# Inverse proportion

**Inverse proportion**

**Inverse proportion** is the opposite of proportion in that if one quantity increases, the other will decrease at the same rate.

For example:

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.

Example 1

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