Ratio Simplifier Calculator
Simplify a ratio like A:B or A:B:C:D to its lowest integer terms — handles whole numbers, decimals, fractions, and mixed numbers, with full steps.
What does a ratio simplifier do?
A ratio simplifier reduces a ratio like 12:18 to its simplest whole-number form — 2:3 — by dividing every term by their greatest common factor (GCF). It works the same way whether the ratio has two terms (A:B) or more (A:B:C:D), and it accepts terms that aren't whole numbers yet: decimals, fractions, and mixed numbers.
Simplifying whole-number ratios
When every term is already an integer, simplifying is one step:
- Find the GCF of all the terms.
- Divide every term by that GCF.
6:10 — GCF(6, 10) = 2 → 3:5.
8:36 — GCF(8, 36) = 4 → 2:9.
3:8 — GCF(3, 8) = 1 → already simplest, 3:8.
Simplifying ratios with decimals, fractions, or mixed numbers
Terms that aren't whole numbers need one extra step first — clear them to integers, then apply the same GCF rule:
| Term type | How it's cleared |
|---|---|
Decimal (0.5) | Multiply every term by the same power of 10 to remove the decimal point |
Simple fraction (1/2) | Multiply every term by the LCD (least common denominator) of all the fractions |
Mixed number (3 1/8) | Convert to an improper fraction first (25/8), then treat it like any other fraction |
Whole number (5) | Nothing to clear — it's already an integer |
Once every term is a whole number, divide all of them by their GCF as usual.
Worked example — decimals
Simplify 0.5:1.5:
- Both terms have one decimal digit, so multiply both by
10:0.5:1.5 → 5:15. - GCF(5, 15) = 5, so divide both terms:
5÷5 : 15÷5 = 1:3. - Result:
0.5:1.5 = 1:3.
Worked example — fractions
Simplify 1/2:3/4:
- The LCD of 2 and 4 is 4, so multiply both terms by 4:
1/2:3/4 → 2:3. - GCF(2, 3) = 1, so the ratio is already in simplest form.
- Result:
1/2:3/4 = 2:3.
Worked example — a full mixed-number ratio
Simplify 5:3 1/8 (matches the classic worked example for this tool):
- Convert the mixed number to an improper fraction:
3 1/8 = 25/8. Now the ratio is5:25/8. - Write the whole number as a fraction too:
5 = 5/1. Now it's5/1:25/8. - The LCD of 1 and 8 is 8. Multiply every term by 8:
5/1:25/8 → 40:25. - GCF(40, 25) = 5, so divide both terms:
40÷5 : 25÷5 = 8:5. - Result:
5:3 1/8 = 8:5.
Worked example — three and four terms
Ratios with more than two terms simplify the same way — find the GCF of every term and divide them all by it.
12:18:24 — GCF(12, 18, 24) = 6 → 2:3:4.
4:6:8:10 — GCF(4, 6, 8, 10) = 2 → 2:3:4:5.
Precision note
Every step uses exact integer (BigInt) arithmetic. Decimals are cleared by a whole power of 10 and fractions by their exact LCD, never by dividing with floating-point numbers — so a ratio like 0.07:0.29 reduces exactly, without landing on a rounding artifact like 7.000000000000001.
Related tools
To reduce a fraction on its own (not a ratio), use the simplifying fractions calculator. To find the GCF of a set of numbers directly, use the GCF calculator. To turn a ratio into a fraction of a whole (rather than just reducing it), see the ratio to fraction calculator or the more general ratio calculator.
Frequently asked questions
- How do you simplify a ratio?
- Divide every term of the ratio by their greatest common factor (GCF). For example, 12:18 has a GCF of 6, so dividing both terms gives 2:3. If a term isn't a whole number yet (a decimal, fraction, or mixed number), clear it to an integer first, then divide by the GCF.
- How do you simplify a ratio with decimals, like 0.5:1.5?
- Multiply every term by the same power of 10 to clear the decimal point — here, by 10, giving 5:15. Then divide both terms by their GCF (5) to get 1:3. Multiplying every term by the same number never changes the ratio, only how it's written.
- How do you simplify a ratio with fractions, like 1/2:3/4?
- Find the LCD (least common denominator) of the fractions — 4 for 1/2 and 3/4 — and multiply every term by it to clear the denominators: 1/2:3/4 becomes 2:3. Since GCF(2, 3) = 1, that ratio is already in simplest form.
- Can a ratio simplifier handle mixed numbers?
- Yes. A mixed number like 3 1/8 is first converted to an improper fraction (25/8). From there it's treated like any other fraction term — cleared to an integer using the LCD, then reduced by the GCF alongside the other terms.
- Can you simplify a ratio with more than two terms, like 12:18:24?
- Yes. The same rule extends to any number of terms: find the GCF of all of them (GCF(12, 18, 24) = 6) and divide every term by it, giving 2:3:4. This calculator accepts 2 to 4 terms at once.
- What if the ratio is already in simplest form?
- Then its GCF is 1, and dividing by 1 leaves the ratio unchanged — 7:13 stays 7:13, since 7 and 13 share no common factor besides 1.
- Can a ratio term be negative or zero?
- No. Ratio terms represent quantities being compared, so this calculator requires every term to be a positive number — zero or negative terms are rejected as invalid input.
- Is Ratio Simplifier the same as the Ratio Calculator?
- They're related but not identical. A ratio calculator typically solves a proportion (A:B = C:?), finding a missing term. A ratio simplifier does one specific job — reduce A:B (or A:B:C:D) to its lowest integer terms — and it's built to accept messier inputs first: decimals, fractions, and mixed numbers, not just whole numbers.