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Proportion

Algebra and Sequences

Recognising it

  • In inverse proportion one quantity rises as the other falls, and it is their product that stays fixed
  • Written in symbols, y ∝ 1 ÷ x, which becomes y = k ÷ x
  • Doubling one quantity halves the other, and multiplying one by 3 divides the other by 3
  • The graph is a curve that approaches each axis without ever touching it, quite unlike the straight line of direct proportion
A graph of an inversely proportional relationship: two curved branches in opposite quadrants, each falling steeply near the y-axis and flattening towards the x-axis without ever meeting either
Source: Inverse proportion by Save My Exams
  • Real contexts are usually a fixed total shared out: more workers means less time, more speed means less travelling time
Worked example

An inverse relationship

T is inversely proportional to n. When n = 5, T = 12. Find T when n = 8.

Solution:

  • The statement gives the equation T = k ÷ n
  • Substitute the given pair: 12 = k ÷ 5
  • Multiply by 5: k = 60
  • The finished equation is T = 60 ÷ n
  • Substitute n = 8: T = 60 ÷ 8
  • So T = 7.5