What is cross multiplication?

Cross multiplication is a method for solving proportions of the form a/b = c/d. You multiply the numerator of each fraction by the denominator of the other: a times d equals b times c. This gives you a linear equation that you can rearrange to find whichever of the four values is unknown.

How do you solve 3/4 = x/12?

Cross multiply: 3 times 12 equals 4 times x. 36 equals 4x. Divide both sides by 4: x equals 9. You can verify by checking that 3/4 and 9/12 are equivalent fractions, which they are since 9/12 simplifies to 3/4.

When does cross multiplication not work?

Cross multiplication requires that neither denominator (b or d) is zero, since dividing by zero is undefined. If you set x as the unknown in a denominator position and the opposite numerator is also zero, the equation has infinitely many solutions. This calculator flags these cases rather than producing a misleading result.

Cross Multiplication Calculator

Cross multiplication is the most direct way to solve a proportion, which is an equation stating that two ratios are equal: a/b = c/d. It is used in unit conversions, scale problems, recipe scaling, map reading, probability, and almost any situation where you know three of four values in a proportional relationship and need to find the fourth. The method works by multiplying across the equals sign: the numerator of the left fraction times the denominator of the right equals the denominator of the left times the numerator of the right. This gives a times d equals b times c, and you rearrange for whichever value is unknown. In this calculator you enter three of the four values A, B, C, D in the proportion A/B = C/D, leave the unknown as x or blank, and choose which position holds the unknown. The calculator solves for it and verifies the result by checking that the two cross products are equal. The defaults show 3/4 = x/12: three known values, with x in the C position. The solution is x = 9 because 3 times 12 = 4 times 9 = 36.

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Solve for

A (numerator of left ratio)

B (denominator of left ratio)

C (numerator of right ratio) - leave blank if solving for C

D (denominator of right ratio)

value of C

Cross product A x D36

Cross product B x C36

Proportion verifiedYes

Proportion: A/B = C/D. Cross multiply: A x D = B x C.

How it works

The proportion A/B = C/D means that A times D equals B times C (the cross products). To find an unknown, isolate it: if solving for C, then C = (A times D) divided by B. If solving for A, then A = (B times C) divided by D. If solving for B, then B = (A times D) divided by C. If solving for D, then D = (B times C) divided by A. Once the result is found, both cross products are computed and compared to verify the proportion holds. Division by zero is flagged as an error.

Worked example

Proportion 3/4 = x/12, solving for C. Cross multiply: A times D = 3 times 12 = 36. Divide by B: 36 divided by 4 = 9. So C = 9. Verify: A times D = 3 times 12 = 36, and B times C = 4 times 9 = 36. Both cross products equal 36, confirming 3/4 = 9/12. These match the defaults pre-filled above.

Related calculators

Completing the Square: rewrite a quadratic in vertex form and find its roots.
Long Multiplication: multiply large numbers with partial products shown step by step.
Binomial Expansion: expand (a+b) to the power n using the binomial theorem.
Percent Error Calculator: percentage deviation between a measured and true value.

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