Ratio & proportion tools
How to Check a Ratio Answer
You already have an answer. Five checks test it from five different directions — including the cases where the arithmetic is right and the question was misread.
A ratio answer can fail in ways that look nothing alike: a reduction that went half way, a split that misses the total by a penny, a percentage measured against the wrong denominator, two ratios that are close but not equal, and units that were never comparable. Each check below isolates one of those, so a failure points at a specific step rather than at the answer as a whole.
Check 1 — Re-multiply the simplified ratio
A simplification claims that the original ratio and the reduced one describe the same relationship. That claim is directly testable: multiply the reduced parts back by the divisor you used and you must land on the original numbers exactly.
Does 12:18 really reduce to 2:3?
- The divisor used was 6.
- 2 × 6 = 12 ✓
- 3 × 6 = 18 ✓
- Both parts reproduce, using the same multiplier, so the reduction is valid.
Failure looks like one part reproducing and the other not. 12:18 → 2:4 fails the moment you try it: 2 × 6 = 12 but 4 × 6 = 24, not 18. That asymmetry always means a different factor was applied to each part, or something was subtracted rather than divided. A separate failure is stopping too early — 6:9 re-multiplies correctly (× 2) yet is not simplest, because 6 and 9 still share a factor of 3.
Check 2 — Sum the shares back to the total
Any answer that divides an amount has a free consistency test: the parts must reconstruct the amount. This catches a wrong value for one part even when the ratio itself was handled correctly.
£1,000 split 2:3:5
- Total ratio parts: 2 + 3 + 5 = 10.
- One part is worth £1,000 ÷ 10 = £100.
- Shares: £200, £300, £500.
- Verify: 200 + 300 + 500 = 1,000 ✓
Money is where this check earns its keep, because a total rarely divides into a whole number of pence. A three-way split of £100 at 1:1:1 cannot give three equal displayed amounts to the penny. SnapRatios resolves the remainder deterministically rather than rounding each share independently, so the displayed shares still add up to exactly the amount entered — if your own answer's shares miss the total by a penny or two, that is the symptom of per-share rounding. The allocation rule itself is documented on the split ratio calculator and in the methodology.
Check 3 — Ask what denominator the percentage uses
Most "wrong" percentages are correct answers to a different question. Before rejecting one, establish what it is a percentage of.
3:4 produces two legitimate percentages
Part-to-part: 3 ÷ 4 = 0.75 = 75%. Part A is 75% of part B.
Part-to-whole: total parts = 3 + 4 = 7, so 3 ÷ 7 ≈ 42.857%. Part A is 42.857% of the whole.
Cross-check the part-to-whole reading: 4 ÷ 7 ≈ 57.143%, and 42.857% + 57.143% = 100% ✓
That last line is the actual test. Part-to-whole percentages must sum to 100% across all parts; part-to-part percentages have no reason to. If your figures sum to something other than 100% and you expected shares of a whole, you divided by the wrong part rather than by the total. Both readings side by side are on ratio to percentage.
Check 4 — Cross-multiply two ratios
To test whether two ratios are equivalent, compare a/b with c/d by cross-multiplying: a × d against b × c. Equal products mean equal quotients, and this avoids decimals entirely, so it never produces a rounding false negative.
Is 2:3 equivalent to 8:12?
- 2 × 12 = 24
- 3 × 8 = 24
- The products match, so 2:3 = 8:12 ✓
Is 2:3 equivalent to 8:11?
- 2 × 11 = 22
- 3 × 8 = 24
- 22 ≠ 24, so the ratios are not equivalent — 8:11 is slightly weighted towards the first part.
What the check proves is narrow and worth stating: it proves the two comparisons are identical. It says nothing about whether either ratio is in simplest form or whether the quantities are the right size. Run it against your own pair in the equivalent ratio calculator.
Check 5 — Confirm both sides share a measurement basis
A ratio compares numbers, and numbers only mean something once the units behind them match. This is the one failure the arithmetic cannot detect, because 500:1 is a perfectly valid ratio of nonsense.
500 g : 1 kg
- Written as raw numbers this reads 500:1, implying one side is 500 times the other.
- Convert to a shared unit: 1 kg = 1000 g.
- The comparison is 500:1000.
- Simplify: 1:2. The second quantity is twice the first, not one five-hundredth of it.
Matching units are necessary but not always sufficient. Two quantities both measured in millilitres are comparable as volumes, yet a 1:1 volume ratio is not a 1:1 mass ratio unless the densities happen to be equal. Converting between a volume basis and a mass basis needs density, not arithmetic — see how mixing ratios work.
Statements that look alike and are not
When two sources disagree about a ratio, the disagreement is often in the wording rather than the maths. The canonical case:
1:10 versus 1 in 10
1:10 as a part-to-part ratio: one part product to ten parts diluent, so 11 total parts.
First component's share: 1 ÷ 11 ≈ 9.09%.
1 in 10: one part in ten parts of finished mixture, so 10 total parts.
First component's share: 1 ÷ 10 = 10%.
Both are arithmetically correct. They describe different mixtures.
Neither number is a calculator error, and neither convention is universally "the" right one — they are different definitions of what the second number counts. The full treatment, including which industries use which, is on the 1:10 page. The general lesson transfers: when two methods disagree by a predictable amount, suspect a definition mismatch before suspecting arithmetic.
Symptom, cause, check
| Symptom | Likely cause | Check | Where to learn more |
|---|---|---|---|
| My percentage looks too high | Divided by the other part instead of the total | Do the part-to-whole figures sum to 100%? | Ratio to percentage |
| My shares do not add to the total | Each share was rounded independently | Sum the shares; compare with the original amount | Split ratio calculator |
| My equivalent ratio looks different | Only one term was scaled, or terms were rounded | Cross-multiply: a × d must equal b × c | Equivalent ratio |
| 1:10 gave 9.09%, not 10% | Parts convention versus one-in-N convention | Count the total parts: 11 or 10? | 1:10 explained |
| My mix changed after converting units | Volume basis swapped for mass basis | Are both sides the same kind of measurement? | How mixing ratios work |
| I simplified but the relationship changed | Subtraction, or a different factor per part | Re-multiply both parts by the same divisor | How to simplify ratios |
| Scaling to a total gave awkward decimals | The total is not a multiple of the sum of parts | k = total ÷ sum of parts; a fractional k is valid | How to scale a ratio |
Each row is a symptom that at least one of the five checks above will detect.
An exact calculation is not an exact measurement
These checks verify the relationship, not the inputs. SnapRatios computes with exact rational arithmetic, so a third of 100 stays 100/3 rather than 33.333, and every check above will pass to the last digit. That is calculation exactness, and it is entirely a property of the maths.
Input accuracy is a separate axis. If a jug was filled to roughly 500 ml, the resulting ratio inherits that roughness no matter how precisely it is computed — the result is exactly the ratio of your approximate numbers. Worth keeping apart when a check passes and the physical outcome still looks wrong: at that point the suspect is the measurement, not the arithmetic.