A method for solving proportions by multiplying the numerator of each fraction by the denominator of the other fraction. If a/b = c/d, then cross-multiplying gives ad = bc.
The term 'cross' refers to the X-pattern formed when drawing lines between the numerators and denominators being multiplied. This technique was formalized in European mathematics during the Renaissance as algebraic methods developed, though the underlying principle was known to ancient mathematicians.
Cross-multiplication works because of a beautiful symmetry in proportional relationships - it's actually just clearing denominators by multiplying both sides by the same quantity! This technique reveals that proportions are fundamentally about equivalent ratios, connecting arithmetic to the deeper algebraic concept of maintaining equality through operations.
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