Glossary
cross multiplication
Cross multiplication solves a proportion by multiplying each numerator by the opposite denominator, then dividing by the remaining number.
Cross multiplication is the standard way to solve a proportion once it is written as two equal fractions. Multiply the top of one side by the bottom of the other, set the two products equal, and divide by the number left over: from 2/1 = 6/x you get 2x = 6, so x = 3. It works because multiplying both sides by both denominators clears them in one step, and it is only valid if the two fractions are a genuine proportion — the same noun in the same position on each side. That is where the errors come from: a proportion set up upside down cross-multiplies perfectly and returns a wrong answer that looks right. Estimate the answer before solving and compare, so an inverted setup shows up as a number that is obviously too large or too small rather than as one more line to re-check.
Taught in
Related terms
- proportion — A proportion is a statement that two ratios are equal, with one of the four values missing — and the missing value is what the calculation returns.
- ratio — A ratio compares two quantities, written a : b, and it stays the same when both sides are multiplied or divided by the same number.
Source: The math guides in this course (ratio and proportion, measurement and conversion, dosage calculation): every definition and worked value above was written for this course, because arithmetic and unit conversion are not a publisher's prose, and each guide shows the method worked. Elsevier's own HESI A2 page, which names math among the areas the exam covers, is the exam-side source. (Elsevier HESI A2 page accessed 2026-10-23; definitions written 2026-10-27)