Proportion Calculator
Proportion calculator — solve the missing term in a/b = c/d with cross-multiplication steps. Free ratio solver with checks.
Equal fractions hide equal cross products. Multiply the diagonals, isolate the blank, and both ratios snap into agreement.
- Grade level
- 6–10
- Curriculum band
- Difficulty
- Intermediate
- For this topic
- Time to master
- 2 weeks
- With daily practice
- Tools on page
- 10 on page
- Calculator + practice
Calculator
a/b = c/d — solve the blank
Leave exactly one field blank — it gets solved. Fill all four to check consistency.
Proportion Summary
Breakdown
| Property | Value |
|---|---|
| Left ratio a ÷ b | 0.75 |
| Right ratio c ÷ d | 0.75 |
| Cross a × d | 24 |
| Cross b × c | 24 |
Results
Solved: d
8
Missing term d via cross-multiplication
24
Left diagonal
24
Right diagonal — must match
0.75
a ÷ b equals c ÷ d when proportional
Cross-multiplication solves the single blank term; with all four given, diagonal equality is tested within tolerance.
Statistics
Live readouts from your current terms — diagonals, ratios and the solution move together.
Solved d
8
Missing term
a × d
24
Left diagonal
b × c
24
Right diagonal
Ratio a/b
0.75
Common value
Visualizations
Four terms side by side
Scaling from first ratio to second
Solved term magnitude
Both ratios share one scale
Formula
Proportions equate two ratios; clearing denominators converts them to a single diagonal equation solvable for any lone blank.
Alternative Form
Variables
| Symbol | Name | Unit | Description |
|---|---|---|---|
| a, b | Left ratio | numbers | Known pair (b ≠ 0) |
| c, d | Right ratio | numbers | One may be blank |
| a×d | Left diagonal | number | Must equal b×c |
| b×c | Right diagonal | number | Known when one blank |
Explanation
Scaling preserves ratios: multiply top and bottom together and equality survives — diagonals encode that.
Derivation
From a/b = c/d multiply by b×d: a×d = b×c (b, d ≠ 0). Isolate any term by dividing: d = b×c/a and siblings. With all four present, diagonal equality is necessary and sufficient for proportionality (tolerance covers float dust).
Step-by-Step Calculation
Follow each step to understand how the result is calculated from your inputs.
Write the proportion as two equal fractions.
Cross-multiply: each numerator times the far denominator.
Isolate the missing term d by dividing both sides.
Compute the arithmetic.
Verify: cross products must agree exactly.
State the solved proportion.
Worked Examples
See how the calculator works with different scenarios.
Scenario
Solve the missing fourth term.
Inputs
Calculation
3d = 24 → d = 8
Result
d = 8
Interpretation
Doubling the top doubles the bottom.
Understanding Your Result
Your Result: Solved: d: 8
Typical range: Integer ratios first, then decimals, units and consistency checks.
What This Means
The headline answer completes your proportion — both ratios now describe the same relationship.
Why It Matters
Recipes, maps, dosages, currency and similar figures all scale through proportions.
Professional Interpretation
Track units diagonally: eggs stay with eggs, pancakes with pancakes.
Recommendations
- •Leave exactly one blank
- •Guard divisors before solving
- •Keep units paired
- •Verify diagonals after
Learn — The Complete Guide
Proportions keep relationships identical while sizes change — the mathematics of fair scaling.
The core concept
Equal ratios share cross products. One blank solves via diagonals; four filled test consistency.
- Equal ratios share cross products
- One blank solves via diagonals
- Four filled test consistency
Derivations — why the formulas work
Clearing denominators
- 1a/b = c/d
- 2× b×d both sides
- 3a×d = b×c ✓
- 4One equation, diagonals exposed
Isolating d
- 1a×d = b×c
- 2÷ a both sides (a ≠ 0)
- 3d = b×c/a ✓
- 4Siblings follow by symmetry
Where you meet this in real life
Learn this first — prerequisites in order
- 1Simplify fractions
- 2Multiply/divide fluently
- 3Read ratio notation
Careers that use this daily
- •Chef — recipe scaling
- •Nurse — weight dosing
- •Surveyor — map scale
- •Trader — conversions
Why it helps
- •Any single blank solves
- •Check mode for all four
- •Diagonal proof on every run
Best practices
- •Pair units before computing
- •Cross-multiply first
- •Isolate, then evaluate
Limitations — what this tool does not do
- •Exactly one blank (or none) per run
- •Divisors must be non-zero
Curriculum map — where this topic lives in school
| Level | Grades | Standards | Skills |
|---|---|---|---|
| Upper Elementary | 5–6 | 5.NF, 6.RP | Equivalent fractions · Ratio tables |
| Middle School | 7–8 | 7.RP, 8.EE | Solve proportions · Unit rates |
| High School | 9+ | HSA | Similarity · Scaling models |
Timeline — how this idea grew up
Ancient
Rule of three
Babylon and India scale by threes.
300 BCE
Euclid’s ratios
Elements Book V formalises proportion.
1500s
Commercial arithmetic
Merchants live by the rule of three.
A little history
- • The rule of three predates algebra.
- • Euclid formalised ratios rigorously.
Exam-day checklist
- • State a/b = c/d.
- • Cross, then isolate.
- • Verify diagonals.
Myths vs facts
Practical Tips
- •One blank only
- •Cross first, isolate second
- •Pair units diagonally
- •Guard zero divisors
- •Verify diagonals
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.
What is a proportion?
How do you solve for a missing term?
Why does cross-multiplication work?
Which term can be blank?
How do I check proportionality?
How do I use this calculator?
Related Calculators
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Related Guides
Deepen your understanding with these educational resources.
Glossary
Technical terms used in mortgage calculations explained in plain language.
- Proportion
- Equality of two ratios.
- Cross product
- A diagonal product: a×d or b×c.
- Missing term
- The blank being solved.
- Consistency
- Diagonal equality when all given.
Authoritative References
Trusted sources and standards referenced by this calculator.
Applicable Standards
Diagrams & Illustrations
Visual intuition for every core idea. Select a card to enlarge it.
Did You Know?
Short intuition builders — great for class warm-ups.
The rule of three is ancient
Babylonians and Indians solved proportions (“a is to b as c is to ?”) millennia before algebra.
Maps are proportions
1 cm : 50,000 cm — every map reading cross-multiplies silently.
3/4 = 6/8 hides 24
Both diagonals equal 24 — the hidden handshake of equal fractions.
Chefs proportion daily
Doubling a recipe doubles every ingredient — proportions seasoned with salt.
Compare Side by Side
Proportional means both ratios — and both cross products — agree.
| Side | Expression | Value |
|---|---|---|
| Left ratio a/b | 3 ÷ 4 | 0.75 |
| Right ratio c/d | 6 ÷ 8 | 0.75 |
| Cross a×d | 3 × 8 | 24 |
| Cross b×c | 4 × 6 | 24 |
Recent Calculations
Your last runs on this page — stored only in this browser, never uploaded.
3/4 = 6/8
Current inputs — live
Study Plan
A week-by-week path from prerequisites to mastery. Your checklist progress saves in this browser.
Prerequisites
- ▸Equivalent fractions
- ▸Multiplication and division fluency
- ▸Reading a/b notation
Mastery progress — 0%
- I extend ratio tables
- I solve any blank term
- I verify via diagonals
- I pair units correctly
- 1
Week 1 · ~15 min/day
Equivalent ratios
Goals
- Build ratio tables
- Spot ×/÷ scaling
- Explain why adding fails
Practice
Extend 5 ratio tables daily; verify each row here in check mode.
- 2
Week 2 · ~20 min/day
Solve the blank
Goals
- Cross-multiply reliably
- Isolate any of a/b/c/d
- Guard divisors
Practice
Solve 8 missing-term proportions daily, one per position.
- 3
Week 3 · ~15 min/day
Applied scaling
Goals
- Scale recipes and maps
- Convert currencies
- Judge reasonableness
Practice
Scale one real recipe or map route daily.
Exam tips
- •Write a/b = c/d first.
- •Cross before isolating.
Practice Problems
0/5 solvedTry each problem first, peek at the hint only if stuck, then reveal the solution and mark it solved.
Solve 3/4 = 6/d.
Solve 2/3 = c/9.
Is 2/5 = 4/9 proportional?
5 km in 40 min; how far in 1 hour at same pace?
£6 buys $7.50. Dollars for £20?
Printable Worksheet
Generate a fresh problem set for class or homework. Print it, or copy the answer key separately.
- 1.18 × 47 =
- 2.8 ÷ 11 =
- 3.38 × 26 =
- 4.35 ÷ 4 =
- 5.21 − 16 =
- 6.2 + 26 =
- 7.14 ÷ 12 =
- 8.23 ÷ 3 =
- 9.49 ÷ 7 =
- 10.22 − 17 =
- 11.41 + 18 =
- 12.47 − 35 =
Formula Cheat Sheet
Every formula on this page in one printable table.
| Formula | Meaning | Example |
|---|---|---|
| a×d = b×c | Diagonal equality | 3×8 = 4×6 = 24 |
| d = b×c/a | Solve fourth | 4×6/3 = 8 |
| c = a×d/b | Solve third | 3×8/4 = 6 |
| Scale ×k both | Grow ratios | 3/4 → 6/8 (×2) |
| Never add across | Scale only | 1/2 ≠ 2/3 by +1 |
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Page Information
2026-09-29
3.1.0-math
Free to use for educational and professional purposes.