Calculator Form
Fill A:B, C:D, or leave exactly one field blank to solve it. Accepted formats: 18, 2.5, -4, 3/4.
Example Data Table
| Case | Input | Output | Notes |
|---|---|---|---|
| Simple reduction | 18 : 27 | 2 : 3 | Both terms divide by 9. |
| Decimal ratio | 2.5 : 3.75 | 2 : 3 | Scale by 100, then reduce. |
| Valid proportion | 8 : 12 = 20 : 30 | 2 : 3 = 2 : 3 | Cross products match exactly. |
| Missing term | 15 : ? = 25 : 35 | 15 : 21 = 25 : 35 | Use cross multiplication. |
| Fraction input | 3/4 : 9/8 | 2 : 3 | Fractions convert before simplification. |
Formula Used
1. Ratio simplification: Convert values to integers with a common decimal scale. Then divide every scaled term by the greatest common divisor.
2. Decimal scaling: Scaled term = original term × 10d, where d is the highest decimal count in the current set.
3. Proportion rule: For a : b = c : d, the equality test is a × d = b × c.
4. Missing term formulas: A = (B × C) ÷ D, B = (A × D) ÷ C, C = (A × D) ÷ B, D = (B × C) ÷ A.
5. Ratio value: Ratio value = first term ÷ second term, provided the second term is not zero.
How to Use This Calculator
- Enter A and B to simplify one ratio only.
- Enter C and D instead if your ratio is on the right side.
- Fill all four terms to compare two ratios as a full proportion.
- Leave exactly one field blank to solve the missing term automatically.
- Choose how many equivalent ratios you want in the generated table.
- Adjust display precision if you expect decimal answers.
- Press Simplify Proportion to show the result above the form.
- Use the CSV or PDF buttons to export the summary and equivalent ratios.
FAQs
1. What does this calculator simplify?
It simplifies single ratios, checks whether two ratios form a true proportion, solves one missing term, generates equivalent ratios, and shows a chart for visual comparison.
2. Can I enter decimals or fractions?
Yes. You can enter whole numbers, decimals, negative values, and simple fractions such as 3/4. The calculator converts them before simplifying.
3. Why are B and D restricted from being zero?
They work as denominator positions in a:b and c:d. A zero denominator makes the ratio undefined, so the calculator blocks that case.
4. How does the missing value feature work?
Leave one field blank and provide the other three terms. The calculator applies cross multiplication to solve the missing term and then simplifies the full result.
5. What does the graph show?
The Plotly chart compares original terms with simplified terms. It helps you see whether both sides reduce to the same ratio or differ after simplification.
6. What is the equivalent ratios table for?
It lists repeated multiples of the simplest ratio. This helps with worksheets, pattern recognition, classroom examples, and quick manual checking.
7. Why does the calculator use scaling before reducing?
Scaling converts decimals into integers. That lets the greatest common divisor method work cleanly and avoids inaccurate manual simplification of decimal ratios.
8. Can I export the result?
Yes. After calculation, use the CSV button for spreadsheet-friendly output or the PDF button for a printable report with the summary and equivalent ratios table.