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Division Property of Equality

Rule

Division Property of Equality

Given an equation, dividing each side of the equation by the same non-zero number yields an equivalent equation.

If a=ba = b and c0,c\neq 0, then a÷c=b÷c.a \div c = b \div c.

The Division Property of Equality also holds true if a,a, b,b, and cc are complex numbers as long as c0.c\neq 0. This property is one of the Properties of Equality that can be used when solving equations. 5x=105x÷5=10÷5x=2\begin{aligned} 5x&=10\\ 5x\textcolor{blue}{\,\div{\,5}}&=10\textcolor{blue}{\,\div{\,5}}\\ x&=2 \end{aligned} To isolate the variable, the multiplication by 55 can be eliminated by dividing both sides of the equation by 5,5, since division is the inverse operation of multiplication.