Ratio & Proportion Calculator
Three tools for the three things ratios are ever asked to do: reduce one to its simplest form, solve a proportion for the term that is missing, and split an amount fairly between shares. Each answer comes with the working, and every sheet prints with its key.
Simplify a ratio
Two terms or more — 8 : 12, 3 : 4 : 5, even 0.25 : 0.75.
Solve a proportion
Fill in three boxes and leave the fourth empty — that is the one being solved for.
Share an amount in a ratio
Split money, sweets, time or work between two or more shares.
Print a worksheet
Twelve problems on one page with the answer key on the second. Press again for a completely fresh set — nothing repeats between prints, so every child can have a different sheet.
What a ratio actually says
A ratio compares quantities to each other, not to the whole — and nearly every mistake made with ratios comes from forgetting that one sentence. In 1 : 4 there are five parts, so the first quantity is a fifth of the mixture rather than a quarter of it. One cup of squash and four cups of water fills five cups. Reading a ratio as a fraction of the total is the single most reliable way to get squash wrong, concrete wrong, and exam questions wrong.
The bar drawn under each answer above exists for that reason. It shows the terms as blocks side by side, so the total number of parts is something you can see rather than something you have to remember to add up.
Simplifying: divide by what they share
A ratio is in its simplest form when its terms share no factor except one. Getting there is a single move — find the greatest common factor of every term and divide them all by it. For 8 : 12 that factor is 4, giving 2 : 3. Halving repeatedly works too and needs no arithmetic at all beyond halving, it just takes more steps: 8 : 12 → 4 : 6 → 2 : 3.
Decimals look harder than they are. Multiply every term by whatever power of ten clears the decimal point — 0.25 : 0.75 becomes 25 : 75 — and then reduce as normal to get 1 : 3. The calculator above scales before it divides for exactly this reason, so the answer is exact rather than a rounded near miss.
Proportions: one cross multiplication
A proportion is two ratios set equal: 3 : 4 = 12 : d. Write it as fractions and the rule falls out — if a/b = c/d then a × d = b × c. Every proportion problem, whichever box is empty, is that one identity rearranged:
- Missing d: d = (b × c) ÷ a
- Missing c: c = (a × d) ÷ b
- Missing b: b = (a × d) ÷ c
- Missing a: a = (b × c) ÷ d
Then check by multiplying the two diagonals: if the cross products match, the answer is right. That check costs five seconds and catches the divide-instead-of-multiply slip that accounts for most lost marks here. The solver above prints it with every answer.
Sharing: count the parts first
Sharing 240 in the ratio 3 : 5 is three steps and the first one is the one people skip:
- Add the terms — 3 + 5 = 8 parts altogether.
- Divide the amount by the parts — 240 ÷ 8 = 30 per part.
- Multiply back out — 3 × 30 = 90 and 5 × 30 = 150.
Finish by adding the shares back: 90 + 150 = 240. If they do not add to what you started with, something went wrong in step two. The method is identical for three shares or more — the only thing that changes is how many terms go into the total.
Using the three sheets
Simplify is the place to start, because reducing is what the other two both lean on. Solve proportions comes next and deliberately moves the blank around all four positions — a class that has only ever seen the blank on the right learns a pattern rather than the method. Share an amount is the applied sheet and the one that matches how ratios show up in exams and in real life. All three print twelve problems on one page with the key on a separate sheet, so it can be handed over or kept back.
Frequently asked questions
How do you simplify a ratio?
Divide every term by their greatest common factor — 8 : 12 has a factor of 4, so it reduces to 2 : 3. Clear any decimals by multiplying through by a power of ten first.
What is the difference between a ratio and a proportion?
A ratio compares quantities (3 : 4). A proportion states that two ratios are equal (3 : 4 = 12 : 16). Solving a proportion means finding the term that makes both sides match.
How do you solve a proportion?
Cross multiply: a/b = c/d means a × d = b × c. Rearrange for the empty box and divide. The same step works whichever of the four positions is blank.
How do you share an amount in a ratio?
Add the terms for the total parts, divide the amount by that total for one part, then multiply back out. 240 in 3 : 5 → 8 parts → 30 each → 90 and 150.
How do you turn a ratio into a percentage?
Divide each term by the total parts and multiply by 100. In 2 : 3 there are 5 parts, so the shares are 40% and 60% — not 20% and 30%.
Does 1 : 4 mean one quarter?
No — it means one part in five. 1 : 4 has five parts altogether, so the first quantity is a fifth of the mixture.
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