Proportion Calculator
The calculator solves a proportion a/b = c/d, finds the unknown term by cross-multiplication and shows the solution with a check.
The proportion calculator finds the unknown term of a proportion wherever it is and shows the solution by cross-multiplication with a check. Whole numbers and decimals are supported.
What is a proportion
A proportion is an equation stating that two ratios are equal:
a/b = c/d or a : b = c : d
The numbers a and d are called the extremes, and b and c the means.
The main property of a proportion
The product of the extremes equals the product of the means (cross-multiplication):
a · d = b · c
So any term can be found from the other three:
- an unknown extreme equals the product of the means divided by the known extreme: a = b · c/d;
- an unknown mean equals the product of the extremes divided by the known mean: b = a · d/c.
Example. 3/5 = 12/x
3 · x = 5 · 12
x = 5 · 12/3 = 20
Word problems with proportions
Proportions solve problems with direct proportionality, where one quantity grows by the same factor as another.
Problem. 3 lb of apples cost $6. How much do 5 lb cost?
3/6 = 5/x, x = 6 · 5/3 = $10
Proportions are also used for map scales, scaling recipes, percentage problems and solution concentrations.