Basic Math Examples

$(- \frac{5}{6} - \frac{4}{5}) - (- \frac{7}{6} - 5)$

Step 1

Find the common denominator.

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Step 1.1

Multiply $\frac{5}{6}$ by $\frac{5}{5}$ .

$- (\frac{5}{6} \cdot \frac{5}{5}) - \frac{4}{5} - (- \frac{7}{6} - 5)$

Step 1.2

Multiply $\frac{5}{6}$ by $\frac{5}{5}$ .

$- \frac{5 \cdot 5}{6 \cdot 5} - \frac{4}{5} - (- \frac{7}{6} - 5)$

Step 1.3

Multiply $\frac{4}{5}$ by $\frac{6}{6}$ .

$- \frac{5 \cdot 5}{6 \cdot 5} - (\frac{4}{5} \cdot \frac{6}{6}) - (- \frac{7}{6} - 5)$

Step 1.4

Multiply $\frac{4}{5}$ by $\frac{6}{6}$ .

$- \frac{5 \cdot 5}{6 \cdot 5} - \frac{4 \cdot 6}{5 \cdot 6} - (- \frac{7}{6} - 5)$

Step 1.5

Write $- (- \frac{7}{6} - 5)$ as a fraction with denominator $1$ .

$- \frac{5 \cdot 5}{6 \cdot 5} - \frac{4 \cdot 6}{5 \cdot 6} + \frac{- (- \frac{7}{6} - 5)}{1}$

Step 1.6

Multiply $\frac{- (- \frac{7}{6} - 5)}{1}$ by $\frac{30}{30}$ .

$- \frac{5 \cdot 5}{6 \cdot 5} - \frac{4 \cdot 6}{5 \cdot 6} + \frac{- (- \frac{7}{6} - 5)}{1} \cdot \frac{30}{30}$

Step 1.7

Multiply $\frac{- (- \frac{7}{6} - 5)}{1}$ by $\frac{30}{30}$ .

$- \frac{5 \cdot 5}{6 \cdot 5} - \frac{4 \cdot 6}{5 \cdot 6} + \frac{- (- \frac{7}{6} - 5) \cdot 30}{30}$

Step 1.8

Reorder the factors of $6 \cdot 5$ .

$- \frac{5 \cdot 5}{5 \cdot 6} - \frac{4 \cdot 6}{5 \cdot 6} + \frac{- (- \frac{7}{6} - 5) \cdot 30}{30}$

Step 1.9

Multiply $5$ by $6$ .

$- \frac{5 \cdot 5}{30} - \frac{4 \cdot 6}{5 \cdot 6} + \frac{- (- \frac{7}{6} - 5) \cdot 30}{30}$

Step 1.10

Multiply $5$ by $6$ .

$- \frac{5 \cdot 5}{30} - \frac{4 \cdot 6}{30} + \frac{- (- \frac{7}{6} - 5) \cdot 30}{30}$

Step 2

Combine the numerators over the common denominator.

$\frac{- 5 \cdot 5 - 4 \cdot 6 - (- \frac{7}{6} - 5) \cdot 30}{30}$

Step 3

Simplify each term.

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Step 3.1

Multiply $- 5$ by $5$ .

$\frac{- 25 - 4 \cdot 6 - (- \frac{7}{6} - 5) \cdot 30}{30}$

Step 3.2

Multiply $- 4$ by $6$ .

$\frac{- 25 - 24 - (- \frac{7}{6} - 5) \cdot 30}{30}$

Step 3.3

To write $- 5$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{- 25 - 24 - (- \frac{7}{6} - 5 \cdot \frac{6}{6}) \cdot 30}{30}$

Step 3.4

Combine $- 5$ and $\frac{6}{6}$ .

$\frac{- 25 - 24 - (- \frac{7}{6} + \frac{- 5 \cdot 6}{6}) \cdot 30}{30}$

Step 3.5

Combine the numerators over the common denominator.

$\frac{- 25 - 24 - \frac{- 7 - 5 \cdot 6}{6} \cdot 30}{30}$

Step 3.6

Simplify the numerator.

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Step 3.6.1

Multiply $- 5$ by $6$ .

$\frac{- 25 - 24 - \frac{- 7 - 30}{6} \cdot 30}{30}$

Step 3.6.2

Subtract $30$ from $- 7$ .

$\frac{- 25 - 24 - \frac{- 37}{6} \cdot 30}{30}$

Step 3.7

Cancel the common factor of $6$ .

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Step 3.7.1

Move the leading negative in $- \frac{- 37}{6}$ into the numerator.

$\frac{- 25 - 24 + \frac{37}{6} \cdot 30}{30}$

Step 3.7.2

Factor $6$ out of $30$ .

$\frac{- 25 - 24 + \frac{37}{6} \cdot (6 (5))}{30}$

Step 3.7.3

Cancel the common factor.

$\frac{- 25 - 24 + \frac{37}{6} \cdot (6 \cdot 5)}{30}$

Step 3.7.4

Rewrite the expression.

$\frac{- 25 - 24 + 37 \cdot 5}{30}$

Step 3.8

Multiply $37$ by $5$ .

$\frac{- 25 - 24 + 185}{30}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Subtract $24$ from $- 25$ .

$\frac{- 49 + 185}{30}$

Step 4.2

Add $- 49$ and $185$ .

$\frac{136}{30}$

Step 4.3

Cancel the common factor of $136$ and $30$ .

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Step 4.3.1

Factor $2$ out of $136$ .

$\frac{2 (68)}{30}$

Step 4.3.2

Cancel the common factors.

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Step 4.3.2.1

Factor $2$ out of $30$ .

$\frac{2 \cdot 68}{2 \cdot 15}$

Step 4.3.2.2

Cancel the common factor.

$\frac{2 \cdot 68}{2 \cdot 15}$

Step 4.3.2.3

Rewrite the expression.

$\frac{68}{15}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{68}{15}$

Decimal Form:

$4.5\overline{3}$

Mixed Number Form:

$4 \frac{8}{15}$