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Rule

# Multiplication Property of Equality

Given an equation, multiplying each side of the equation by the same number yields an equivalent equation.

If $a = b,$ then $a \times c = b \times c.$

The Multiplication Property of Equality also holds true if $a,$ $b,$ and $c$ are complex numbers. This property is one of the Properties of Equality that can be used when solving equations. \begin{aligned} x\div{4}&=2\\ x\div{4}\textcolor{blue}{\,\times{\,4}}&=2\textcolor{blue}{\,\times{\,4}}\\ x&=8 \end{aligned} To isolate the variable, the division by $4$ can be eliminated by multiplying both sides of the equation by $4,$ since multiplication is the inverse operation of division.