Algebra Examples

$- (- \frac{7}{10} - \frac{3}{5}) - (\frac{1}{6} + \frac{2}{3}) - (- \frac{2}{15})$

Step 1

Simplify each term.

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Step 1.1

To write $- \frac{3}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- (- \frac{7}{10} - \frac{3}{5} \cdot \frac{2}{2}) - (\frac{1}{6} + \frac{2}{3}) - (- \frac{2}{15})$

Step 1.2

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

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Step 1.2.1

Multiply $\frac{3}{5}$ by $\frac{2}{2}$ .

$- (- \frac{7}{10} - \frac{3 \cdot 2}{5 \cdot 2}) - (\frac{1}{6} + \frac{2}{3}) - (- \frac{2}{15})$

Step 1.2.2

Multiply $5$ by $2$ .

$- (- \frac{7}{10} - \frac{3 \cdot 2}{10}) - (\frac{1}{6} + \frac{2}{3}) - (- \frac{2}{15})$

Step 1.3

Combine the numerators over the common denominator.

$- \frac{- 7 - 3 \cdot 2}{10} - (\frac{1}{6} + \frac{2}{3}) - (- \frac{2}{15})$

Step 1.4

Simplify the numerator.

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Step 1.4.1

Multiply $- 3$ by $2$ .

$- \frac{- 7 - 6}{10} - (\frac{1}{6} + \frac{2}{3}) - (- \frac{2}{15})$

Step 1.4.2

Subtract $6$ from $- 7$ .

$- \frac{- 13}{10} - (\frac{1}{6} + \frac{2}{3}) - (- \frac{2}{15})$

Step 1.5

Move the negative in front of the fraction.

$- - \frac{13}{10} - (\frac{1}{6} + \frac{2}{3}) - (- \frac{2}{15})$

Step 1.6

Multiply $- - \frac{13}{10}$ .

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Step 1.6.1

Multiply $- 1$ by $- 1$ .

$1 (\frac{13}{10}) - (\frac{1}{6} + \frac{2}{3}) - (- \frac{2}{15})$

Step 1.6.2

Multiply $\frac{13}{10}$ by $1$ .

$\frac{13}{10} - (\frac{1}{6} + \frac{2}{3}) - (- \frac{2}{15})$

Step 1.7

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

$\frac{13}{10} - (\frac{1}{6} + \frac{2}{3} \cdot \frac{2}{2}) - (- \frac{2}{15})$

Step 1.8

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.8.1

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

$\frac{13}{10} - (\frac{1}{6} + \frac{2 \cdot 2}{3 \cdot 2}) - (- \frac{2}{15})$

Step 1.8.2

Multiply $3$ by $2$ .

$\frac{13}{10} - (\frac{1}{6} + \frac{2 \cdot 2}{6}) - (- \frac{2}{15})$

Step 1.9

Combine the numerators over the common denominator.

$\frac{13}{10} - \frac{1 + 2 \cdot 2}{6} - (- \frac{2}{15})$

Step 1.10

Simplify the numerator.

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Step 1.10.1

Multiply $2$ by $2$ .

$\frac{13}{10} - \frac{1 + 4}{6} - (- \frac{2}{15})$

Step 1.10.2

Add $1$ and $4$ .

$\frac{13}{10} - \frac{5}{6} - (- \frac{2}{15})$

Step 1.11

Multiply $- (- \frac{2}{15})$ .

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Step 1.11.1

Multiply $- 1$ by $- 1$ .

$\frac{13}{10} - \frac{5}{6} + 1 (\frac{2}{15})$

Step 1.11.2

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

$\frac{13}{10} - \frac{5}{6} + \frac{2}{15}$

Step 2

Find the common denominator.

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Step 2.1

Multiply $\frac{13}{10}$ by $\frac{3}{3}$ .

$\frac{13}{10} \cdot \frac{3}{3} - \frac{5}{6} + \frac{2}{15}$

Step 2.2

Multiply $\frac{13}{10}$ by $\frac{3}{3}$ .

$\frac{13 \cdot 3}{10 \cdot 3} - \frac{5}{6} + \frac{2}{15}$

Step 2.3

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

$\frac{13 \cdot 3}{10 \cdot 3} - (\frac{5}{6} \cdot \frac{5}{5}) + \frac{2}{15}$

Step 2.4

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

$\frac{13 \cdot 3}{10 \cdot 3} - \frac{5 \cdot 5}{6 \cdot 5} + \frac{2}{15}$

Step 2.5

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

$\frac{13 \cdot 3}{10 \cdot 3} - \frac{5 \cdot 5}{6 \cdot 5} + \frac{2}{15} \cdot \frac{2}{2}$

Step 2.6

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

$\frac{13 \cdot 3}{10 \cdot 3} - \frac{5 \cdot 5}{6 \cdot 5} + \frac{2 \cdot 2}{15 \cdot 2}$

Step 2.7

Reorder the factors of $10 \cdot 3$ .

$\frac{13 \cdot 3}{3 \cdot 10} - \frac{5 \cdot 5}{6 \cdot 5} + \frac{2 \cdot 2}{15 \cdot 2}$

Step 2.8

Multiply $3$ by $10$ .

$\frac{13 \cdot 3}{30} - \frac{5 \cdot 5}{6 \cdot 5} + \frac{2 \cdot 2}{15 \cdot 2}$

Step 2.9

Reorder the factors of $6 \cdot 5$ .

$\frac{13 \cdot 3}{30} - \frac{5 \cdot 5}{5 \cdot 6} + \frac{2 \cdot 2}{15 \cdot 2}$

Step 2.10

Multiply $5$ by $6$ .

$\frac{13 \cdot 3}{30} - \frac{5 \cdot 5}{30} + \frac{2 \cdot 2}{15 \cdot 2}$

Step 2.11

Reorder the factors of $15 \cdot 2$ .

$\frac{13 \cdot 3}{30} - \frac{5 \cdot 5}{30} + \frac{2 \cdot 2}{2 \cdot 15}$

Step 2.12

Multiply $2$ by $15$ .

$\frac{13 \cdot 3}{30} - \frac{5 \cdot 5}{30} + \frac{2 \cdot 2}{30}$

Step 3

Combine the numerators over the common denominator.

$\frac{13 \cdot 3 - 5 \cdot 5 + 2 \cdot 2}{30}$

Step 4

Simplify each term.

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Step 4.1

Multiply $13$ by $3$ .

$\frac{39 - 5 \cdot 5 + 2 \cdot 2}{30}$

Step 4.2

Multiply $- 5$ by $5$ .

$\frac{39 - 25 + 2 \cdot 2}{30}$

Step 4.3

Multiply $2$ by $2$ .

$\frac{39 - 25 + 4}{30}$

Step 5

Reduce the expression by cancelling the common factors.

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Step 5.1

Subtract $25$ from $39$ .

$\frac{14 + 4}{30}$

Step 5.2

Add $14$ and $4$ .

$\frac{18}{30}$

Step 5.3

Cancel the common factor of $18$ and $30$ .

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Step 5.3.1

Factor $6$ out of $18$ .

$\frac{6 (3)}{30}$

Step 5.3.2

Cancel the common factors.

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Step 5.3.2.1

Factor $6$ out of $30$ .

$\frac{6 \cdot 3}{6 \cdot 5}$

Step 5.3.2.2

Cancel the common factor.

$\frac{6 \cdot 3}{6 \cdot 5}$

Step 5.3.2.3

Rewrite the expression.

$\frac{3}{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{5}$

Decimal Form:

$0.6$