“A statement of equality of two ratios is called proportion”
Four numbers a, b, c, d are said to be in proportion when the ratio first two a and b is equal to ratio of last two c and d.
i.e. or a : b = c : d
e.g. or 2 : 3 = 6 : 9
Some authors used the notation for proportion as a : b :: c : d, but this notation is not preferred now.
Here or a : b = c : d
If four numbers are in proportion, then we can also derived some other proportion from it.
Let be the given proportion, then
are called the Derived Proportions.
Here or a : b = c : d, then
The numbers a and d are called extremes of proportion, and the numbers b and c are called means of proportion.
Hence Product of extremes = Product of Means
To solve proportion, we use above principal, A single term in the proportion is called proportional.
“a” is the 1st proportional.
Find the 3rd proportional in 2 : 3 = : 15
Let 2 : 3 = : 15
3 x = 2 x 15 (by the principle of proportion)
3 = 30
Find the missing value in : 8 = 9 : 12
Let : 8 = 9 : 12
12 = 9 x 8 (by the principle of proportion)
12 = 72