Simplify a ratio or find a missing value
Choose Simplify A:B and enter both nonnegative parts. The result is an equivalent ratio in the smallest whole-number parts. For Find a missing value, choose the unknown A, B, C or D, then enter the other three in A:B = C:D. Here the notation means A/B = C/D, so B and D must be nonzero.
Try example fills the current task without calculating. Changing the task or unknown clears all values and the result. Reset returns to the empty Simplify task. Editing removes the old answer and copy action.
Exact method and examples
For whole numbers, divide both parts by their greatest common divisor (GCD). For 18:24, GCD is 6, so the simplified ratio is 3:4.
Finite decimals first become exact fractions with a common integer scale. For 1.5:2.5, multiplying both parts by 10 gives 15:25; dividing by 5 gives 3:5. The same result follows from 150:250. No preliminary decimal rounding is used. 0:5 reduces to 0:1, while 0:0 is undefined and rejected. A ratio such as 5:0 reduces to 1:0; its quotient A/B is undefined.
For a proportion, cross multiplication gives A × D = B × C. In 4:6 = 10:D, 4D = 60, so D = 15. Unknown A is B × C / D; unknown B is A × D / C; unknown C is A × D / B; unknown D is B × C / A, provided the divisor is nonzero and the resulting B and D remain nonzero.
When the coefficient of the unknown is zero, a nonzero product gives no solution; a zero product gives infinitely many solutions, with no unique answer. For example, 0:1 = 2:D has no solution, while 0:1 = 0:D has infinitely many admissible nonzero D values. The calculator reports these cases without dividing by zero.
Quotient versus share of a total
For 3:4, the quotient A/B is 3/4, while A’s share of the combined total A/(A+B) is 3/7. The result labels both so these quantities are not confused. Use the Fraction Calculator for arithmetic with those exact fractions or the Percentage Calculator for a percentage calculation. The Average Calculator handles lists of values.
Limits and precision
Each known input must be between zero and 1,000,000,000,000 with at most six decimal places. Use a decimal point, no thousands separators and no scientific notation. There are exactly two parts per ratio. Negative values and three-part ratios are outside this version.
Integer ratios and fraction solutions are exact and reduced using BigInt arithmetic. A missing value also has a decimal approximation displayed to at most 12 places; this approximation does not replace the exact answer. This mathematical tool does not provide medication dosages, concrete mix designs or chemical formulations.