**Ratio** of the two terms is denoted by a:b and is measured by a/b. The a in the numerator is called as antecedent and the denominator b is called as consequent.

The ratio basically means how many multiples or parts is a of b.

**Proportion: **The numbers are in proportion when two ratios of the two terms are equal to ratio of other two terms, if a:b=c:d then a,b,c and d are in proportions

**Variations: ** The 2 quantities are said to be in direct or inverse proportion (variation) when a change in one quantity directly effects the other one. There can be direct effect that is known as direct proportion ( Like increase in “a” causes increase in “b”) and Inverse proportion when ( increase in “a” causes decrease in b).

Have understood what is meant by Ratio, Proportion and Variations: we will consider some important points and rules related to these subjects

**Ratios:** Some important points are as follows:

- Both the antecedent and consequent should be in the same unit of measure
- If the units are given in different measures then we need to combine units by compounding. e.g. ( m:n) and (a:b) then compounded ratio is (mxa)/(nxb)

- Ratio would remain unchanged when a constant number is multiplied or divided by antecedent or consequent

**Some imp. Rules for Ratios**

**Rules of Invertendo, Atlterendo, Componendo, Dividendo and Compendo and Dividendo in Ratios**

**Important Rules for Proportions:**

1. If a:b=c:d then ad = bc

2. If in case we have a:b=b:c then this is a case of continued proportions and we can have b^{2} = ac, thus we can say b is mean of “a” and “c” and can be called as mean proportional

The concept of mean proportional and continued proportions can be useful finding one of the missing ratios in a set of 4 ratios for e.g.

**Important rules on Variations are as follows:**

If you liked my contribution, please donate, a little that will be generated will all be donated for noble cause. [paypal-donation]