RATIO AND PROPORTION

                                                  RATIO AND PROPORTION

Ratio of numbers- A ratio is formed when two quantities are compared by division i.e.

                                                In the ratio we call  the first term or antecedent and  the second term or consequent.

                                e.g.-  is a ratio in which first term is 3 and the second term is 5 and we define  .

ð  If a quantity increases (or decreases) in the ratio , then the new quantity  of the original quantity  is called a multiplying factor.

ð  If we have to divide a given number A in the ratio  , then,

First part =

Second part =

Third part =

Proportion- An equality of two ratios is called a proportion.

                Or, If two ratios are equal, we say that they are in proportion and use the symbol ‘: :’ or ‘=’ to equate the two ratios.

ð  The first and fourth terms of a proportion are called extremes and second and third terms are called means.

ð  Four quantities  are said to be in proportion if.

 

                                                i.e., Product of extremes = Product of means

                                e.g.-

                                         In

                                                Product of extremes =

                                                Product of extremes =  = 270.

                                                 Product of extremes = product of means.

ð  In a proportion  is called the fourth proportional.

ð  Three quantities are said to be in continued proportion if

 i.e.,

ð  In a continued proportion  is called the mean proportional between  and, and  is called the third proportional.

Unitary Method – The method of finding the value of the required number of a quantity by first finding the value of the unit quantity is called Unitary Method.