Cross Products

In an equation of the form

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

we can multiply both sides by $bd$ to get the equation

$ad=bc$ .

This is known by many names: cross-multiplying, taking cross-products, the means-extremes property, or the reciprocal property.

Example:

Solve for $x$ .

$\frac{3}{7}=\frac{x+1}{9}$

Use the means-extremes property to get a simpler equation.

$3\left(9\right)=7\left(x+1\right)$

Now simplify and solve.

$\begin{array}{l}27=7x+7\\ 7x=20\\ x=\frac{20}{7}\end{array}$