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Standard Results/Definitions on Ratio/Proportion

  1. Continued proportion
     
    ab and c are said to be in continued proportion
     
    if Description: 2467.png
     
    So, b2 = ac. Here b is known as the mean proportion.
     
    Similarly, if abc and d are in continued proportion, then we get:
    Description: 2477.png 
  2. Componendo
     
    Description: 2486.png
  3. Dividendo
     
    If Description: 2495.png
  4. Componendo and Dividendo
     
    If Description: 2504.png
  5. Invertendo
     
    If Description: 2513.png
  6. Alterando
     
    If Description: 2522.png
  7. Description: 2531.png
     
    In general, if Description: 2540.png
     
    Then, Description: 2549.png = (any combination of the numerator/any combination of the corresponding denominator)
     
    For example, 1/2 = 3/6 = 4/8 =…= (1 + 3 + 4)/ (2 + 6 + 8) = (3 + 4)/(6 + 8)
  8. If we multiply the numerator and the denominator of a ratio by any number N (N ≠ 0), then the ratio remains same.
     
    A/B = NA/NB
  9. If we divide the numerator and the denominator of a ratio by any number N (N ≠ 0), then the ratio remains same.
     
    A/B = (A/N)/(B/N)
  10. If a/bc/de/f …etc., are all unequal ratios, then the value of (a + c + e +…)/(b + d + f +…) lies in between the minimum and the maximum of all these ratios.




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