“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 of the first two, a and b, is equal to the ratio of the last two, c and d.
i.e. or a : b = c : d
e.g. or 2 : 3 = 6 : 9
Some authors use the notation a : b :: c : d for proportion, but this notation is not preferred.
Here or a : b = c : d
If four numbers are in proportion, then we can also derive some other proportions from them.
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 the proportion, we use the above principal, A single term in the proportion is called a proportional.
“a” is the 1st proportional.
“b” is the 2nd proportional.
“c” is the 3rd proportional.
“d” is the 4th 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
Find the 2nd proportional in 4, 20, 30.
Let be the 2nd proportional
4 : =20 : 30
x 20 = 4 x 30
= = 6