Ratio and Proportion
Ratio
Comparison of two quantities in the same unit is called a ratio.
E.g. 2:3   or   2/3   or   2 3

Proportion
Equality of two ratios is called a proportion.
E.g. 2:3 :: 4:6   or   2 3 = 4 6
Laws of Ratio and Proportion
If a b = c d , then ad = bc
Alternendo
If a b = c d , then a c = b d
Invertendo
If a b = c d , then b a = d c
Componendo
If a b = c d , then a + b b = c + d d
Dividendo
If a b = c d , then a − b b = c − d d
Componendo and Dividendo
If a b = c d , then a − b b = c − d d
Theorem on Equal Ratios
If a b = c d , then a b = c d = xa + yc xb + yd