Ratios & Proportions
Solving for the missing term
Multiply the known quantity by the other half of the complete pair, then divide by the remaining half. Cross multiplication a x d = b x c gives the same result.
The Formula
d = c x b / a
Multiply the known quantity by the other half of the complete pair, then divide by the remaining half. Cross multiplication a x d = b x c gives the same result.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| a | First member of the known pair | number | Such as the number of units whose price you already know. |
| b | Second member of the known pair | number | Such as the cost of those units. Must sit opposite a on the other side. |
| c | The new value of the first quantity | number | What you are scaling to. |
| d | The unknown result | same as b | Measured in the same units as b. |
What Each Symbol Means
anumber
First member of the known pair
Such as the number of units whose price you already know.
bnumber
Second member of the known pair
Such as the cost of those units. Must sit opposite a on the other side.
cnumber
The new value of the first quantity
What you are scaling to.
dsame as b
The unknown result
Measured in the same units as b.
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.