Proportions

A proportion is a term used to state that two ratios are equal.

• If a/b = c/d, then the ratio ‘a/b’ is proportionate to a ratio ‘c/d’. The equal ratios can be written as ‘a/b = c/d’ or ‘a:b = c:d’.
• When two ratios are equal, then the cross product of the ratios are equal. Thus the proportion ‘a:b = c:d’ is equal to ‘a x d = b x c’.
• Cross product of ratios is also used to find a missing term.

Example

        Find a value of ‘n’ in the following proportion

2/3 = n/9

                        2 x 9 = n x 3 (cross multiply)

18 = 3n

3n = 18

            n = 18/3 = 6

        Answer: 6

Directly proportional

Two variables are directly proportional if a change (increase or decrease) in one variable always accompanies the other variable. So if one variable increases, the other too will increase and vice versa.

Example

        Consider two variables Temperature (T) and Pressure (P), where the temperature is directly proportional (α) to pressure. That means the pressure increases corresponding to the temperature increase or the pressure decreases corresponding to the temperature decrease.

                T α P

                This can be written as T = kP (Where k is a constant)

Inversely proportional

Two variables are said to be inversely proportional to each other, if one value decreases at the same rate that the other increases.

Example

        Consider two variables Volume (V) and Pressure (P), where the pressure is inversely proportional to volume. That means the volume increases corresponding to the pressure decrease or the volume decreases corresponding to the pressure increase.