Algebra Examples

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

Step 1

Find the common denominator.

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

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

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

Step 1.4

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

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

Step 1.5

Write $- 6$ as a fraction with denominator $1$ .

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

Step 1.6

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

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

Step 1.7

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

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

Step 1.8

Reorder the factors of $3 \cdot 2$ .

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

Step 1.9

Multiply $2$ by $3$ .

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

Step 1.10

Multiply $2$ by $3$ .

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

Step 2

Combine the numerators over the common denominator.

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

Step 3

Simplify the expression.

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Step 3.1

Multiply $- 6$ by $6$ .

$\frac{2 - 3 - 36}{6}$

Step 3.2

Subtract $3$ from $2$ .

$\frac{- 1 - 36}{6}$

Step 3.3

Subtract $36$ from $- 1$ .

$\frac{- 37}{6}$

Step 3.4

Move the negative in front of the fraction.

$- \frac{37}{6}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- \frac{37}{6}$

Decimal Form:

$- 6.1\overline{6}$

Mixed Number Form:

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