Math

Cross-Multiplying When It Does Not Apply

Students cross-multiply whenever they see fractions, even when the problem is not a proportion.

Quick check

Why students make it

They remember cross-multiplication as a powerful shortcut and apply it to any fraction problem. They confuse an equation of two equal ratios with adding, subtracting, or simplifying fractions.

The rule done right

Cross-multiply only when two fractions or rational expressions are set equal, such as ab=cd\frac{a}{b}=\frac{c}{d} with b≠0b \ne 0 and d≠0d \ne 0. It is not a rule for adding, subtracting, multiplying, dividing, or simplifying fractions.

Related resources

fractionsproportionsrational-expressions