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Ratio and Proportion

Maharashtra Board · Class 9 · Mathematics

Quick revision notes for Ratio and Proportion — Maharashtra Board Class 9 Mathematics. Key concepts, formulas, and definitions for last-minute revision.

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Key Topics to Revise

1

Ratio – Basics and Properties

  • The ratio of two quantities a and b is written as a:b or a/b, where a is the predecessor (first term) and b is the successor (second term).
  • Both quantities in a ratio must be expressed in the SAME unit before comparing.
  • A ratio is a unitless (dimensionless) quantity.
2

Direct and Inverse Proportion

  • In Direct Proportion, as one quantity increases, the other also increases in the SAME ratio. Their ratio (x/y) is constant.
  • In Inverse Proportion, as one quantity increases, the other decreases. Their PRODUCT (x × y) is constant.
  • Direct proportion: x/y = k (constant), so x₁/y₁ = x₂/y₂.
3

Operations on Equal Ratios (Properties)

  • These 5 properties apply when a/b = c/d and a, b, c, d are positive numbers.
  • INVERTENDO: Flip both fractions. If a/b = c/d, then b/a = d/c.
  • ALTERNANDO: Swap the means. If a/b = c/d, then a/c = b/d.
4

Theorem of Equal Ratios

  • If a/b = c/d, then a/b = c/d = (a+c)/(b+d). This is the Theorem of Equal Ratios.
  • Extended form: If a/b = c/d = e/f = ... then each ratio = (a+c+e+...)/(b+d+f+...).
  • General form with multipliers: If a/b = c/d = e/f and l, m, n are non-zero numbers, then each ratio = (al+cm+en)/(bl+dm+fn).

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Full Notes

Key Concepts

A ratio is a comparisonWhen comparing more than two quantitiesKey properties includeTo compare two ratios a/bIf a/b = c/d

Frequently 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 and Proportion – Complete Chapter Overview, Ratio and Proportion - Concept Overview, Flowchart showing the process of creating a ratio from two quantities. These are the concepts Maharashtra Board Class 9 examiners draw on most — study them first, then practise related questions.
How to score full marks in Ratio and Proportion — Maharashtra Board Class 9 Mathematics?
Understand the core concepts first, then work through the 58 practice questions available for this chapter. Revise formulas and 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.

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