Cross multiplication, done for you
Solve a : b = c : x for the missing value, with the ratio reduced to its simplest form and the scale factor shown.
Proportions turn up constantly outside maths class: scaling a recipe, resizing an image without distorting it, mixing paint or fuel, reading a map scale.
The method is cross multiplication — multiply the outer pair and the inner pair, then solve. Getting the order of the terms wrong is the usual source of a wrong answer.
What this calculator shows
- The missing fourth term of the proportion
- The ratio reduced to lowest terms
- The scale factor between the two sides
What to keep in mind
- Solves a : b = c : x, so the unknown is always the fourth term.
- The first two terms cannot be zero — a ratio with zero in it has no meaningful scale.
FAQs
How does cross multiplication work?
In a : b = c : x, multiply a by x and b by c, then set them equal. Solving for x gives x = b × c ÷ a.
What is a ratio in simplest form?
One where both terms share no common factor. 12 : 16 reduces to 3 : 4, which describes the same relationship in smaller numbers.
Are ratios and fractions the same thing?
Closely related but not identical. 3 : 4 as a fraction is 3/4 when comparing part to whole, but a ratio can also compare two separate quantities that never form one total.
Where is this used in everyday life?
Map scales, screen aspect ratios, recipe scaling, fuel mixes and currency conversion are all proportion problems wearing different clothes.
Worked example
Scaling a photo
Input: 3 : 4 = 9 : x
Output: x = 12
Note: A 3:4 image widened to 9 units must be 12 tall to keep its shape. Any other height stretches it.