**Ratio:** When two category are compared to ascertain how many times the first contains the other, this kind of comparison is known as ratio between the two quantities. Ratio has no unit and a fraction.

Mathematical Symbol of ratio: The mathematical symbol of ratio is represented by the sign “ : ”

Example: Ratio of TK 5 and TK 4 is 4:5

**Different kind of ratio:**

**Simple ratio:** The ratio having two quantities is called simple ratio.

The 1st quantity of simple ratio is called antecedent and the 2nd quantity is called subsequent.

Example: 4:5 ( here 4 is antecedent and 5 is subsequent).

**Ratio of less inequality:** If the antecedent is smaller than the subsequent of a simple ratio, then the ratio is called ratio of less inequality.

Example: 5:8

**Ratio of greater inequality:** If the antecedent is greater than the subsequent of a simple ratio, then the ratio is called ratio of greater inequality.

Example: 8:5

**Unit ratio:** The ratio in which the antecedent and subsequent are equal is called unit ratio.

Example: The number of mangoes is 21 and the number of apple is 21 in a box then the ratio of mangoes and apple is 21:21 or, 1:1.

So it is unit ratio.

**Inverse ratio:** The ratio formed by interchanging the antecedent and subsequent of a simple ratio is called inverse ratio.

Example: Inverse ratio of 4:5 is 5:4.

**Mixed ratio or Compound ratio:** The ratio obtained by whose antecedent and subsequent are formed by the products of antecedents and subsequent of two or more ratio is called mixed or compound ratio.

Example: Mixed ratio of 1:2,2:3and 3:4is 6:24 or 1:4

**Duplicate ratio:** The ratio formed by squaring the antecedent and subsequent of the given ratio as its antecedent and subsequent , then the ratio is called duplicate ratio.

Example: Duplicate ratio of 2:3 is 4:9.

**Sub duplicate ratio:** The ratio formed by taking the square roots of both the antecedent and subsequent of the given ratio is said to be the sub duplicate ratio of the given ratio.

Example: Sub duplicate ratio of 16:9 is 4:3.

**Successive ratio:** If two ratio A:B and B:C then there successive ratio is A:B:C.

**Proportion:** If the ratio of the 1st quantity and 2nd quantity is equal to the ratio of 3rd quantity and 4th quantity of given four quantities , then these four quantities form a proportion.

Example: 2:4=6:12

i) The four quantities are called proportional’s.

ii) The fourth quantity of the proportionality is said to be the 4th proportional of 1st , 2nd and 3rd proportional’s.

iii) The 1st and 4th quantities of the proportional are called extreme elements or simply extreme.

iv) The 2nd and 3rd quantities of the proportional are called mid elements or middle element.

Four quantities will same , it is no need.

v) 1st quantity*4th quantity=2nd quantity*3rd quantity in proportional.

**Continued proportion:** When the ratio of the 1st to the 2nd is the same as the ratio of the 2nd to the 3rd of the three given quantities of taken units are said to be continued proportion.

Example: let three quantities are 4 years, 6 years and 12 years. By these quantity two ratio will formed that’s are 4:6 and 6:12.

Here 4:6=6:12

2nd quantity of continued proportion is mean proportion or mid term of 1st and 3rd quantity.

1st quantity*3rd quantity=(2nd quantity)**2

Three quantities are same in continued proportion.

**Note that:** * indicate multiply and ** indicate power or index.