Algebra Examples

$- \frac{5}{3} - {(\frac{1}{2})}^{3} \div \frac{6}{7} \div \frac{3}{4} \div {(- 1)}^{3}$

Step 1

Simplify each term.

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Step 1.1

Rewrite the division as a fraction.

$- \frac{5}{3} - \frac{{(\frac{1}{2})}^{3} \div \frac{6}{7} \div \frac{3}{4}}{{(- 1)}^{3}}$

Step 1.2

Multiply the numerator by the reciprocal of the denominator.

$- \frac{5}{3} - ({(\frac{1}{2})}^{3} \div \frac{6}{7} \div \frac{3}{4} \cdot \frac{1}{{(- 1)}^{3}})$

Step 1.3

Combine.

$- \frac{5}{3} - \frac{{(\frac{1}{2})}^{3} \div \frac{6}{7} \cdot 1}{\frac{3}{4} {(- 1)}^{3}}$

Step 1.4

Simplify the numerator.

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Step 1.4.1

Apply the product rule to $\frac{1}{2}$ .

$- \frac{5}{3} - \frac{\frac{1^{3}}{2^{3}} \div \frac{6}{7} \cdot 1}{\frac{3}{4} {(- 1)}^{3}}$

Step 1.4.2

One to any power is one.

$- \frac{5}{3} - \frac{\frac{1}{2^{3}} \div \frac{6}{7} \cdot 1}{\frac{3}{4} {(- 1)}^{3}}$

Step 1.4.3

Raise $2$ to the power of $3$ .

$- \frac{5}{3} - \frac{\frac{1}{8} \div \frac{6}{7} \cdot 1}{\frac{3}{4} {(- 1)}^{3}}$

Step 1.5

Multiply $\frac{1}{8} \div \frac{6}{7}$ by $1$ .

$- \frac{5}{3} - \frac{\frac{1}{8} \div \frac{6}{7}}{\frac{3}{4} {(- 1)}^{3}}$

Step 1.6

Combine $\frac{3}{4}$ and ${(- 1)}^{3}$ .

$- \frac{5}{3} - \frac{\frac{1}{8} \div \frac{6}{7}}{\frac{3 {(- 1)}^{3}}{4}}$

Step 1.7

Raise $- 1$ to the power of $3$ .

$- \frac{5}{3} - \frac{\frac{1}{8} \div \frac{6}{7}}{\frac{3 \cdot - 1}{4}}$

Step 1.8

Multiply $3$ by $- 1$ .

$- \frac{5}{3} - \frac{\frac{1}{8} \div \frac{6}{7}}{\frac{- 3}{4}}$

Step 1.9

Simplify the numerator.

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Step 1.9.1

To divide by a fraction, multiply by its reciprocal.

$- \frac{5}{3} - \frac{\frac{1}{8} \cdot \frac{7}{6}}{\frac{- 3}{4}}$

Step 1.9.2

Multiply $\frac{1}{8} \cdot \frac{7}{6}$ .

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Step 1.9.2.1

Multiply $\frac{1}{8}$ by $\frac{7}{6}$ .

$- \frac{5}{3} - \frac{\frac{7}{8 \cdot 6}}{\frac{- 3}{4}}$

Step 1.9.2.2

Multiply $8$ by $6$ .

$- \frac{5}{3} - \frac{\frac{7}{48}}{\frac{- 3}{4}}$

Step 1.10

Move the negative in front of the fraction.

$- \frac{5}{3} - \frac{\frac{7}{48}}{- \frac{3}{4}}$

Step 1.11

Multiply the numerator by the reciprocal of the denominator.

$- \frac{5}{3} - (\frac{7}{48} (- \frac{4}{3}))$

Step 1.12

Cancel the common factor of $4$ .

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Step 1.12.1

Move the leading negative in $- \frac{4}{3}$ into the numerator.

$- \frac{5}{3} - (\frac{7}{48} \cdot \frac{- 4}{3})$

Step 1.12.2

Factor $4$ out of $48$ .

$- \frac{5}{3} - (\frac{7}{4 (12)} \cdot \frac{- 4}{3})$

Step 1.12.3

Factor $4$ out of $- 4$ .

$- \frac{5}{3} - (\frac{7}{4 \cdot 12} \cdot \frac{4 \cdot - 1}{3})$

Step 1.12.4

Cancel the common factor.

$- \frac{5}{3} - (\frac{7}{4 \cdot 12} \cdot \frac{4 \cdot - 1}{3})$

Step 1.12.5

Rewrite the expression.

$- \frac{5}{3} - (\frac{7}{12} \cdot \frac{- 1}{3})$

Step 1.13

Multiply $\frac{7}{12}$ by $\frac{- 1}{3}$ .

$- \frac{5}{3} - \frac{7 \cdot - 1}{12 \cdot 3}$

Step 1.14

Multiply $7$ by $- 1$ .

$- \frac{5}{3} - \frac{- 7}{12 \cdot 3}$

Step 1.15

Multiply $12$ by $3$ .

$- \frac{5}{3} - \frac{- 7}{36}$

Step 1.16

Move the negative in front of the fraction.

$- \frac{5}{3} - - \frac{7}{36}$

Step 1.17

Multiply $- - \frac{7}{36}$ .

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Step 1.17.1

Multiply $- 1$ by $- 1$ .

$- \frac{5}{3} + 1 (\frac{7}{36})$

Step 1.17.2

Multiply $\frac{7}{36}$ by $1$ .

$- \frac{5}{3} + \frac{7}{36}$

Step 2

To write $- \frac{5}{3}$ as a fraction with a common denominator, multiply by $\frac{12}{12}$ .

$- \frac{5}{3} \cdot \frac{12}{12} + \frac{7}{36}$

Step 3

Write each expression with a common denominator of $36$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{5}{3}$ by $\frac{12}{12}$ .

$- \frac{5 \cdot 12}{3 \cdot 12} + \frac{7}{36}$

Step 3.2

Multiply $3$ by $12$ .

$- \frac{5 \cdot 12}{36} + \frac{7}{36}$

Step 4

Combine the numerators over the common denominator.

$\frac{- 5 \cdot 12 + 7}{36}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $- 5$ by $12$ .

$\frac{- 60 + 7}{36}$

Step 5.2

Add $- 60$ and $7$ .

$\frac{- 53}{36}$

Step 6

Move the negative in front of the fraction.

$- \frac{53}{36}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{53}{36}$

Decimal Form:

$- 1.47\overline{2}$

Mixed Number Form:

$- 1 \frac{17}{36}$