Third, Fourth and inverse proportion

13/07/2020 1 By indiafreenotes

The equality of any two ratios is called a proportion. For example, if we have any four numbers or quantities that we represent as ‘a’, ‘b’, ‘c’, and ‘d’ respectively, then we may write the proportion of these four quantities as:

16 : 9

a:b = c:d or a:b :: c:d. From this, we will now define the proportionals. Let us begin by defining the fourth proportional.

Similar to the f=definition of the fourth proportional, we define the term known as the third proportional. The third proportional of a proportion is the second term of the mean terms. For example, if we have a:b = c:d, then the term ‘c’ is the third proportional to ‘a’ and ‘b’.

Fourth Proportional

If a : b :: c:d or in other words a:b = c: d, then the quantity ‘d’ is what we call the fourth proportional to a, b and c.

For example, if we have 2, 3 and 4, 5 are in the proportion such that 2 and 5 are the extremes, then 5 is the fourth proportional to 2, 3, and 4.

Inversely Proportional

Inversely Proportional: when one value decreases at the same rate that the other increases.

Example: speed and travel time

Speed and travel time are Inversely Proportional because the faster we go the shorter the time.

  • As speed goes up, travel time goes down
  • And as speed goes down, travel time goes up

This: y is inversely proportional to x

Is the same thing as: y is directly proportional to 1/x

Which can be written:

y = k / x