Cross Multiplication Solver
Use this calculator to solve a missing value in a proportion or verify whether two ratios are equal.
Plotly Graph
The chart compares values or cross products from your latest calculation.
Example Data Table
These sample proportions show how cross multiplication solves or checks equality.
| Example | Proportion | Unknown | Cross Multiplication | Answer |
|---|---|---|---|---|
| Recipe scaling | 2 / 5 = 8 / x | x | 2x = 40 | x = 20 |
| Map distance | x / 4 = 9 / 6 | x | 6x = 36 | x = 6 |
| Class ratio check | 3 / 4 = 6 / 8 | None | 3×8 = 4×6 | Equal |
| Price comparison | 7 / x = 14 / 10 | x | 70 = 14x | x = 5 |
Formula Used
For a proportion written as a / b = c / d, cross multiplication gives:
a × d = b × c
To solve any missing term, isolate the unknown after multiplying diagonally. Examples:
- If d is unknown: d = (b × c) / a
- If c is unknown: c = (a × d) / b
- If b is unknown: b = (a × d) / c
- If a is unknown: a = (b × c) / d
To verify a proportion, compare the two cross products. Equal cross products mean the ratios are equal.
How to Use This Calculator
- Select whether you want to solve a missing value or verify a proportion.
- Choose the unknown position when solving for x.
- Enter the known numbers into the proportion fields.
- Set your preferred decimal precision for the result.
- Click Calculate to show the result above the form.
- Review the worked steps, ratios, and chart.
- Download the output as CSV or PDF for records.
Frequently Asked Questions
1. What does cross multiplication help me do?
It solves a missing value in a proportion or checks whether two ratios are equal. It is useful in algebra, unit rates, maps, recipes, scaling, and percentage problems.
2. When can I use this solver?
Use it when two fractions or ratios should represent the same relationship. The calculator works for classroom equations, real-world comparisons, and fast validation tasks.
3. What is the main formula behind the result?
The core rule is a × d = b × c for a / b = c / d. Once the diagonal products are equal, the proportion is valid.
4. Can the calculator verify a proportion without solving x?
Yes. In verify mode, it compares the two cross products directly. If both products match, the ratios are proportional. Otherwise, they are not equal.
5. What happens if a denominator is zero?
Zero denominators make a ratio undefined. The calculator warns you when a value would create an invalid or unsolvable proportion.
6. Why are rounding controls included?
Rounding helps present results clearly for homework, worksheets, or reports. You can keep more decimal places when accuracy matters and fewer when readability matters.
7. What do the CSV and PDF downloads contain?
They store the latest result summary, ratios, cross products, and status. This makes it easier to save calculations, share them, or attach them to notes.
8. Does this tool work for negative and decimal values?
Yes. The solver accepts integers, decimals, and negative numbers. It applies the same proportion rule as long as the expression remains mathematically defined.