Two ratios are equivalent when their cross-products are equal.
Formula
A:B = C:D → A×D = B×C
Explanation
Write proportions as A:B = C:D or A/B = C/D. Cross-multiplying gives A·D = B·C. Use that identity to solve for any missing term, or simplify A:B by dividing both parts by their GCD.
Variables
A, Bfirst ratio terms
C, Dsecond ratio terms (or scale factor partners)
When to use
Maps, recipes, aspect ratios, mixture problems, and similar-figure scaling.