Evaluate -(-1/5+(-1/7+1/3-(-1/5-1/2)))-2

$- (- \frac{1}{5} + (- \frac{1}{7} + \frac{1}{3} - (- \frac{1}{5} - \frac{1}{2}))) - 2$

Step 1

Remove parentheses.

$- (- \frac{1}{5} - \frac{1}{7} + \frac{1}{3} - (- \frac{1}{5} - \frac{1}{2})) - 2$

Step 2

Simplify each term.

Find the common denominator.

Multiply $\frac{1}{5}$ by $\frac{21}{21}$ .

$- (- (\frac{1}{5} \cdot \frac{21}{21}) - \frac{1}{7} + \frac{1}{3} - (- \frac{1}{5} - \frac{1}{2})) - 2$

Multiply $\frac{1}{5}$ by $\frac{21}{21}$ .

$- (- \frac{21}{5 \cdot 21} - \frac{1}{7} + \frac{1}{3} - (- \frac{1}{5} - \frac{1}{2})) - 2$

Multiply $\frac{1}{7}$ by $\frac{15}{15}$ .

$- (- \frac{21}{5 \cdot 21} - (\frac{1}{7} \cdot \frac{15}{15}) + \frac{1}{3} - (- \frac{1}{5} - \frac{1}{2})) - 2$

Multiply $\frac{1}{7}$ by $\frac{15}{15}$ .

$- (- \frac{21}{5 \cdot 21} - \frac{15}{7 \cdot 15} + \frac{1}{3} - (- \frac{1}{5} - \frac{1}{2})) - 2$

Multiply $\frac{1}{3}$ by $\frac{35}{35}$ .

$- (- \frac{21}{5 \cdot 21} - \frac{15}{7 \cdot 15} + \frac{1}{3} \cdot \frac{35}{35} - (- \frac{1}{5} - \frac{1}{2})) - 2$

Multiply $\frac{1}{3}$ by $\frac{35}{35}$ .

$- (- \frac{21}{5 \cdot 21} - \frac{15}{7 \cdot 15} + \frac{35}{3 \cdot 35} - (- \frac{1}{5} - \frac{1}{2})) - 2$

Write $- (- \frac{1}{5} - \frac{1}{2})$ as a fraction with denominator $1$ .

$- (- \frac{21}{5 \cdot 21} - \frac{15}{7 \cdot 15} + \frac{35}{3 \cdot 35} + \frac{- (- \frac{1}{5} - \frac{1}{2})}{1}) - 2$

Multiply $\frac{- (- \frac{1}{5} - \frac{1}{2})}{1}$ by $\frac{105}{105}$ .

$- (- \frac{21}{5 \cdot 21} - \frac{15}{7 \cdot 15} + \frac{35}{3 \cdot 35} + \frac{- (- \frac{1}{5} - \frac{1}{2})}{1} \cdot \frac{105}{105}) - 2$

Multiply $\frac{- (- \frac{1}{5} - \frac{1}{2})}{1}$ by $\frac{105}{105}$ .

$- (- \frac{21}{5 \cdot 21} - \frac{15}{7 \cdot 15} + \frac{35}{3 \cdot 35} + \frac{- (- \frac{1}{5} - \frac{1}{2}) \cdot 105}{105}) - 2$

Multiply $5$ by $21$ .

$- (- \frac{21}{105} - \frac{15}{7 \cdot 15} + \frac{35}{3 \cdot 35} + \frac{- (- \frac{1}{5} - \frac{1}{2}) \cdot 105}{105}) - 2$

Multiply $7$ by $15$ .

$- (- \frac{21}{105} - \frac{15}{105} + \frac{35}{3 \cdot 35} + \frac{- (- \frac{1}{5} - \frac{1}{2}) \cdot 105}{105}) - 2$

Multiply $3$ by $35$ .

$- (- \frac{21}{105} - \frac{15}{105} + \frac{35}{105} + \frac{- (- \frac{1}{5} - \frac{1}{2}) \cdot 105}{105}) - 2$

Combine the numerators over the common denominator.

$- \frac{- 21 - 15 + 35 - (- \frac{1}{5} - \frac{1}{2}) \cdot 105}{105} - 2$

Simplify each term.

To write $- \frac{1}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{- 21 - 15 + 35 - (- \frac{1}{5} \cdot \frac{2}{2} - \frac{1}{2}) \cdot 105}{105} - 2$

To write $- \frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{- 21 - 15 + 35 - (- \frac{1}{5} \cdot \frac{2}{2} - \frac{1}{2} \cdot \frac{5}{5}) \cdot 105}{105} - 2$

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{5}$ by $\frac{2}{2}$ .

$- \frac{- 21 - 15 + 35 - (- \frac{2}{5 \cdot 2} - \frac{1}{2} \cdot \frac{5}{5}) \cdot 105}{105} - 2$

Multiply $5$ by $2$ .

$- \frac{- 21 - 15 + 35 - (- \frac{2}{10} - \frac{1}{2} \cdot \frac{5}{5}) \cdot 105}{105} - 2$

Multiply $\frac{1}{2}$ by $\frac{5}{5}$ .

$- \frac{- 21 - 15 + 35 - (- \frac{2}{10} - \frac{5}{2 \cdot 5}) \cdot 105}{105} - 2$

Multiply $2$ by $5$ .

$- \frac{- 21 - 15 + 35 - (- \frac{2}{10} - \frac{5}{10}) \cdot 105}{105} - 2$

Combine the numerators over the common denominator.

$- \frac{- 21 - 15 + 35 - \frac{- 2 - 5}{10} \cdot 105}{105} - 2$

Subtract $5$ from $- 2$ .

$- \frac{- 21 - 15 + 35 - \frac{- 7}{10} \cdot 105}{105} - 2$

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{- 7}{10}$ into the numerator.

$- \frac{- 21 - 15 + 35 + \frac{7}{10} \cdot 105}{105} - 2$

Factor $5$ out of $10$ .

$- \frac{- 21 - 15 + 35 + \frac{7}{5 (2)} \cdot 105}{105} - 2$

Factor $5$ out of $105$ .

$- \frac{- 21 - 15 + 35 + \frac{7}{5 \cdot 2} \cdot (5 \cdot 21)}{105} - 2$

Cancel the common factor.

$- \frac{- 21 - 15 + 35 + \frac{7}{5 \cdot 2} \cdot (5 \cdot 21)}{105} - 2$

Rewrite the expression.

$- \frac{- 21 - 15 + 35 + \frac{7}{2} \cdot 21}{105} - 2$

Combine $\frac{7}{2}$ and $21$ .

$- \frac{- 21 - 15 + 35 + \frac{7 \cdot 21}{2}}{105} - 2$

Multiply $7$ by $21$ .

$- \frac{- 21 - 15 + 35 + \frac{147}{2}}{105} - 2$

Find the common denominator.

Write $- 21$ as a fraction with denominator $1$ .

$- \frac{\frac{- 21}{1} - 15 + 35 + \frac{147}{2}}{105} - 2$

Multiply $\frac{- 21}{1}$ by $\frac{2}{2}$ .

$- \frac{\frac{- 21}{1} \cdot \frac{2}{2} - 15 + 35 + \frac{147}{2}}{105} - 2$

Multiply $\frac{- 21}{1}$ by $\frac{2}{2}$ .

$- \frac{\frac{- 21 \cdot 2}{2} - 15 + 35 + \frac{147}{2}}{105} - 2$

Write $- 15$ as a fraction with denominator $1$ .

$- \frac{\frac{- 21 \cdot 2}{2} + \frac{- 15}{1} + 35 + \frac{147}{2}}{105} - 2$

Multiply $\frac{- 15}{1}$ by $\frac{2}{2}$ .

$- \frac{\frac{- 21 \cdot 2}{2} + \frac{- 15}{1} \cdot \frac{2}{2} + 35 + \frac{147}{2}}{105} - 2$

Multiply $\frac{- 15}{1}$ by $\frac{2}{2}$ .

$- \frac{\frac{- 21 \cdot 2}{2} + \frac{- 15 \cdot 2}{2} + 35 + \frac{147}{2}}{105} - 2$

Write $35$ as a fraction with denominator $1$ .

$- \frac{\frac{- 21 \cdot 2}{2} + \frac{- 15 \cdot 2}{2} + \frac{35}{1} + \frac{147}{2}}{105} - 2$

Multiply $\frac{35}{1}$ by $\frac{2}{2}$ .

$- \frac{\frac{- 21 \cdot 2}{2} + \frac{- 15 \cdot 2}{2} + \frac{35}{1} \cdot \frac{2}{2} + \frac{147}{2}}{105} - 2$

Multiply $\frac{35}{1}$ by $\frac{2}{2}$ .

$- \frac{\frac{- 21 \cdot 2}{2} + \frac{- 15 \cdot 2}{2} + \frac{35 \cdot 2}{2} + \frac{147}{2}}{105} - 2$

Combine the numerators over the common denominator.

$- \frac{\frac{- 21 \cdot 2 - 15 \cdot 2 + 35 \cdot 2 + 147}{2}}{105} - 2$

Simplify each term.

Multiply $- 21$ by $2$ .

$- \frac{\frac{- 42 - 15 \cdot 2 + 35 \cdot 2 + 147}{2}}{105} - 2$

Multiply $- 15$ by $2$ .

$- \frac{\frac{- 42 - 30 + 35 \cdot 2 + 147}{2}}{105} - 2$

Multiply $35$ by $2$ .

$- \frac{\frac{- 42 - 30 + 70 + 147}{2}}{105} - 2$

Subtract $30$ from $- 42$ .

$- \frac{\frac{- 72 + 70 + 147}{2}}{105} - 2$

Add $- 72$ and $70$ .

$- \frac{\frac{- 2 + 147}{2}}{105} - 2$

Add $- 2$ and $147$ .

$- \frac{\frac{145}{2}}{105} - 2$

Multiply the numerator by the reciprocal of the denominator.

$- (\frac{145}{2} \cdot \frac{1}{105}) - 2$

Cancel the common factor of $5$ .

Factor $5$ out of $145$ .

$- (\frac{5 (29)}{2} \cdot \frac{1}{105}) - 2$

Factor $5$ out of $105$ .

$- (\frac{5 \cdot 29}{2} \cdot \frac{1}{5 \cdot 21}) - 2$

Cancel the common factor.

$- (\frac{5 \cdot 29}{2} \cdot \frac{1}{5 \cdot 21}) - 2$

Rewrite the expression.

$- (\frac{29}{2} \cdot \frac{1}{21}) - 2$

Multiply $\frac{29}{2}$ by $\frac{1}{21}$ .

$- \frac{29}{2 \cdot 21} - 2$

Multiply $2$ by $21$ .

$- \frac{29}{42} - 2$

Step 3

To write $- 2$ as a fraction with a common denominator, multiply by $\frac{42}{42}$ .

$- \frac{29}{42} - 2 \cdot \frac{42}{42}$

Step 4

Combine $- 2$ and $\frac{42}{42}$ .

$- \frac{29}{42} + \frac{- 2 \cdot 42}{42}$

Step 5

Combine the numerators over the common denominator.

$\frac{- 29 - 2 \cdot 42}{42}$

Step 6

Simplify the numerator.

Multiply $- 2$ by $42$ .

$\frac{- 29 - 84}{42}$

Subtract $84$ from $- 29$ .

$\frac{- 113}{42}$

Step 7

Move the negative in front of the fraction.

$- \frac{113}{42}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- \frac{113}{42}$

Decimal Form:

$- 2.69047619 \dots$

Mixed Number Form:

$- 2 \frac{29}{42}$

Evaluate -(-1/5+(-1/7+1/3-(-1/5-1/2)))-2

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