Proportion Equation Calculator
Solve a/b = c/d for any missing term with cross-multiplication steps and ratio verification. Free proportion solver.
Calculator
Proportion Terms
Its field value is ignored
Proportion Summary
Results
Missing d
12
Solved by cross-multiplication
0.75
Left side as a decimal
0.75
Right side as a decimal
3
Multiplier from first to second ratio
Cross-multiplication is exact; the solved proportion is re-checked as a decimal ratio match within 1e-9.
Visualizations
Both Ratios Compared
Proportion Status
Formula
Cross-multiplication clears both denominators at once, turning a ratio equality into a plain product equation solvable in one division.
Alternative Form
Variables
| Symbol | Name | Unit | Description |
|---|---|---|---|
| a, b | First ratio | numbers | Numerator and denominator, b ≠ 0 |
| c, d | Second ratio | numbers | Numerator and denominator, d ≠ 0 |
| missing | Unknown term | letter | The one term solved for |
| scale | Scale factor | number | Multiplier between the ratios |
Explanation
Proportions assert identical shapes at different scales; cross-multiplication enforces that by equating the two diagonal products.
Derivation
a/b = c/d → multiply by bd: ad = bc → divide by the coefficient of the unknown.
Step-by-Step Calculation
Follow each step to understand how the result is calculated from your inputs.
Write the proportion with the unknown marked.
Cross-multiply: products across the diagonal are equal.
Isolate the missing term by dividing.
Verify: both ratios must match as decimals.
Worked Examples
See how the calculator works with different scenarios.
Scenario
Equivalent fraction completion.
Inputs
Calculation
d = 4×9/3 = 12; check 0.75 = 0.75
Result
d = 12
Interpretation
Scale factor 3 applied top and bottom.
Understanding Your Result
Your Result: Missing proportion term found by cross-multiplication with ratio proof
Typical range: Denominators b, d must be nonzero; the divisor on the unknown diagonal must be nonzero.
What This Means
The missing term is whatever value makes both ratios identical decimals.
Why It Matters
Recipes, maps, dosages and similar figures all scale through proportions — one unknown, one cross-product away.
Professional Interpretation
Always finish with the decimal check: equal ratios are the definition of a correct proportion answer.
Recommendations
- •Mark the missing term first
- •Cross-multiply before dividing
- •Verify with decimal ratios
- •Watch zero divisors
- •Read the scale factor for meaning
Educational Content
Introduction
A proportion equates two ratios; cross-multiplication converts it into a solvable product equation.
Concept Explanation
Multiplying both sides by both denominators clears fractions: ad = bc. Isolating the unknown takes one division.
Applications
Benefits
- •Any of four terms solvable
- •Cross-product made visible
- •Decimal ratio proof
- •Scale factor reported
- •Zero-divisor honesty
Limitations
- •Single proportion only
- •Numeric terms
- •Nonzero denominators
Best Practices
- •Name the missing term
- •Write ad = bc explicitly
- •Divide once to isolate
- •Check decimals match
- •Interpret the scale factor
Common Misconceptions
Practical Tips
- •Circle the unknown first
- •Write the cross equation out
- •Divide by the unknown’s partner
- •Check both decimals
- •Keep unit pairs consistent
- •Note the scale factor
- •Reject zero divisors
Common Mistakes
Assumptions
This calculator makes the following assumptions to provide estimates:
Limitations
Be aware of these limitations when using this calculator:
Frequently Asked Questions
Answers to common questions about this calculator.
How do I solve 3/4 = 9/d?
What is cross-multiplication?
Can I solve for a numerator instead?
How do I verify a proportion?
What is the scale factor?
What if a denominator is zero?
Where are proportions used?
Do units matter in proportions?
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Glossary
Technical terms used in mortgage calculations explained in plain language.
- Proportion
- Equality of two ratios a/b = c/d.
- Ratio
- Quotient comparing two quantities.
- Cross-multiplication
- Diagonal clearing to ad = bc.
- Scale factor
- Multiplier between equivalent ratios.
- Missing term
- The single unknown solved for.
- Equivalent fractions
- Fractions naming the same ratio.
- Diagonal products
- ad and bc — equal in proportion.
- Denominator
- Lower term; never zero.
- Verification
- Decimal equality proof.
Authoritative References
Trusted sources and standards referenced by this calculator.
Applicable Standards
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Page Information
2026-09-29
2.0.0
Free to use for educational and professional purposes.