The rule
a ÷ b = c ÷ d, so a × d = b × c
Why it works
A proportion says two ratios are equal. Cross-multiplying turns that into a single equation — the product of the extremes equals the product of the means — and from there any one missing term falls out.
How to do it by hand
- Leave one term empty
- Multiply the two terms that do not sit beside the unknown
- Divide by the remaining one
- Check that the two cross products agree
What is worth knowing
The extremes are the outer terms, a and d; the means are the inner ones, b and c. Their products being equal is the definition of a proportion, and it is also the test: give it four numbers and it tells you whether they form one. That test is what underlies similar triangles, map scales, recipe scaling and every unit conversion, all of which are proportions with different names. The golden ratio is the case where the proportion refers back to itself: a is to b as a+b is to a.