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Wiktionary
cross-multiplication

n. (context mathematics English) An instance, or the process, of cross-multiplying.

Wikipedia
Cross-multiplication

In mathematics, specifically in elementary arithmetic and elementary algebra, given an equation between two fractions or rational expressions, one can cross-multiply to simplify the equation or determine the value of a variable.

Given an equation like:


$$\frac a b = \frac c d$$

(where and are not zero), one can cross-multiply to get:


$$ad = bc \qquad \mathrm{or} \qquad a = \frac {bc} d.$$

In Euclidean geometry the same calculation can be achieved by considering the ratios as those of similar triangles.