How a proportion is solved
In a proportion a : b = c : x, the product of the extremes equals the product of the means: a × x = b × c. Solving for x gives the formula below.
- a, b — the known ratio
- c — the term matched to the unknown x
- x — the value solved for
More detail
Extremes and means
In a : b = c : x, a and x are the “extremes” (outer terms) and b and c are the “means” (inner terms). The rule that extreme × extreme = mean × mean (a·x = b·c) is what lets you solve for any single missing term once you know the other three.
Recipe scaling. To scale a recipe, set a : b to your original two ingredient amounts, enter the new amount of one ingredient as c, and x gives you the matching amount of the other — keeping the same proportion.
Frequently asked questions
If 2 : 3 = 10 : x, what is x?
Using extremes × means: x = (b × c) / a = (3 × 10) / 2 = 15. Enter A=2, B=3, C=10 above to confirm.
How do I reduce 4 : 6 to its simplest form?
The greatest common divisor of 4 and 6 is 2, so 4 : 6 simplifies to 2 : 3. Enter A=4, B=6 above (C doesn't affect the simplified ratio) to see it.
How do I set up a proportion a : b = c : x?
Write the known ratio as a : b, then match c to whichever side corresponds to a. Cross-multiplying (a × x = b × c) and dividing by a gives x — that's exactly what this calculator does.
Why can't A be 0?
A proportion a : b = c : x means a × x = b × c. If a = 0, solving for x would require dividing by zero, which is undefined — so the calculator has no result when A is 0.