Pre-Algebra Examples

$\frac{1}{2} + - \frac{1}{3}$

Step 1

Replace all occurrences of $+$ $-$ with a single $-$ . A plus sign followed by a minus sign has the same mathematical meaning as a single minus sign because $1 \cdot - 1 = - 1$

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

Step 2

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

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

Step 3

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

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

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

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

Step 4.2

Multiply $2$ by $3$ .

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

Step 4.3

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

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

Step 4.4

Multiply $3$ by $2$ .

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

Step 5

Combine the numerators over the common denominator.

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

Step 6

Subtract $2$ from $3$ .

$\frac{1}{6}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{6}$

Decimal Form:

$0.1\overline{6}$