Inverse proportion is the opposite of proportion in that if one quantity increases, the other will decrease at the same rate.
It takes one person 1 hour to put 150 phones into boxes. The more who help, the less time it will take.
If, 5 people will take a fifth of the time to put the same number of letters in the envelopes. One fifth of the time is 12 minutes for 5 people to put the 150 phones into boxes.
Note: the number of phones and time time it takes to put them in boxes is directly proportional
Equations and inverse proportion
The equation for two quantities (x and y) being inversely proportional to each other can be linked them with the symbol and is expressed as:
This is then linked with the variables to the following equation, in the equation below, k is called the constant of proportionality.
This equation can then be rearranged to k = xy, where x and y are variables.
This can then be written as:
Using proportionality to write formulae
A good example to use in this context if the rule that the wavelength of a sound wave is inversely proportional to its frequency f.
Therefore when the wavelength of a sound wave traveling through air is 0.4 m its frequency is 825 Hz. Instead of using x and y as the variables, and f is used instead.
The formula above when then be used to solve problems involving wavelength and frequency of sound waves.
For example, a sound wave has a wavelength of 1.2 m. What is the frequency?
Once the equation is re arranged, insert 1.2 in the place of λ
f = 330 ÷ 1.2
f = 275 Hz