Cross Multiplication Calculator — Solve Proportions
Set up the proportion a/b = c/x, enter three values, and the calculator solves for x by cross multiplication — with a clear step-by-step solution showing exactly how the answer is reached.
3/5 = 6/x → x = 10
Write the proportion
Cross multiply
Simplify the right side
Divide both sides by 3
Result
- 1
Right-hand cross product (b × c)
5 × 6 = 30 - 2
Divide by a to isolate x
30 ÷ 3 = 10From a × x = b × c, dividing both sides by a gives x = (b × c) ÷ a.
How does this calculator work?
Cross multiplication solves a/b = c/x by rearranging to x = (b × c) / a. Enter a, b, and c to find x instantly. For example, 3/5 = 6/x gives x = (5 × 6) / 3 = 10. The cross-product check verifies: 3 × 10 = 5 × 6 = 30. Works for any proportion with a ≠ 0.
Formula
How this is calculated
Cross multiplication is the standard technique for solving a proportion (an equation stating that two ratios are equal). Given a/b = c/x, multiplying both sides of the equation by b·x clears both denominators: a·x = b·c. Dividing both sides by a then isolates x: x = (b × c) ÷ a. The result is valid as long as a ≠ 0 and the inputs are real numbers.
The cross-product property (a·x = b·c) can also be used to check whether two ratios are equal: if a·d = b·c then a/b = c/d. This is why the check columns in the StatGrid both show b × c — confirming the proportion holds exactly.
Cross multiplication applies to any proportion problem: unit prices, recipe scaling, map distances, similar-triangle side lengths, and currency conversions. It does not apply to ratios involving complex numbers, vectors, or matrices, where the algebra of fractions is more nuanced.
Frequently asked questions
Cross multiplication is the process of multiplying the numerator of each fraction by the denominator of the other to solve a proportion. For a/b = c/d, cross multiplying gives a·d = b·c, which you then solve for the unknown.
No. Cross multiplication solves proportions (equalities of ratios). To add fractions a/b + c/d, you find a common denominator: (a·d + b·c) / (b·d). This uses the same "cross multiply the numerators" idea but produces a sum, not an equation to solve.
If a = 0, the left ratio a/b = 0, so the proportion 0/b = c/x forces c = 0 for any x, making x undefined (infinitely many solutions). Division by zero is not defined, so the calculator requires a ≠ 0.
Also known as
TG we-Calculate Editorial Team. (2026). Cross Multiplication Calculator — Solve Proportions [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/cross-multiplication-calculator
TG we-Calculate Editorial Team. "Cross Multiplication Calculator — Solve Proportions." TG we-Calculate. 2026. https://we-calculate.com/calculator/cross-multiplication-calculator.
TG we-Calculate Editorial Team, "Cross Multiplication Calculator — Solve Proportions," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/cross-multiplication-calculator
@misc{wecalculate_cross_multiplication_calculator, title = {Cross Multiplication Calculator — Solve Proportions}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/cross-multiplication-calculator}}, year = {2026}, note = {TG we-Calculate} }
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