Algebra Examples

$x - \frac{1}{9} = \frac{1}{6}$

Step 1

Add $\frac{1}{9}$ to both sides of the equation.

$x = \frac{1}{6} + \frac{1}{9}$

Step 2

To write $\frac{1}{6}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$x = \frac{1}{6} \cdot \frac{3}{3} + \frac{1}{9}$

Step 3

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

$x = \frac{1}{6} \cdot \frac{3}{3} + \frac{1}{9} \cdot \frac{2}{2}$

Step 4

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

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Step 4.1

Multiply $\frac{1}{6}$ by $\frac{3}{3}$ .

$x = \frac{3}{6 \cdot 3} + \frac{1}{9} \cdot \frac{2}{2}$

Step 4.2

Multiply $6$ by $3$ .

$x = \frac{3}{18} + \frac{1}{9} \cdot \frac{2}{2}$

Step 4.3

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

$x = \frac{3}{18} + \frac{2}{9 \cdot 2}$

Step 4.4

Multiply $9$ by $2$ .

$x = \frac{3}{18} + \frac{2}{18}$

Step 5

Combine the numerators over the common denominator.

$x = \frac{3 + 2}{18}$

Step 6

Add $3$ and $2$ .

$x = \frac{5}{18}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \frac{5}{18}$

Decimal Form:

$x = 0.2\overline{7}$