Pre-Algebra Examples

$x + \frac{1}{2} = \frac{1}{3}$

Step 1

Subtract $\frac{1}{2}$ from both sides of the equation.

$x = \frac{1}{3} - \frac{1}{2}$

Step 2

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$x = \frac{1}{3} \cdot \frac{2}{2} - \frac{1}{2}$

Step 3

To write $- \frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$x = \frac{1}{3} \cdot \frac{2}{2} - \frac{1}{2} \cdot \frac{3}{3}$

Step 4

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{1}{3}$ by $\frac{2}{2}$ .

$x = \frac{2}{3 \cdot 2} - \frac{1}{2} \cdot \frac{3}{3}$

Step 4.2

Multiply $3$ by $2$ .

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

Step 4.3

Multiply $\frac{1}{2}$ by $\frac{3}{3}$ .

$x = \frac{2}{6} - \frac{3}{2 \cdot 3}$

Step 4.4

Multiply $2$ by $3$ .

$x = \frac{2}{6} - \frac{3}{6}$

Step 5

Combine the numerators over the common denominator.

$x = \frac{2 - 3}{6}$

Step 6

Subtract $3$ from $2$ .

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

Step 7

Move the negative in front of the fraction.

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

Step 8

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = - 0.1\overline{6}$