A proportion is a statement that two ratios are equal: A/B = C/D. Its defining property is that the cross products are equal — A × D = B × C — which lets you solve for any one missing term from the other three. So in 3/4 = 9/D, cross-multiplying gives 3D = 36 and D = 12. This calculator takes any three values, finds the fourth, and shows the cross-check.
Reviewed: June 20, 2026 · Author: Naveen P N, Founder — AI Calculator · Verified against: the cross-multiplication property of proportions, recomputed in code.
Cross-multiplication
Because the two ratios are equal, multiplying each numerator by the opposite denominator must give the same product. That single identity, A × D = B × C, is the engine behind every proportion problem. Rearranging it isolates whichever letter is unknown. The same identity also tests proportionality: if the cross products match, the ratios are equal; if not, they aren't.
Worked example — 3/4 = 9/D
Scenario: find the missing denominator.
Setting the cross products equal gives 3D = 36, so D = 12 and the full proportion is 3/4 = 9/12 (both equal 0.75). The same method solves for any position: 2/5 = C/20 gives C = (2 × 20)/5 = 8, and ?/4 = 9/12 gives A = (4 × 9)/12 = 3. Just leave the unknown box blank and the calculator picks the right rearrangement.
Frequently Asked Questions
A statement that two ratios are equal: A/B = C/D. 3/4 = 9/12 because both equal 0.75. Know three values, solve the fourth.
Cross-multiply (A×D = B×C), then divide. 3/4 = 9/D → 3D = 36 → D = 12.
Multiplying each numerator by the opposite denominator: A×D and B×C, which are equal in a true proportion.
Cross-multiply and compare. 3/4 & 9/12: 3×12 = 36 = 4×9, so yes. Different cross products mean not proportional.
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