Rule

Division Property of Equality

Dividing each side of an equation by the same nonzero number yields an equivalent equation. Let

a,

b,

and

c

be real numbers.

If $a = b$ and $c \neq = 0,$ then $a \div c = b \div c .$

The Division Property of Equality is an axiom, so it does not need a proof to be accepted as true. This property is one of the Properties of Equality that can be used when solving equations.

5 x 5 x \div 5 x = 10 = 10 \div 5 = 2

As can be observed, by dividing both sides of the equation by

5,

the variable

x

was isolated and the solution of the equation was found. Note that the Division Property of Equality also holds true if

a,

b,

and

c

are complex numbers.

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Rule

Division Property of Equality

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