#### Proportion

A proportion states that two ratios are equal.

A proportion comparing two ratios can be expressed as:

*a* is to *b* as *c* is to* d*
*a* : *b* = *c* : *d*
*a*/*b* = *c*/*d*

You can solve for any term in a proportion: *a*, *b*, *c* or *d*.

##### Example

Find the value of *x*. 35/84 = *x*/24

#### Inversely Proportional

Two quantities are directly proportional if one equals the other multiplied by a constant, or *y* = *cx* where *c* is a constant.

The Examples above were all directly proportional.

4/15 = 16/*x* is the same as 4 × 4/15 × 4 = 16/*x*

35/84 = *x*/24 is the same as 35/84 = 3.5*x*/3.5 × 24

When two quantities are directly proportional, both values increase or both values decrease.

Two quantities are inversely proportional if one decreases when the other increases.

One value is equal to a constant divided by the other, or:

*y* = *c*/*x*

This can be rewritten as:

*xy* = *c*

Here are some examples of inverse proportions:

- The unemployment rate is inversely proportional to economic growth. Unemployment goes up when economic growth goes down.
- The interest rate a company pays is inversely proportional to its credit rating. The better the credit rating, the lower the interest rate.

##### Example

Roger drove 90 miles in 1.5 hours. How far would he go in 2.5 hours?