# Solving Equations Using the Multiplication Property

The Multiplication Property for Equations states that an equation can be multiplied or divided by the same number on each side of the equation without changing the solution to the equation.

Example 1:

Solve for w: 13w = -52

Solution:

Isolate the w by dividing each side of the equation by 13.

$\frac{13w}{13} = \frac{-52}{13}$

w = -4

Example 2:

Solve for f:$-\frac{3}{7} = -\frac{2}{5}f$

Solution:

Isolate the f-term by multiplying each side of the equation by the reciprocal of its coefficient. The coefficient of f is $-\frac{2}{5}$ . The reciprocal of the f-coefficient is $-\frac{5}{2}$ . Multiply each side of the equation by $-\frac{5}{2}$ .

$-\frac{3}{7} \cdot (-\frac{5}{2}) = -\frac{2}{5}f \cdot (-\frac{5}{2})$

Multiply the fractions on the left side of the equation. On the right side of the equation, the constants cancel to leave a coefficient of 1.

$\frac{15}{14} = f$

The solution to $-\frac{3}{7} = -\frac{2}{5}f$ is $f = \frac{15}{14}$ .

Solve for W. -6W = 54
Solve for z: $\frac{2}{3}z = 18$