How it works
A proportion says two ratios are equal. If 2 is to 3 as 4 is to x, then 2/3 = 4/x. Cross multiplying gives 2x = 12, so x = 6.
This "rule of three" is used for scaling recipes, converting units, map scales, and unit pricing: if 2 pounds cost $3, then 4 pounds cost $6.
Formula
a/b = c/x ⇒ a·x = b·c ⇒ x = b·c ÷ a
Questions people ask
What is cross multiplication?
In a/b = c/d, multiply the numerator of each side by the denominator of the other: a·d = b·c. It removes the fractions so you can solve for the unknown.
How do I use a proportion for unit conversion?
Set the known ratio equal to the unknown one with matching units: 1 in / 2.54 cm = 12 in / x cm, so x = 30.48 cm.
What if the unknown is in a different position?
Rearrange so the unknown is last. For x/b = c/d, x = b·c ÷ d. Proportions can be flipped (b/a = x/c) without changing the answer.