Lesson 4: Solving Equations Using Multiplication or Division

Property

Multiplication Property of Equality: Multiplying both sides of an equation by the same non-zero number maintains the equality. If $a=b$ and $c \neq 0$, then $ac = bc$.

Division Property of Equality: Dividing both sides of an equation by the same non-zero number maintains the equality. If $a=b$ and $c \neq 0$, then $\frac{a}{c} = \frac{b}{c}$. These properties are used to isolate variables in equations.

Property

To solve equations involving multiplication or division, we apply the rules of equivalence to isolate the variable. For equations in the form $px = q$, we find the solution by dividing both sides by $p$ (where $p \neq 0$). For equations in the form $\frac{x}{p} = q$, we find the solution by multiplying both sides by $p$ (where $p \neq 0$). All numbers $p$, $q$, and $x$ are rational numbers.

Examples