Cross-multiplying when adding fractions
"The Cross-Multiply Confusion"
The Mistake in Action
Calculate $\frac{2}{x} + \frac{3}{y}$
Wrong: $= \frac{2y + 3x}{1}$ (cross-multiplied and added)
Why It Happens
Students confuse cross-multiplication (for equations) with finding common denominators (for adding fractions).
The Fix
Cross-multiplication is for solving equations like $\frac{a}{b} = \frac{c}{d}$ (giving $ad = bc$).
Adding fractions requires a common denominator:
$\frac{2}{x} + \frac{3}{y} = \frac{2y}{xy} + \frac{3x}{xy} = \frac{2y + 3x}{xy}$
The denominator does NOT disappear!
Spot the Mistake
Can you identify where this student went wrong?
$\frac{2}{x} + \frac{3}{y}$
$= \frac{2y + 3x}{1}$
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: