Algebra Examples

$- (\frac{4}{5} - \frac{2}{3} (\frac{4}{5} + \frac{1}{2})) \div \frac{1}{5}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$- (\frac{4}{5} - \frac{2}{3} \cdot (\frac{4}{5} + \frac{1}{2})) \cdot 5$

Step 2

Simplify each term.

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Step 2.1

To write $\frac{4}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- (\frac{4}{5} - \frac{2}{3} \cdot (\frac{4}{5} \cdot \frac{2}{2} + \frac{1}{2})) \cdot 5$

Step 2.2

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

$- (\frac{4}{5} - \frac{2}{3} \cdot (\frac{4}{5} \cdot \frac{2}{2} + \frac{1}{2} \cdot \frac{5}{5})) \cdot 5$

Step 2.3

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

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Step 2.3.1

Multiply $\frac{4}{5}$ by $\frac{2}{2}$ .

$- (\frac{4}{5} - \frac{2}{3} \cdot (\frac{4 \cdot 2}{5 \cdot 2} + \frac{1}{2} \cdot \frac{5}{5})) \cdot 5$

Step 2.3.2

Multiply $5$ by $2$ .

$- (\frac{4}{5} - \frac{2}{3} \cdot (\frac{4 \cdot 2}{10} + \frac{1}{2} \cdot \frac{5}{5})) \cdot 5$

Step 2.3.3

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

$- (\frac{4}{5} - \frac{2}{3} \cdot (\frac{4 \cdot 2}{10} + \frac{5}{2 \cdot 5})) \cdot 5$

Step 2.3.4

Multiply $2$ by $5$ .

$- (\frac{4}{5} - \frac{2}{3} \cdot (\frac{4 \cdot 2}{10} + \frac{5}{10})) \cdot 5$

Step 2.4

Combine the numerators over the common denominator.

$- (\frac{4}{5} - \frac{2}{3} \cdot \frac{4 \cdot 2 + 5}{10}) \cdot 5$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $4$ by $2$ .

$- (\frac{4}{5} - \frac{2}{3} \cdot \frac{8 + 5}{10}) \cdot 5$

Step 2.5.2

Add $8$ and $5$ .

$- (\frac{4}{5} - \frac{2}{3} \cdot \frac{13}{10}) \cdot 5$

Step 2.6

Cancel the common factor of $2$ .

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Step 2.6.1

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$- (\frac{4}{5} + \frac{- 2}{3} \cdot \frac{13}{10}) \cdot 5$

Step 2.6.2

Factor $2$ out of $- 2$ .

$- (\frac{4}{5} + \frac{2 (- 1)}{3} \cdot \frac{13}{10}) \cdot 5$

Step 2.6.3

Factor $2$ out of $10$ .

$- (\frac{4}{5} + \frac{2 \cdot - 1}{3} \cdot \frac{13}{2 \cdot 5}) \cdot 5$

Step 2.6.4

Cancel the common factor.

$- (\frac{4}{5} + \frac{2 \cdot - 1}{3} \cdot \frac{13}{2 \cdot 5}) \cdot 5$

Step 2.6.5

Rewrite the expression.

$- (\frac{4}{5} + \frac{- 1}{3} \cdot \frac{13}{5}) \cdot 5$

Step 2.7

Multiply $\frac{- 1}{3}$ by $\frac{13}{5}$ .

$- (\frac{4}{5} + \frac{- 1 \cdot 13}{3 \cdot 5}) \cdot 5$

Step 2.8

Multiply $- 1$ by $13$ .

$- (\frac{4}{5} + \frac{- 13}{3 \cdot 5}) \cdot 5$

Step 2.9

Multiply $3$ by $5$ .

$- (\frac{4}{5} + \frac{- 13}{15}) \cdot 5$

Step 2.10

Move the negative in front of the fraction.

$- (\frac{4}{5} - \frac{13}{15}) \cdot 5$

Step 3

To write $\frac{4}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- (\frac{4}{5} \cdot \frac{3}{3} - \frac{13}{15}) \cdot 5$

Step 4

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{4}{5}$ by $\frac{3}{3}$ .

$- (\frac{4 \cdot 3}{5 \cdot 3} - \frac{13}{15}) \cdot 5$

Step 4.2

Multiply $5$ by $3$ .

$- (\frac{4 \cdot 3}{15} - \frac{13}{15}) \cdot 5$

Step 5

Combine the numerators over the common denominator.

$- \frac{4 \cdot 3 - 13}{15} \cdot 5$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $4$ by $3$ .

$- \frac{12 - 13}{15} \cdot 5$

Step 6.2

Subtract $13$ from $12$ .

$- \frac{- 1}{15} \cdot 5$

Step 7

Cancel the common factor of $5$ .

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Step 7.1

Move the leading negative in $- \frac{- 1}{15}$ into the numerator.

$\frac{1}{15} \cdot 5$

Step 7.2

Factor $5$ out of $15$ .

$\frac{1}{5 (3)} \cdot 5$

Step 7.3

Cancel the common factor.

$\frac{1}{5 \cdot 3} \cdot 5$

Step 7.4

Rewrite the expression.

$\frac{1}{3}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{3}$

Decimal Form:

$0.\overline{3}$