Simplify, solve, scale and divide by a ratio.
What it's for
Work with ratios: reduce one to its simplest form, find the missing number in a : b = c : x, scale a ratio up, or split an amount of money by a ratio, to the centavo.
Before you start
Have the numbers of your ratio, such as 2 : 3 for a mix or a profit share, and the amount to split if you are dividing money.
Choose what to do
Pick Simplify to reduce a ratio, Solve for x to find a missing number, Scale to multiply every part, or Split an amount to divide money in that ratio.
Type the ratio
Type each part in Term 1, Term 2 and so on. Press + Term for a third part or more, and ✕ to remove the last one.
Add the extra number
For Solve for x, written a : b = c : x, put a and b in the two terms and c in = this : x. For Scale, type the multiplier in Multiply by. For Split an amount, type the money in Amount to split.
Press Calculate
Press Calculate. The answer already updates as you type; the button brings it into view. Each step is listed under Working.
Reading the result
If it goes wrong
Four things a ratio gets asked to do: reduce to its smallest terms, fill in a missing one, scale up to real quantities, and divide something in proportion. Every mode also shows the ratio as percentages and as fractions, because that is usually what it is being turned into.
The split is the one worth the tool. Money rarely divides evenly, and rounding each share on its own leaves the total short — so the leftover centavos are handed out rather than lost, and the shares always add back to what you started with.
Because the amount does not divide evenly, and the tool refuses to lose the difference. Splitting ₱1,000 three ways is ₱333.333… each; rounding every share on its own gives ₱999.99, a centavo short of money that actually exists. So the leftover centavos go one each to the largest remainders, and the shares add back to exactly ₱1,000. The one that received a centavo is marked.
Choose "Solve for x", put a and b in the two term boxes, and c in the third field. The tool cross multiplies: x = b × c ÷ a. That is the same arithmetic behind scaling a recipe, converting a map distance, or working out a missing dimension from a drawing.
No, which is the point. Multiplying every term by the same factor changes the numbers but not the proportions, so 2 : 3 scaled by four is 8 : 12 — which simplifies straight back to 2 : 3. Use it when you need the actual quantities rather than the relationship.
Yes. A ratio like 1.5 : 2 is scaled up to whole numbers before being reduced, giving 3 : 4. Taking the greatest common divisor of a decimal directly would be meaningless.
Each term over the total. 1 : 3 is one part in four, so 25% and 75%. Both the percentages and the fractions are shown on every mode, because they are usually what the ratio is being converted into anyway.
A centavo is not much until it is the centavo three people are arguing about. The share that received it is marked, so the difference is explained rather than mysterious.
Scaled to whole numbers first — the greatest common divisor of a decimal means nothing.
Important
Where an amount does not divide evenly, leftover centavos go to the largest remainders so the shares sum to the total exactly. Nothing you type here is sent to our servers — the calculation runs entirely in your browser.
