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.

The method is also occasionally known as the "cross your heart" method because lines resembling a heart outline can be drawn to remember which things to multiply together.

Given an equation like

${\displaystyle {\frac {a}{b}}={\frac {c}{d}},}$

where b and d are not zero, one can cross-multiply to get

${\displaystyle ad=bc\quad {\text{or}}\quad a={\frac {bc}{d}}.}$

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