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.
Find the value of x. 35/84 = x/24
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 = 3.5x/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.
Roger drove 90 miles in 1.5 hours. How far would he go in 2.5 hours?