How to simplify a ratio
A ratio such as 12 : 18 compares two quantities. To simplify it, divide both terms by their greatest common divisor. Since the greatest common divisor of 12 and 18 is 6, the simplified ratio is 2 : 3. The calculator uses exact whole-integer arithmetic for this step.
Solving proportions
A proportion states that two ratios are equal. For a : b = c : x, cross-multiplication gives a × x = b × c. Rearranging gives x = (b × c) ÷ a. If x is not a whole number, this calculator keeps the exact fractional answer and also shows a decimal form.
Splitting a total by ratio
To divide a total in the ratio 2 : 3, first add the parts to get 5. The first share is 2/5 of the total and the second share is 3/5. This is useful for budgets, mixtures, allocations, ownership shares, and other proportional distributions.
Why exact integer arithmetic matters
Ratio simplification and proportion solving use integer-based arithmetic instead of truncating values to ordinary JavaScript integers. That keeps large whole-number ratios exact and avoids silently losing precision during the simplification step.
Common mistakes
Reversing the order: 2 : 3 and 3 : 2 represent different comparisons, so preserve the order of the quantities.
Using a zero denominator: a ratio interpreted as a fraction cannot have zero as its second term in simplify or proportion mode.
Using negative split weights: splitting a practical total requires positive ratio parts because each part represents a positive share of the whole.
Frequently asked questions
Can a simplified ratio contain a negative term?
Yes. Negative ratios are accepted in simplify mode. The sign is normalized so the second term is positive.
Can the proportion answer be a fraction?
Yes. The exact fractional result is preserved instead of being rounded to a whole number.
Does ratio splitting round the shares?
The calculator keeps the underlying numeric result and formats it for readability. Depending on the ratio, displayed shares can contain decimals.