Advanced cross division solver for ratios, fractions, and proportion checks instantly. Get detailed steps, error flags, visual cues, and alternative solution paths shown. Designed for students, tutors, engineers, and everyday problem solving confidence in calculations. Master ratios confidently using clear visuals, hints, and explanations.
| # | Mode | Inputs / Expression | Result | Key Steps |
|---|
| Example | Mode | Given Values | Unknown | Solution |
|---|---|---|---|---|
| 1 | Proportion A/B = C/D | A = 8, B = 4, C = 6 | D | D = (B × C) / A = (4 × 6) / 8 = 3 |
| 2 | Cross division x = (A × B) / C | A = 12, B = 5, C = 4 | x | x = (12 × 5) / 4 = 15 |
| 3 | Proportion check | A = 3, B = 4, C = 6, D = 8 | - | 3/4 = 6/8 is true (cross products both 24) |
Cross division, often called cross multiplication, is a method used to solve or compare ratios and fractions of the form A/B and C/D. Instead of dividing directly, we multiply diagonally: A × D and B × C. If these products match, the ratios are equivalent. When one term is unknown, we rearrange the same relationship to isolate the missing value quickly and accurately.
For any proportion A/B = C/D, multiply across the diagonal to obtain A × D = B × C. This equality is written compactly as ad = bc. It means the product of the extremes (A and D) equals the product of the means (B and C). By rearranging ad = bc, you can solve for any single unknown term.
This same logic drives the calculation engine in the Cross Division Calculator, ensuring consistent, stepwise, and transparent results for students and professionals.
Cross multiplication also helps when three related values are known and the fourth is missing. Suppose you know A, B, and C in the proportion A/B = C/D. Instead of working with two separate fractions, use ad = bc:
The calculator automates this three-known-one-unknown pattern. Simply choose the unknown in proportion mode, enter the other three values, and the tool performs the cross multiplication accurately with a clear stepwise breakdown.
In a direct proportion, one quantity increases when the other increases, so y₁/x₁ = y₂/x₂. Cross multiplication quickly checks this: x₁y₂ = x₂y₁. In an inverse proportion, one quantity increases while the other decreases, so x₁y₁ = x₂y₂. Cross products reveal which relationship fits your data.
When a fraction equation involves an unknown, cross multiplication isolates x immediately. For example, if x/5 = 3/10, multiply across:
The calculator follows the same pattern: enter the fractions, mark the unknown, and it generates the cross products and final x step by step.
This tool eliminates manual mistakes when working with ratios, mixing problems, percentage comparisons, scaling diagrams, map reading, financial ratios, and physics formulas involving proportional relationships. It is suitable for classroom demonstrations, self-study, and professional calculations where clarity and traceable steps are important.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.