Proportion – Complete Chapter Overview
The map in words
- Ratio and Proportion
- Ratio Basics
- Definition a:b or a/b
- Predecessor First Term
- Successor Second Term
- Same unit required
- Unitless quantity
- Equivalent ratios ak:bk
- Proportion Types
- Direct Proportion
- x/y = k constant
- More x means more y
- Inverse Proportion
- x times y = k constant
- More x means less y
- Direct Proportion
- Properties of Equal Ratios
- Invertendo
- b/a = d/c
- Alternando
- a/c = b/d
- Componendo
- a+b over b = c+d over d
- Dividendo
- a-b over b = c-d over d
- Componendo-Dividendo
- a+b over a-b = c+d over c-d
- General Form with m
- Invertendo
- Theorem of Equal Ratios
- a/b = c/d = a+c over b+d
- Extended to many ratios
- With multipliers l m n
- Continued Proportion
- a/b = b/c
- b squared = ac
- Mean Proportional b
- b = root of ac
- k-Method
- Each ratio equals k
- a = bk and c = dk
- Substitute and simplify
- Powerful for proofs
- Multi-term Ratios
- a:b:c = p:q:r
- a=pk b=qk c=rk
- Find k from conditions
- Ratio Basics
Ratio and Proportion - Concept Overview
The map in words
- Ratio and Proportion
- Ratio Basics
- Definition a:b
- Same Units Required
- Unitless Property
- Simplification Methods
- Extended Ratios
- Three or More Terms
- k-Method Application
- Real-World Examples
- Properties of Ratios
- Invertendo
- Alternando
- Componendo
- Dividendo
- Componendo-Dividendo
- Comparison Methods
- Cross Multiplication
- Equal Ratios
- Theorem of Equal Ratios
- Special Concepts
- Continued Proportion
- Geometric Mean
- Mean Proportional
- Variation Types
- Direct Proportion
- Inverse Proportion
- Constant Relationships
- Problem Solving
- k-Method Steps
- Recipe Problems
- Distance Problems
- Mixture Problems
- Ratio Basics
Flowchart showing the process of creating a ratio from two quantities
The map in words
- Two Quantities
- Same Unit?
- Yes: Write as Ratio a:b
- a = Predecessor b = Successor
- Ratio is Unitless
- a = Predecessor b = Successor
- No: Convert to Same Unit
- Yes: Write as Ratio a:b
- Same Unit?
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Explore DiagramsFrequently Asked Questions
What are the important topics in Ratio and Proportion for Maharashtra Board Class 9 Mathematics?
Key topics in Ratio and Proportion include Ratio – Basics and Properties, Direct and Inverse Proportion, Operations on Equal Ratios (Properties), Theorem of Equal Ratios. Study these first, then practise questions on each for Class 9 exams.
What do the concept maps for Ratio and Proportion show?
The 3 maps show how the ideas in Ratio and Proportion connect: Ratio and Proportion – Complete Chapter Overview; Ratio and Proportion - Concept Overview. Each map is also written out as an outline on this page.
How should I revise Ratio and Proportion for Class 9 exams?
Learn the core ideas first, then work through the 58 practice questions on Ratio and Proportion. Revise definitions regularly and use flashcards for quick recall before the exam.
Sources & Official References
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
More resources for Ratio and Proportion
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