RATIO AND PROPORTION

Ratio:

The ratio of two quantities a and b in the same units, is the fraction and we write it as a : b.

In the ratio a : b, we call a as the first term or antecedent and b, the second term or consequent.

Eg. 

The ratio 5 : 9 represents antecedent = 5; consequent = 9.

Rule:
The multiplication or division of each term of a ratio by the same non-zero number does not affect the ratio.

Eg. 
4 : 5 = 8 : 10 = 12 : 15.
Also, 4 : 6 = 2 : 3.

Proportion:

The equality of two ratios is called proportion. 

If a : b = c : d, we write a : b :: c : d

and we say that a, b, c, d are in proportion. 

Here a and d are called extremes, while b and c are called mean terms.

Product of means = Product of extremes. 

Thus, for a : b :: c : d,

(b x c) = (a x d).

Comparison of Ratios:

We say that 

(a : b) > (c : d) ==> (a / b)> (c / d ) .

Compounded Ratio: 
The compounded ratio of the ratios: (a : b), (c : d), (e : f) is (ace : bdf).

Duplicate Ratios:

Duplicate ratio of (a : b) is (a^2 : b^2).
Sub-duplicate ratio of (a : b) is (a^1/2 : b^1/2). 

Triplicate ratio of (a : b) is (a^3 : b^3).
Sub-triplicate ratio of (a : b) is (a^1/3 : b^1/3).

If a/b = c/d, then (a + b) / (a - b) = (c + d) / (c - d).