Ratio and Proportion — Formula Sheet
Maharashtra Board · Class 9 · Mathematics
10 formulas from Ratio and Proportion (Maharashtra Board Class 9 Mathematics) on one page, grouped by topic. Includes Direct proportion, INVERTENDO.
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Formulas and Key Relations
Direct and Inverse Proportion
Direct proportion
x/y = k (constant), so x₁/y₁ = x₂/y₂.
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.
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).
Key relations
Key properties include
(1) A ratio remains unchanged if both terms are multiplied or divided by the same non-zero number (3:4 = 6:8 = 9:12 = 12:16).
If ad = bc, then a/b = c/d.
If a/b = c/d, then b/a = d/c (reversing both fractions).
For example, if 2/3 = 4/6, then 3/2 = 6/4.
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Sources & Official References
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
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