Cross Multiplication Calculator

Cross multiplication is a method used to solve equations where two fractions are set equal to each other, forming a proportion expressed as a/b = c/d. When you cross multiply, you multiply the numerator of the first fraction by the denominator of the second fraction, and set it equal to the product of the denominator of the first fraction and the numerator of the second fraction. Mathematically, this is written as a * d = b * c. If you are solving for a missing variable like d, you isolate it by rearranging the formula to d = (b * c) / a, or depending on which variable is missing, using c = (a * d) / b.

Imagine you are scaling a recipe or analyzing a map scale where the proportion is set up as 3/4 = x/12. Here, your known variables are a = 3, b = 4, and d = 12, while you need to find the missing numerator c (which represents x). First, apply the cross multiplication formula: c = (a * d) / b. Next, substitute the numbers into the equation: c = (3 * 12) / 4. Multiply the numerator values to get 36. Finally, divide by 4, which gives you c = 9. Thus, the missing value is 9, making the balanced proportion 3/4 = 9/12.

Always double-check that your fractions are properly aligned as direct proportions before performing the calculation. Ensure that units match across numerators and denominators—for instance, comparing meters to meters and seconds to seconds. Lastly, verify your final answer by dividing both sides of the solved fraction to confirm that both ratios equal the exact same decimal value.