Basic Math Examples

$- \frac{2}{3} - \frac{5}{3} - \frac{1}{6} - (- \frac{2}{3} + \frac{1}{3})$

Step 1

Combine the numerators over the common denominator.

$- (- \frac{2}{3} + \frac{1}{3}) + \frac{- 2 - 5}{3} + \frac{- 1}{6}$

Step 2

Subtract $5$ from $- 2$ .

$- (- \frac{2}{3} + \frac{1}{3}) + \frac{- 7}{3} + \frac{- 1}{6}$

Step 3

Find the common denominator.

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Step 3.1

Write $- (- \frac{2}{3} + \frac{1}{3})$ as a fraction with denominator $1$ .

$\frac{- (- \frac{2}{3} + \frac{1}{3})}{1} + \frac{- 7}{3} + \frac{- 1}{6}$

Step 3.2

Multiply $\frac{- (- \frac{2}{3} + \frac{1}{3})}{1}$ by $\frac{6}{6}$ .

$\frac{- (- \frac{2}{3} + \frac{1}{3})}{1} \cdot \frac{6}{6} + \frac{- 7}{3} + \frac{- 1}{6}$

Step 3.3

Multiply $\frac{- (- \frac{2}{3} + \frac{1}{3})}{1}$ by $\frac{6}{6}$ .

$\frac{- (- \frac{2}{3} + \frac{1}{3}) \cdot 6}{6} + \frac{- 7}{3} + \frac{- 1}{6}$

Step 3.4

Multiply $\frac{- 7}{3}$ by $\frac{2}{2}$ .

$\frac{- (- \frac{2}{3} + \frac{1}{3}) \cdot 6}{6} + \frac{- 7}{3} \cdot \frac{2}{2} + \frac{- 1}{6}$

Step 3.5

Multiply $\frac{- 7}{3}$ by $\frac{2}{2}$ .

$\frac{- (- \frac{2}{3} + \frac{1}{3}) \cdot 6}{6} + \frac{- 7 \cdot 2}{3 \cdot 2} + \frac{- 1}{6}$

Step 3.6

Reorder the factors of $3 \cdot 2$ .

$\frac{- (- \frac{2}{3} + \frac{1}{3}) \cdot 6}{6} + \frac{- 7 \cdot 2}{2 \cdot 3} + \frac{- 1}{6}$

Step 3.7

Multiply $2$ by $3$ .

$\frac{- (- \frac{2}{3} + \frac{1}{3}) \cdot 6}{6} + \frac{- 7 \cdot 2}{6} + \frac{- 1}{6}$

Step 4

Combine the numerators over the common denominator.

$\frac{- (- \frac{2}{3} + \frac{1}{3}) \cdot 6 - 7 \cdot 2 - 1}{6}$

Step 5

Simplify each term.

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Step 5.1

Combine the numerators over the common denominator.

$\frac{- \frac{- 2 + 1}{3} \cdot 6 - 7 \cdot 2 - 1}{6}$

Step 5.2

Add $- 2$ and $1$ .

$\frac{- \frac{- 1}{3} \cdot 6 - 7 \cdot 2 - 1}{6}$

Step 5.3

Cancel the common factor of $3$ .

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Step 5.3.1

Move the leading negative in $- \frac{- 1}{3}$ into the numerator.

$\frac{\frac{1}{3} \cdot 6 - 7 \cdot 2 - 1}{6}$

Step 5.3.2

Factor $3$ out of $6$ .

$\frac{\frac{1}{3} \cdot (3 (2)) - 7 \cdot 2 - 1}{6}$

Step 5.3.3

Cancel the common factor.

$\frac{\frac{1}{3} \cdot (3 \cdot 2) - 7 \cdot 2 - 1}{6}$

Step 5.3.4

Rewrite the expression.

$\frac{2 - 7 \cdot 2 - 1}{6}$

Step 5.4

Multiply $- 7$ by $2$ .

$\frac{2 - 14 - 1}{6}$

Step 6

Simplify the expression.

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Step 6.1

Subtract $14$ from $2$ .

$\frac{- 12 - 1}{6}$

Step 6.2

Subtract $1$ from $- 12$ .

$\frac{- 13}{6}$

Step 6.3

Move the negative in front of the fraction.

$- \frac{13}{6}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{13}{6}$

Decimal Form:

$- 2.1\overline{6}$

Mixed Number Form:

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