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Ratio and Proportion — Revision Notes

Maharashtra Board · Class 9 · Mathematics

Ratio and Proportion revision notes for Maharashtra Board Class 9 Mathematics: 4 topics in quick points. Includes Ratio – Basics and Properties, Direct.

58 questions10 formulas & key relations5 concepts

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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 – 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.
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

All Maharashtra Board Class 9 Mathematics Revision Notes

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