Cross Multiplication Calculator
Set up a proportion — two equal fractions — enter the three values you know, and the calculator cross multiplies to find the missing one, showing the multiply-then-divide steps.
Example: with First fraction: numerator (A) 2 · First fraction: denominator (B) 3 · Known value of the second fraction (C) 8 · What is missing? The denominator: A/B = C/X → Missing value (X): X = 12.
Computed by the calculator below using its default values. Change any input to see your own numbers.
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Check it outHow cross multiplication works
In a proportion, two fractions are equal: A/B = C/D. Cross multiplying multiplies each numerator by the opposite denominator and sets the products equal — A × D = B × C — which clears both denominators in one move. That turns a fraction equation into a plain one you can solve by dividing. For 2/3 = 8/X: cross multiply to get 2X = 3 × 8 = 24, then divide by 2 to find X = 12.
It’s the fastest route through everyday ratio problems. If 3 pounds of apples cost $4.50, what do 5 pounds cost? Set up 3/4.50 = 5/X, cross multiply: 3X = 22.50, so X = $7.50. The same trick compares fractions without common denominators: for 5/8 vs 7/11, compare the cross products 5 × 11 = 55 and 8 × 7 = 56 — 56 is bigger, so 7/11 is the larger fraction.
How it’s calculated
For A/B = C/X the calculator cross multiplies to A × X = B × C and solves X = (B × C) ÷ A; for A/B = X/C it uses B × X = A × C, so X = (A × C) ÷ B. Cross multiplication is valid because it is just multiplying both sides of the equation by both denominators, which preserves equality as long as no denominator is zero — inputs that would force a division by zero return no result.
Results update as you type and are estimates, not professional advice — verify important decisions with a qualified professional.
Common mistakes
- Multiplying straight across (A×C and B×D) instead of diagonally — straight-across is how you multiply fractions, not how you solve a proportion.
- Forgetting the final divide: cross multiplying 2/3 = 8/X gives 2X = 24; the answer is 24 ÷ 2, not 24.
- Setting the proportion up with mismatched units — keep the same quantity in both numerators (e.g. pounds on top, dollars on the bottom, in both fractions).
Frequently asked questions
How do you cross multiply?
Multiply each fraction's numerator by the other fraction's denominator and set the two products equal. For 2/3 = 8/X: 2 × X = 3 × 8, so 2X = 24 and X = 12.
Why does cross multiplication work?
It is shorthand for multiplying both sides of A/B = C/D by B × D. The denominators cancel, leaving A × D = B × C — no fraction rules needed after that.
Can I cross multiply to compare two fractions?
Yes. For 5/8 vs 7/11, compare 5 × 11 = 55 with 8 × 7 = 56. The larger cross product sits with the larger fraction, so 7/11 > 5/8.
How do I use cross multiplication for percent problems?
Write the percent as part/whole = percent/100. To find 35% of 80: X/80 = 35/100, cross multiply to 100X = 2,800, so X = 28.
What is the rule of three?
It is the same cross multiply and divide routine: when three values of a proportion are known, multiply the two diagonal knowns and divide by the third to get the unknown.