Mathematics · Numbers and arithmetic
Simplify a ratio A : B
Two integers in, a reduced ratio out (8 : 12 becomes 2 : 3), plus the quotient A/B and each term’s weight in the sum of absolute values — not “A as a percent of B.”
Calculate
How the calculator works
The GCF of A and B divides both terms. The page also shows A/B as a decimal and the shares |A| / (|A|+|B|) and |B| / (|A|+|B|) as percents. Those shares describe a two-part mix, not “A is what percent of B.”
Formula and method
A : B → (A ÷ g) : (B ÷ g) with g = GCF(A, B)
8 : 12, g = 4 → 2 : 3.
part A = |A| / (|A| + |B|) × 100
For 8 and 12: 8/20 = 40% and 12/20 = 60%. That is not 8/12.
Terms are integers. B cannot be 0 because A/B is also reported. A = B = 0 is rejected. Signs are kept on the reduced terms; mix shares use absolute values so a negative term still contributes a positive weight in the mix view.
Worked example
8 : 12
A = 8, B = 12
- GCF(8, 12) = 4.
- Reduced ratio 2 : 3.
- Quotient 8/12 ≈ 0.667.
- Shares 40% and 60%.
2 : 3, with a 40/60 split of the absolute mix.
Input notes
- First term (A)
- First integer. Zero is allowed if B is not also zero.
- Second term (B)
- Second integer, nonzero so A/B exists.
Assumptions and limits
Assumptions
- You want a reduced colon ratio of two integers.
- Mix percents use absolute values.
Limits
- Only two terms; no A : B : C.
- Not a recipe scaler beyond the reduced pair.
How to read the result
2 : 3 means two parts to three parts. The 40% is A’s share of the combined size, which is the right number for a blend. “8 is what percent of 12?” is 66.7% and lives on the percentage page.
Common mistakes
Reading 40% as “A is 40% of B.”
40% is A / (A+B). A as a percent of B is 8/12 ≈ 66.7%.
Reducing 8 : 12 to 8 : 12 and calling that simplified.
Divide both by 4 to get 2 : 3.
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Frequently asked questions
Is 2 : 3 the same as 2/3?
As a quotient, yes. As a mix, you still have two parts plus three parts.
2/3 ≈ 0.667 is A/B. The ratio 2 : 3 also says how a whole splits: 2 of 5 parts and 3 of 5 parts.
Why can’t B be zero?
The page also reports the quotient A/B.
A ratio A : 0 is not used here. If you only need a fraction with a zero numerator, use the fractions page.
Do negative terms work?
Yes. The reduced ratio keeps signs; mix shares use absolute values.
−8 : 12 reduces by GCF 4 to −2 : 3. The mix view still splits 40/60 on the magnitudes.
Author and update
Written by Rédaction HexaCalc (editorial team). Content last updated: August 25, 2026. No third-party medical or financial review is claimed.
This calculation uses a standard mathematical identity. See also the methodology.
Part of a single total
If you want “8 is what percent of 12?” rather than a 2 : 3 mix, use the part-over-whole percentage tool.
Calculate a percentageCategory: Mathematics