Guide · Method
Cross Multiplication Calculator
Updated: June 2026
Cross-multiplication is the engine inside the rule of three. It is the single move that turns two equal fractions into a plain multiplication and division you can solve in seconds. This guide shows exactly what crosses with what, walks through solving for x, and points out the small slips that trip people up.
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The idea in one picture
Whenever two fractions are equal, the product of one numerator and the opposite denominator equals the product of the other pair. Starting from a/b = c/d, you multiply diagonally:
a × d = b × c
This works because multiplying both sides of the equation by b and by d clears the denominators. Nothing is lost; you have just rewritten the same statement without fractions, which is much easier to solve.
Solving for x step by step
Say the unknown sits in the bottom right: a/b = c/x. Cross-multiply, then isolate x:
a × x = b × c
x = b × c ÷ a
With numbers, 2/10 = 5/x becomes 2x = 50, so x = 25. The position of the unknown changes only which value you divide by at the end — the calculator handles every position, so you can drop the missing number anywhere.
Worked examples for each position
| Proportion | Cross product | Answer |
|---|---|---|
| x/4 = 9/12 | 12x = 36 | x = 3 |
| 3/x = 6/20 | 6x = 60 | x = 10 |
| 7/14 = x/40 | 14x = 280 | x = 20 |
| 5/8 = 15/x | 5x = 120 | x = 24 |
Notice the pattern: whatever shares its fraction bar with x is the number you divide by last; the other two multiply together first.
Common mistakes to avoid
- Multiplying straight across. Cross-multiplication is diagonal, not numerator-times-numerator.
a × cis wrong. - Mixing up units. Keep like with like: the same kind of quantity on top of both fractions, and the matching kind on the bottom.
- Dividing by zero. If the value sharing x's bar is 0, there is no solution. The calculator flags this rather than returning nonsense.
- Using it on a sum. Cross-multiplication only applies to two fractions that are equal, not to fractions being added or compared with < or >.
Why cross-multiplying is faster than finding a common denominator
You could solve a proportion by scaling both fractions to a shared denominator, but that adds steps and bigger numbers. Cross-multiplication skips straight to a single linear equation. For homework, currency conversions, scaling drawings or checking a unit price at the supermarket, it is the most direct route — and because it is just two operations, it is easy to do in your head once the numbers are friendly.
Frequently asked questions
What does it mean to cross-multiply?
It turns a/b = c/d into a × d = b × c by multiplying each numerator by the opposite denominator, clearing the fractions.
How do I solve for x by cross-multiplying?
For a/b = c/x, cross-multiply to get a × x = b × c, then divide by a: x = b × c ÷ a.
When can I not cross-multiply?
Only on a single equation of two equal fractions. It is not valid for adding fractions or comparisons, and a denominator can never be 0.