Live raw ↔ simplified twin for a:b, with part:whole rewrite, share-split strip, unit-ratio peel, and an equivalent-forms rail.
Educational ratio literacy only. Not a CAS or exam oracle. Confirm methods with your course when grades matter.
By Ahmet C. Toplutaş·Site owner & editor · Math tools
Last updated May 21, 2026 · Reviewed May 21, 2026 · Planning estimates only - not tax, medical, or investment advice
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A ratio a : b compares two quantities. Simplifying divides both parts by a common factor so the comparison stays the same with smaller integers when possible.
This page's framing is a raw ↔ simplified twin, with a part:part ↔ part:whole twin, a share-split strip, a unit-ratio peel, and an equivalent-forms rail. It is not the proportion cross-product board for a:b = c:d, not discount list↔pocket, and not percentage-of jobs.
Decision framing: “What is the simplest a:b, how does it read as parts of a whole, and how do I split a total?”
Educational ratio literacy only. Not a computer-algebra system or exam oracle. Confirm methods with your course when grades are on the line. See our disclaimers.
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Part:part keeps a:b. Part:whole rewrites each simplified part against a + b, which matches mixture language (“2 parts in every 5”). Percent-of-whole on the twin is the same idea in percent form.
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Unit ratios answer “how many of a per one of b” and the reverse. Decimal a/b is the same comparison as a single number. Use them when a problem asks for a rate-style rewrite instead of colon notation.
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GCD simplify, part:whole, and share split.
Example: 12:18 → g = 6 → 2:3. Split 10 → 4 and 6. Unit a per 1 b = 2/3.
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Sibling math boards when the question becomes equality of two ratios or percent jobs.
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Scenario A: Recipe. 2:3 with total 10 → shares 4 and 6. Twin already shows simplest form.
Load Simplify: 12:18 → 2:3 on the twin. Add a total later if you need a share split.
Scenario B: Budget. 3:5 of 800 → 300 and 500. Part:whole reads 3:8 and 5:8.
Scenario C: Scale ×4. 5:2 scaled by 4 → 20:8 on the rail (same ratio as 5:2). Simplified twin stays 5:2.
Scenario D: Need a missing fourth. When the story is “this ratio equals that ratio,” hand off to proportion instead of forcing a single-ratio board.
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Stop here for simplifying and rewriting one ratio, and for splitting a total. Hand off when two ratios must be equal, when you need percent-of/percent-change jobs, or when exact fraction arithmetic is the goal.
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It simplifies a:b with a GCD peel into a raw ↔ simplified twin, shows part:part beside part:whole, peels unit ratios (A per one B and B per one A), lists equivalent scaled forms, and optionally splits a total into shares by the simplified parts.
Raw is the ratio you typed. Simplified divides both parts by their greatest common divisor (working in thousandths so common decimals still reduce). Equivalent ratios keep the same comparison with smaller integers when possible.
Part:part is a:b. Part:whole compares each part to a+b, which is useful for mixture and share language (“2 out of 5 parts”).
Enter a total (cups, dollars, seats). The strip divides that whole in the simplified ratio so the two shares add back to the total.
Proportion solves or checks a:b = c:d with cross-products. This page owns a single ratio: simplify, rewrite as part:whole, scale equivalent forms, and split a total. Hand off to proportion when two ratios must be equal.
Yes. The simplifier scales by thousandths before GCD, so values like 2.5:3.5 reduce toward 5:7. Exact symbolic CAS behavior is out of scope.
No. It is educational ratio literacy for homework and quick checks. Confirm methods with your course when grades are on the line.
LIVE RATIO BOARD
Raw ↔ simplified →Scene presets
Cups, $, seats…
On simplified parts
RAW ↔ SIMPLIFIED TWIN
Raw
2:3
Simplified
2:3
Scaled form at ×1: 2:3
PART:PART ↔ PART:WHOLE
Part : part
2:3
Part : whole
2:5 · 3:5
Shares of whole: 40.0% / 60.0%
UNIT-RATIO PEEL
SHARE-SPLIT STRIP
EQUIVALENT FORMS RAIL
Updates as you type. Share writes board state; typing does not rewrite the address bar.
Simplified
2:3
Split 4 / 6
A ratio compares two quantities. Simplifying divides both parts by a common factor. Part:whole and share-split restate the same comparison against a total; unit ratios answer “how many of one per one of the other.”
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