Solve for b b/9-1/2=5/18

$\frac{b}{9} - \frac{1}{2} = \frac{5}{18}$

Step 1

Move all terms not containing $b$ to the right side of the equation.

Add $\frac{1}{2}$ to both sides of the equation.

$\frac{b}{9} = \frac{5}{18} + \frac{1}{2}$

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{b}{9} = \frac{5}{18} + \frac{1}{2} \cdot \frac{9}{9}$

Write each expression with a common denominator of $18$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{2}$ by $\frac{9}{9}$ .

$\frac{b}{9} = \frac{5}{18} + \frac{9}{2 \cdot 9}$

Multiply $2$ by $9$ .

$\frac{b}{9} = \frac{5}{18} + \frac{9}{18}$

Combine the numerators over the common denominator.

$\frac{b}{9} = \frac{5 + 9}{18}$

Add $5$ and $9$ .

$\frac{b}{9} = \frac{14}{18}$

Cancel the common factor of $14$ and $18$ .

Factor $2$ out of $14$ .

$\frac{b}{9} = \frac{2 (7)}{18}$

Cancel the common factors.

Factor $2$ out of $18$ .

$\frac{b}{9} = \frac{2 \cdot 7}{2 \cdot 9}$

Cancel the common factor.

$\frac{b}{9} = \frac{2 \cdot 7}{2 \cdot 9}$

Rewrite the expression.

$\frac{b}{9} = \frac{7}{9}$

Step 2

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$b = 7$