How this calculator works
To simplify, divide both whole-number terms by their greatest common divisor. A negative second term moves its sign to the first term. To solve equal ratios, use cross multiplication with the three known terms. Simplification requires safe integers; solving accepts finite decimal values.
Formula
Simplified a:b = (a/g):(b/g), where g is the signed gcd. For a:b = c:d, d = bc/a or c = ad/b.
Worked example
24:36 reduces to 2:3. In 3:4 = 9:d, the missing d is 12. In 3:4 = c:16, the missing c is also 12.
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Frequently asked questions
Can a ratio contain zero?
One zero term can be simplified, such as 0:4 to 0:1. The pair 0:0 has no defined ratio. A solve mode rejects a zero term when that term is the divisor.
Do the terms need the same units?
Convert comparable quantities to consistent units before simplifying. Ratios of different kinds of quantity can instead describe a rate, whose units should be retained separately.
Can I simplify terms that are decimals?
No. Simplify mode requires whole numbers. The solve modes accept decimal values for the three known terms.