Thursday 17 September 2020

Math Formulae: Ratio And Proportion

 Some important Ratio and Proportion formulae:


 In ratio a : b (or  a ), a (numerator) is called antecedent and b (denominator) is called consequent.
b


 2.  Qualities to be expressed as ratio should have same units (like both should be in cm or in kg, but not one in kg and other in gram).


 3.  Ratio has no units.


 4.  Value of ratio (a : b) is not changed when both a and b are multiplied (or divide) by same number.


 5.  a/b  =  a  ×  d
c/dbc


 6.  Compounded ratio is result of multiplication of two or more ratios.


 7.  Duplicate ratio of (a : b) = ( a )2.
b


 8.  Sub-Duplicate ratio of (a : b) = ( a )1/2.
b


 9.  Triplicate ratio of (a : b) = ( a )3.
b


10.  Sub-triplicate ratio of (a : b) = ( a )1/3.
b


11.  a  =  (c + a.n) , if and only if,  a  =  c
b(d + b.n)bd


12.  (a + c)  >  a , if,  a  <  c
(b + d)bbd


13.  (a + c)  <  a , if,  a  >  c
(b + d)bbd


14.  If  a  >  1,  then,  (a + x)  <  a
b(b + x)b


15.  If  a  <  1,  then,  (a + x)  >  a
b(b + x)b


16.  If  a  >  1,  then,  (a - x)  >  a
b(b - x)b


17.  If  a  <  1,  then,  (a - x)  <  a
b(b - x)b


18.  If      a : b = a1:b1
    and   b : c = b2:c1
    then,  a : b : c = (a1.b2) : (b2.b1) : (b1.c1)


19.  If      a : b = a1:b1
    and   b : c = b2:c1
    and   c : d = c2:d1
    then,  a : b : c : d = (a1.b2.c2) : (b2.b1.c2) : (b1.c1.c2) : (b1.c1.d1)


20.  Proportion is equality of two ratios, i.e. a : b :: c : d. a and d are called extremes and b and c are called means.
  Here, a is 1st proportional, b is 2nd proportional,
            c is 3rd proportional, and d is 4th proportional.


21.  Product of extremes = Product of means, i.e. a × d = c × d


22.  If a : b = b : c then a, b, c are said to be in (continued) proportion.


23.  If a : b = b : c, then b2 = a × c. Here, b is said to be mean proportional between a and cand c is called third proportional.


24.  Invertendo: 
     If,  a  =  c , then,  b  =  d
bdac


25.  Alternando: 
     If,  a  =  c , then,  a  =  b
bdcd
26.  Componendo: 
     If,  a  =  c , then,  (a + b)  =  (c + d)
bdbd


27.  Dividendo: 
     If,  a  =  c , then,  (a - b)  =  (c - d)
bdbd


28.  Componendo and Dividendo: 
     If,  a  =  c , then,  (a + b)  =  (c + d)
bd(a - b)(c - d)


29.  Direct Variation:   If X ∝ Y, then
     X = k.Y,   or,      X  =  k
Y
     Where, k is constant of proportionality
     Also,    X1  =  X2
Y1Y2


30.  Inverse Variation:
     If    X ∝  1
Y
     then,    X  =  k,   or,      X.Y  =  k
Y
     Where, k is constant of proportionality
     Also,    X1.Y1  =  X2.Y2,    or,    

X1  =  Y2
X2Y1

To, readily access formula book on your mobile, you can open tools section in Tricky Maths App.

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