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Ratio and Proportion — Class 9 Maharashtra SSC Mathematics revision notes

A 4-page visual revision sheet for Ratio and Proportion, written for Class 9 Maharashtra SSC Mathematics. Formulas, diagrams and the traps that cost marks, laid out to be read the night before rather than the term before. Free, and it opens inside CapCompass.

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Ratio and Proportion in one look

comparing two quantities by division, and the operations that keep a proportion true

Ratio, and the rules it obeys

  • a ratio compares two quantities of the same kind by division, written a : b and meaning a/b
  • the first term a is the antecedent and the second b the consequent
  • the two quantities must be in the same units before the ratio is written, so 50 cm to 2 m becomes 50 : 200
  • a ratio itself has no units, since the units cancel in the division
  • multiplying or dividing both terms by the same non zero number leaves the ratio unchanged, so 6 : 8 is 3 : 4
  • a ratio is normally given in its lowest terms, with the two parts having no common factor

Proportion, and the means and extremes

  • four quantities are in proportion when a : b = c : d, written a : b :: c : d
  • a and d are the extremes, the outer pair, and b and c the means, the inner pair
  • the defining property is that the product of the extremes equals the product of the means, so ad = bc
  • that cross multiplication is what turns any proportion into an ordinary equation
  • three quantities are in continued proportion when a : b = b : c, and then b is the mean proportional between a and c
  • in that case b^2 = ac, so the mean proportional is √ac

Operations that preserve a proportion

  • the basic property, cross multiplication a/b = c/d ⇒ ad = bc
  • invertendo, turn both sides over b/a = d/c
  • alternendo, swap the means a/c = b/d
  • componendo, add one to each side a+b/b = c+d/d
  • dividendo, subtract one from each side a-b/b = c-d/d
  • componendo and dividendo together a+b/a-b = c+d/c-d

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