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Properties of Ratio

  • The order of the terms in a ratio is very important.
  • Ratio between two quantities should be in the most simplified form.
  • Ratio is a comparison of two or more quantities of the same kind only.
  • If the ratio of two quantities can be expressed as a ratio of two integers, the quantities are said to be commensurable; otherwise, they are said to be incommensurable.
  • Continued ratio is the relation between the magnitudes of three or more quantities of the same kind. The continued ratio of three similar quantities a, b, c is written as a:b:c.
  • Whenever a ratio a:b is given between two magnitudes, we always express the actual magnitudes as ka and kb,where k is a constant.
  • If a:b and c:d are two ratios, then ac:bd is their compound ratio.
  • a2:b2 is the duplicate ratio of a:b.
  • a3:b3 is the triplicate ratio of a:b.
  • Description: 12861.pngis the sub-duplicate ratio of a:b.
  • Description: 12855.pngis the sub-triplicate ratio of a:b.
  • If a given number N has to be divided into two parts A and B which are in the ratio a:b, then Description: 12849.png
  • If a given number N has to be divided into three parts A, B and C which are in the ratio of a:b:c; then,Description: 12843.png

Properties of Proportion

  • If Description: 12837.png, then Description: 12831.png (Invertendo)
  • If Description: 12823.png, then Description: 12817.png (Alternendo)
  • If Description: 12811.png, then Description: 12805.png (Componendo)
  • If Description: 12799.png, then Description: 12793.png (Dividendo)
  • If Description: 13218.png, then Description: 13212.png (Componendo and Dividendo)
  • Description: 13206.png (Addendo)
  • Description: 13200.png (Subtrahendo)

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