Each simplified term with its fraction of the total and that fraction as a percentage
Term
Of the whole
As a percentage
2
2/5
40%
3
3/5
60%
A ratio is not a fraction. 2 : 3 means the first share is 2/5 of the total, not 2/3of it — the denominator is the SUM of the terms.
Each side's share of the whole is its term over the SUM of the terms, not over the other term. 2 : 3 means 2/5 and 3/5 of the total — a ratio is not a fraction.
Dividing every term by 6 leaves no common factor, which is what "simplest form" means.
Terms are scaled to whole numbers before anything is divided, so 1.5 : 2.25 gives 2 : 3 rather than a decimal.
What this tool shows
12 : 18 is 2 : 3. And in a 3 : 2 split the first share is three fifths of the total, not three halves — the denominator is the SUM of the terms. That single point is where most ratio answers go wrong.
Any ratio reduced to its simplest form
Decimal and fractional terms, scaled exactly
Each term’s share of the whole, as a fraction and a percentage
A total divided in that ratio
The ratio as a single fraction and as a decimal
Ratios of three terms or more
Simplest form Shares of the whole Split a total Two terms or eight
Updated 7 September 2026 · Works in any browser, no installation
Divide every term by their greatest common factor. 12 : 18 both divide by 6, giving 2 : 3. If the terms are decimals or fractions, multiply them all up to whole numbers first — the ratio is unchanged, because every term is scaled by the same amount.
At a glance
Formula shown
Multiply every term by the least common multiple of the denominators to clear fractions, then divide every term by their greatest common divisor. Each term\u2019s share of the whole is that term over the sum of all the terms.
Scenario support
Splitting a bill or a payout in an agreed ratio; reducing an aspect ratio or a mix ratio; checking whether two ratios describe the same relationship.
Educational estimate
Planning support from the values you enter — not professional advice.
A ratio is not a fraction
This is the mistake worth spending a paragraph on, because it is the one that produces wrong answers rather than untidy ones.
If sweets are shared 3 : 2, the first person gets three fifths. Not three halves. The 2 is not a denominator; it is another share. The denominator is the total number of parts, which is 3 + 2 = 5.
So 3 : 2 corresponds to the fractions 3/5 and 2/5, which is 60% and 40%. The page computes those and shows them, because writing 3 : 2 does not make them visible and every ratio question eventually needs them.
The related slip: a ratio of 3 : 2 does mean the first quantity is 3/2 of the SECOND. That is true, and it is a different statement from its share of the total. Both are on the page, separately labelled.
How simplifying works
A ratio stays the same when every term is multiplied or divided by the same number. Simplifying means dividing until nothing is left to divide by.
Whole numbers: divide by the greatest common factor. 12 : 18 share 6, leaving 2 : 3.
Decimals: multiply up first. 1.5 : 2.25 becomes 6 : 9 when both are multiplied by 4, and then 2 : 3.
Fractions: multiply by the least common multiple of the denominators. 3/4 : 1/2 becomes 3 : 2 when both are multiplied by 4.
The page does the scaling on exact fractions, so no step ever introduces a rounding error that a later division would then bake in.
Sharing a total
Split £240 in the ratio 5 : 3. There are 8 parts, so one part is 30, and the shares are 150 and 90.
Three steps: add the terms to get the number of parts, divide the total by that to get one part, then multiply out. The check is that the shares add back to the total.
Where the split does not land on whole numbers — £100 in the ratio 1 : 1 : 1 — the page says so. For money, carry the exact amounts through and round once at the end, then give the leftover penny to one party as a deliberate decision rather than letting the rounding pick.
Three terms and more
Everything generalises. 2 : 3 : 5 has ten parts, so a total of 1,000 splits into 200, 300 and 500.
Simplifying works the same way: divide all the terms by their common factor. 4 : 6 : 10 becomes 2 : 3 : 5.
One thing that does NOT generalise is writing the ratio as a single fraction. 3 : 4 can be written 3/4; 2 : 3 : 5 cannot be written as one fraction at all, and the page leaves that field blank rather than inventing something.
Where ratios turn up
Mixing. Concrete at 1 : 2 : 4, a cocktail at 2 : 1, fertiliser at 10 : 10 : 10. The share-of-whole figures are what you actually measure out.
Aspect ratios. 16 : 9 and 4 : 3 are already in simplest form, which is why those particular numbers are the ones everyone knows.
Scale. A 1 : 50 drawing means one unit on paper is fifty in reality. Model railways and maps use the same notation.
Finance. Debt-to-equity, price-to-earnings, current ratio — all comparisons of two quantities in the same units, which is what makes them ratios rather than rates.
Odds. Odds of 3 : 1 mean three losing outcomes to one winning, so the probability is 1/4 — another case where the share-of-whole reading is the one that matters.
Ratio, rate and proportion
Three words that get used interchangeably and should not be.
A ratio compares two quantities of the SAME kind: three boys to two girls. It has no units, because they cancel.
A rate compares different kinds: 60 miles per hour, £12 per kilogram. It carries units, and that is what makes it a rate.
A proportion is a statement that two ratios are EQUAL: 3 : 4 = 9 : 12. It is an equation, not a quantity, and solving one is what the Proportion Calculator is for.
Sources and methodology
Ratio notation and the share-of-whole convention are curriculum standards; these are the references.
Method. Terms are carried as exact rationals and scaled to whole numbers by the least common multiple of their denominators before anything is divided, so 1.5 : 2.25 gives 2 : 3 rather than a decimal. The share-of-whole figures come from the same integers, so they always sum to exactly 100%. The suite asserts across four thousand generated ratios that the simplified terms share no common factor and that their shares add back to the reported total. That engine is verified on every change against 81 hand-written assertions, including that the simplified terms share no factor above 1 across four thousand generated ratios, and that a shared total matches a direct division on fifteen hundred splits. The count and the per-case breakdown are published on the formula verification page.
Related calculators
Where this goes next:
ProportionSolve a : b = c : d for whichever term you leave blank, with cross multiplication derived rather than asserted — or fill all four and have it checked.
Simplify FractionsReduce a fraction to lowest terms with both routes to the divisor shown side by side — Euclid line by line and the shared primes — and a stated proof when nothing can be cancelled.
GCFThe greatest common factor of two to six numbers with all three routes shown — the shared primes to their lower powers, Euclid line by line, and the full factor lists when they are short enough to be honest.
PercentageSolve X% of Y, what percent X is of Y, reverse percentage, increase/decrease, discounts, and tax, tip, or commission.
Fraction to PercentConvert a fraction, mixed number, or decimal to a percent and back, with every step of the working shown.
Average PercentageAveraging 50% and 100% gives 99.02%, not 75%, when the groups are 2 and 100 — the page weights by group size and shows the naive answer beside it.
To solve for a missing term rather than simplify — a : b = c : x — the Proportion Calculator does the cross multiplication and shows the working.
Educational use disclaimer
This is an educational tool. The arithmetic is exact; when a split does not land on whole numbers, decide deliberately who gets the leftover unit rather than letting rounding decide.
Published the ratio page computing each term's share of the whole, because a ratio does not show it and 3 : 2 meaning three fifths rather than three halves is where most ratio answers go wrong.
Terms are scaled to whole numbers by the least common multiple of their denominators before anything is divided, so 1.5 : 2.25 gives 2 : 3 rather than a decimal.
Restores a slug that had been answering 410 Gone since an old content purge, with a page that earns it.
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