Ratios & Proportions
Cross-product check
Multiply the diagonals. Equality confirms the proportion was set up consistently, and inequality means one side was inverted.
The Formula
a x d = b x c
Multiply the diagonals. Equality confirms the proportion was set up consistently, and inequality means one side was inverted.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| a x d | Product down one diagonal | product | Should equal the other diagonal exactly, up to rounding. |
| b x c | Product down the other diagonal | product | Disagreement here is the signal, not a rounding artefact. |
What Each Symbol Means
a x dproduct
Product down one diagonal
Should equal the other diagonal exactly, up to rounding.
b x cproduct
Product down the other diagonal
Disagreement here is the signal, not a rounding artefact.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to solve a proportion page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Solve A Proportion, filed under Math. Every number the guide produces comes from substituting into this one line.