Basic Math Examples

$\frac{\frac{{(2 - \frac{1}{5})}^{2}}{{(3 - \frac{2}{9})}^{- 1}}}{\frac{{(\frac{6}{7} - \frac{5}{4} - \frac{\frac{2}{7}}{\frac{1}{2}})}^{3}}{\frac{1}{2} - \frac{1}{3} \cdot \frac{\frac{1}{4}}{\frac{1}{5}}}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{{(2 - \frac{1}{5})}^{2}}{{(3 - \frac{2}{9})}^{- 1}} \cdot \frac{\frac{1}{2} - \frac{1}{3} \cdot \frac{\frac{1}{4}}{\frac{1}{5}}}{{(\frac{6}{7} - \frac{5}{4} - \frac{\frac{2}{7}}{\frac{1}{2}})}^{3}}$

Step 2

Move ${(3 - \frac{2}{9})}^{- 1}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(2 - \frac{1}{5})}^{2} (3 - \frac{2}{9}) \frac{\frac{1}{2} - \frac{1}{3} \cdot \frac{\frac{1}{4}}{\frac{1}{5}}}{{(\frac{6}{7} - \frac{5}{4} - \frac{\frac{2}{7}}{\frac{1}{2}})}^{3}}$

Step 3

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

${(2 \cdot \frac{5}{5} - \frac{1}{5})}^{2} (3 - \frac{2}{9}) \frac{\frac{1}{2} - \frac{1}{3} \cdot \frac{\frac{1}{4}}{\frac{1}{5}}}{{(\frac{6}{7} - \frac{5}{4} - \frac{\frac{2}{7}}{\frac{1}{2}})}^{3}}$

Step 4

Combine $2$ and $\frac{5}{5}$ .

${(\frac{2 \cdot 5}{5} - \frac{1}{5})}^{2} (3 - \frac{2}{9}) \frac{\frac{1}{2} - \frac{1}{3} \cdot \frac{\frac{1}{4}}{\frac{1}{5}}}{{(\frac{6}{7} - \frac{5}{4} - \frac{\frac{2}{7}}{\frac{1}{2}})}^{3}}$

Step 5

Combine the numerators over the common denominator.

${(\frac{2 \cdot 5 - 1}{5})}^{2} (3 - \frac{2}{9}) \frac{\frac{1}{2} - \frac{1}{3} \cdot \frac{\frac{1}{4}}{\frac{1}{5}}}{{(\frac{6}{7} - \frac{5}{4} - \frac{\frac{2}{7}}{\frac{1}{2}})}^{3}}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $2$ by $5$ .

${(\frac{10 - 1}{5})}^{2} (3 - \frac{2}{9}) \frac{\frac{1}{2} - \frac{1}{3} \cdot \frac{\frac{1}{4}}{\frac{1}{5}}}{{(\frac{6}{7} - \frac{5}{4} - \frac{\frac{2}{7}}{\frac{1}{2}})}^{3}}$

Step 6.2

Subtract $1$ from $10$ .

${(\frac{9}{5})}^{2} (3 - \frac{2}{9}) \frac{\frac{1}{2} - \frac{1}{3} \cdot \frac{\frac{1}{4}}{\frac{1}{5}}}{{(\frac{6}{7} - \frac{5}{4} - \frac{\frac{2}{7}}{\frac{1}{2}})}^{3}}$

Step 7

Apply the product rule to $\frac{9}{5}$ .

$\frac{9^{2}}{5^{2}} (3 - \frac{2}{9}) \frac{\frac{1}{2} - \frac{1}{3} \cdot \frac{\frac{1}{4}}{\frac{1}{5}}}{{(\frac{6}{7} - \frac{5}{4} - \frac{\frac{2}{7}}{\frac{1}{2}})}^{3}}$

Step 8

Raise $9$ to the power of $2$ .

$\frac{81}{5^{2}} (3 - \frac{2}{9}) \frac{\frac{1}{2} - \frac{1}{3} \cdot \frac{\frac{1}{4}}{\frac{1}{5}}}{{(\frac{6}{7} - \frac{5}{4} - \frac{\frac{2}{7}}{\frac{1}{2}})}^{3}}$

Step 9

Raise $5$ to the power of $2$ .

$\frac{81}{25} (3 - \frac{2}{9}) \frac{\frac{1}{2} - \frac{1}{3} \cdot \frac{\frac{1}{4}}{\frac{1}{5}}}{{(\frac{6}{7} - \frac{5}{4} - \frac{\frac{2}{7}}{\frac{1}{2}})}^{3}}$

Step 10

To write $3$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{81}{25} (3 \cdot \frac{9}{9} - \frac{2}{9}) \frac{\frac{1}{2} - \frac{1}{3} \cdot \frac{\frac{1}{4}}{\frac{1}{5}}}{{(\frac{6}{7} - \frac{5}{4} - \frac{\frac{2}{7}}{\frac{1}{2}})}^{3}}$

Step 11

Combine $3$ and $\frac{9}{9}$ .

$\frac{81}{25} (\frac{3 \cdot 9}{9} - \frac{2}{9}) \frac{\frac{1}{2} - \frac{1}{3} \cdot \frac{\frac{1}{4}}{\frac{1}{5}}}{{(\frac{6}{7} - \frac{5}{4} - \frac{\frac{2}{7}}{\frac{1}{2}})}^{3}}$

Step 12

Combine the numerators over the common denominator.

$\frac{81}{25} \cdot \frac{3 \cdot 9 - 2}{9} \frac{\frac{1}{2} - \frac{1}{3} \cdot \frac{\frac{1}{4}}{\frac{1}{5}}}{{(\frac{6}{7} - \frac{5}{4} - \frac{\frac{2}{7}}{\frac{1}{2}})}^{3}}$

Step 13

Simplify the numerator.

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Step 13.1

Multiply $3$ by $9$ .

$\frac{81}{25} \cdot \frac{27 - 2}{9} \frac{\frac{1}{2} - \frac{1}{3} \cdot \frac{\frac{1}{4}}{\frac{1}{5}}}{{(\frac{6}{7} - \frac{5}{4} - \frac{\frac{2}{7}}{\frac{1}{2}})}^{3}}$

Step 13.2

Subtract $2$ from $27$ .

$\frac{81}{25} \cdot \frac{25}{9} \frac{\frac{1}{2} - \frac{1}{3} \cdot \frac{\frac{1}{4}}{\frac{1}{5}}}{{(\frac{6}{7} - \frac{5}{4} - \frac{\frac{2}{7}}{\frac{1}{2}})}^{3}}$

Step 14

Reduce the expression by cancelling the common factors.

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Step 14.1

Cancel the common factor of $9$ .

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Step 14.1.1

Factor $9$ out of $81$ .

$\frac{9 (9)}{25} \cdot \frac{25}{9} \frac{\frac{1}{2} - \frac{1}{3} \cdot \frac{\frac{1}{4}}{\frac{1}{5}}}{{(\frac{6}{7} - \frac{5}{4} - \frac{\frac{2}{7}}{\frac{1}{2}})}^{3}}$

Step 14.1.2

Cancel the common factor.

$\frac{9 \cdot 9}{25} \cdot \frac{25}{9} \frac{\frac{1}{2} - \frac{1}{3} \cdot \frac{\frac{1}{4}}{\frac{1}{5}}}{{(\frac{6}{7} - \frac{5}{4} - \frac{\frac{2}{7}}{\frac{1}{2}})}^{3}}$

Step 14.1.3

Rewrite the expression.

$\frac{9}{25} \cdot 25 \frac{\frac{1}{2} - \frac{1}{3} \cdot \frac{\frac{1}{4}}{\frac{1}{5}}}{{(\frac{6}{7} - \frac{5}{4} - \frac{\frac{2}{7}}{\frac{1}{2}})}^{3}}$

Step 14.2

Cancel the common factor of $25$ .

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Step 14.2.1

Cancel the common factor.

$\frac{9}{25} \cdot 25 \frac{\frac{1}{2} - \frac{1}{3} \cdot \frac{\frac{1}{4}}{\frac{1}{5}}}{{(\frac{6}{7} - \frac{5}{4} - \frac{\frac{2}{7}}{\frac{1}{2}})}^{3}}$

Step 14.2.2

Rewrite the expression.

$9 \frac{\frac{1}{2} - \frac{1}{3} \cdot \frac{\frac{1}{4}}{\frac{1}{5}}}{{(\frac{6}{7} - \frac{5}{4} - \frac{\frac{2}{7}}{\frac{1}{2}})}^{3}}$

Step 15

Simplify the numerator.

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Step 15.1

Multiply the numerator by the reciprocal of the denominator.

$9 \frac{\frac{1}{2} - \frac{1}{3} \cdot (\frac{1}{4} \cdot 5)}{{(\frac{6}{7} - \frac{5}{4} - \frac{\frac{2}{7}}{\frac{1}{2}})}^{3}}$

Step 15.2

Combine $\frac{1}{4}$ and $5$ .

$9 \frac{\frac{1}{2} - \frac{1}{3} \cdot \frac{5}{4}}{{(\frac{6}{7} - \frac{5}{4} - \frac{\frac{2}{7}}{\frac{1}{2}})}^{3}}$

Step 15.3

Multiply $- \frac{1}{3} \cdot \frac{5}{4}$ .

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Step 15.3.1

Multiply $\frac{5}{4}$ by $\frac{1}{3}$ .

$9 \frac{\frac{1}{2} - \frac{5}{4 \cdot 3}}{{(\frac{6}{7} - \frac{5}{4} - \frac{\frac{2}{7}}{\frac{1}{2}})}^{3}}$

Step 15.3.2

Multiply $4$ by $3$ .

$9 \frac{\frac{1}{2} - \frac{5}{12}}{{(\frac{6}{7} - \frac{5}{4} - \frac{\frac{2}{7}}{\frac{1}{2}})}^{3}}$

Step 15.4

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$9 \frac{\frac{1}{2} \cdot \frac{6}{6} - \frac{5}{12}}{{(\frac{6}{7} - \frac{5}{4} - \frac{\frac{2}{7}}{\frac{1}{2}})}^{3}}$

Step 15.5

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 15.5.1

Multiply $\frac{1}{2}$ by $\frac{6}{6}$ .

$9 \frac{\frac{6}{2 \cdot 6} - \frac{5}{12}}{{(\frac{6}{7} - \frac{5}{4} - \frac{\frac{2}{7}}{\frac{1}{2}})}^{3}}$

Step 15.5.2

Multiply $2$ by $6$ .

$9 \frac{\frac{6}{12} - \frac{5}{12}}{{(\frac{6}{7} - \frac{5}{4} - \frac{\frac{2}{7}}{\frac{1}{2}})}^{3}}$

Step 15.6

Combine the numerators over the common denominator.

$9 \frac{\frac{6 - 5}{12}}{{(\frac{6}{7} - \frac{5}{4} - \frac{\frac{2}{7}}{\frac{1}{2}})}^{3}}$

Step 15.7

Subtract $5$ from $6$ .

$9 \frac{\frac{1}{12}}{{(\frac{6}{7} - \frac{5}{4} - \frac{\frac{2}{7}}{\frac{1}{2}})}^{3}}$

Step 16

Simplify the denominator.

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Step 16.1

Multiply the numerator by the reciprocal of the denominator.

$9 \frac{\frac{1}{12}}{{(\frac{6}{7} - \frac{5}{4} - (\frac{2}{7} \cdot 2))}^{3}}$

Step 16.2

Multiply $\frac{2}{7} \cdot 2$ .

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Step 16.2.1

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

$9 \frac{\frac{1}{12}}{{(\frac{6}{7} - \frac{5}{4} - \frac{2 \cdot 2}{7})}^{3}}$

Step 16.2.2

Multiply $2$ by $2$ .

$9 \frac{\frac{1}{12}}{{(\frac{6}{7} - \frac{5}{4} - \frac{4}{7})}^{3}}$

Step 16.3

To write $\frac{6}{7}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$9 \frac{\frac{1}{12}}{{(\frac{6}{7} \cdot \frac{4}{4} - \frac{5}{4} - \frac{4}{7})}^{3}}$

Step 16.4

To write $- \frac{5}{4}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$9 \frac{\frac{1}{12}}{{(\frac{6}{7} \cdot \frac{4}{4} - \frac{5}{4} \cdot \frac{7}{7} - \frac{4}{7})}^{3}}$

Step 16.5

Write each expression with a common denominator of $28$ , by multiplying each by an appropriate factor of $1$ .

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Step 16.5.1

Multiply $\frac{6}{7}$ by $\frac{4}{4}$ .

$9 \frac{\frac{1}{12}}{{(\frac{6 \cdot 4}{7 \cdot 4} - \frac{5}{4} \cdot \frac{7}{7} - \frac{4}{7})}^{3}}$

Step 16.5.2

Multiply $7$ by $4$ .

$9 \frac{\frac{1}{12}}{{(\frac{6 \cdot 4}{28} - \frac{5}{4} \cdot \frac{7}{7} - \frac{4}{7})}^{3}}$

Step 16.5.3

Multiply $\frac{5}{4}$ by $\frac{7}{7}$ .

$9 \frac{\frac{1}{12}}{{(\frac{6 \cdot 4}{28} - \frac{5 \cdot 7}{4 \cdot 7} - \frac{4}{7})}^{3}}$

Step 16.5.4

Multiply $4$ by $7$ .

$9 \frac{\frac{1}{12}}{{(\frac{6 \cdot 4}{28} - \frac{5 \cdot 7}{28} - \frac{4}{7})}^{3}}$

Step 16.6

Combine the numerators over the common denominator.

$9 \frac{\frac{1}{12}}{{(\frac{6 \cdot 4 - 5 \cdot 7}{28} - \frac{4}{7})}^{3}}$

Step 16.7

Simplify the numerator.

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Step 16.7.1

Multiply $6$ by $4$ .

$9 \frac{\frac{1}{12}}{{(\frac{24 - 5 \cdot 7}{28} - \frac{4}{7})}^{3}}$

Step 16.7.2

Multiply $- 5$ by $7$ .

$9 \frac{\frac{1}{12}}{{(\frac{24 - 35}{28} - \frac{4}{7})}^{3}}$

Step 16.7.3

Subtract $35$ from $24$ .

$9 \frac{\frac{1}{12}}{{(\frac{- 11}{28} - \frac{4}{7})}^{3}}$

Step 16.8

To write $- \frac{4}{7}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$9 \frac{\frac{1}{12}}{{(\frac{- 11}{28} - \frac{4}{7} \cdot \frac{4}{4})}^{3}}$

Step 16.9

Write each expression with a common denominator of $28$ , by multiplying each by an appropriate factor of $1$ .

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Step 16.9.1

Multiply $\frac{4}{7}$ by $\frac{4}{4}$ .

$9 \frac{\frac{1}{12}}{{(\frac{- 11}{28} - \frac{4 \cdot 4}{7 \cdot 4})}^{3}}$

Step 16.9.2

Multiply $7$ by $4$ .

$9 \frac{\frac{1}{12}}{{(\frac{- 11}{28} - \frac{4 \cdot 4}{28})}^{3}}$

Step 16.10

Combine the numerators over the common denominator.

$9 \frac{\frac{1}{12}}{{(\frac{- 11 - 4 \cdot 4}{28})}^{3}}$

Step 16.11

Simplify the numerator.

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Step 16.11.1

Multiply $- 4$ by $4$ .

$9 \frac{\frac{1}{12}}{{(\frac{- 11 - 16}{28})}^{3}}$

Step 16.11.2

Subtract $16$ from $- 11$ .

$9 \frac{\frac{1}{12}}{{(\frac{- 27}{28})}^{3}}$

Step 16.12

Move the negative in front of the fraction.

$9 \frac{\frac{1}{12}}{{(- \frac{27}{28})}^{3}}$

Step 16.13

Apply the product rule to $- \frac{27}{28}$ .

$9 \frac{\frac{1}{12}}{{(- 1)}^{3} {(\frac{27}{28})}^{3}}$

Step 16.14

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

$9 \frac{\frac{1}{12}}{- {(\frac{27}{28})}^{3}}$

Step 16.15

Apply the product rule to $\frac{27}{28}$ .

$9 \frac{\frac{1}{12}}{- \frac{27^{3}}{28^{3}}}$

Step 16.16

Raise $27$ to the power of $3$ .

$9 \frac{\frac{1}{12}}{- \frac{19683}{28^{3}}}$

Step 16.17

Raise $28$ to the power of $3$ .

$9 \frac{\frac{1}{12}}{- \frac{19683}{21952}}$

Step 17

Multiply the numerator by the reciprocal of the denominator.

$9 (\frac{1}{12} (- \frac{21952}{19683}))$

Step 18

Cancel the common factor of $4$ .

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Step 18.1

Move the leading negative in $- \frac{21952}{19683}$ into the numerator.

$9 (\frac{1}{12} \cdot \frac{- 21952}{19683})$

Step 18.2

Factor $4$ out of $12$ .

$9 (\frac{1}{4 (3)} \cdot \frac{- 21952}{19683})$

Step 18.3

Factor $4$ out of $- 21952$ .

$9 (\frac{1}{4 \cdot 3} \cdot \frac{4 \cdot - 5488}{19683})$

Step 18.4

Cancel the common factor.

$9 (\frac{1}{4 \cdot 3} \cdot \frac{4 \cdot - 5488}{19683})$

Step 18.5

Rewrite the expression.

$9 (\frac{1}{3} \cdot \frac{- 5488}{19683})$

Step 19

Multiply $\frac{1}{3}$ by $\frac{- 5488}{19683}$ .

$9 \frac{- 5488}{3 \cdot 19683}$

Step 20

Multiply $3$ by $19683$ .

$9 (\frac{- 5488}{59049})$

Step 21

Cancel the common factor of $9$ .

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Step 21.1

Factor $9$ out of $59049$ .

$9 \frac{- 5488}{9 (6561)}$

Step 21.2

Cancel the common factor.

$9 \frac{- 5488}{9 \cdot 6561}$

Step 21.3

Rewrite the expression.

$\frac{- 5488}{6561}$

Step 22

Move the negative in front of the fraction.

$- \frac{5488}{6561}$

Step 23

The result can be shown in multiple forms.

Exact Form:

$- \frac{5488}{6561}$

Decimal Form:

$- 0.83645785 \dots$