Basic Math Examples

$(2 \frac{1}{5} \cdot 1 \frac{3}{22}) - {(9 \frac{1}{5} \div 2 \frac{4}{23})}^{5 \frac{4}{3}}$

Step 1

Convert $2 \frac{1}{5}$ to an improper fraction.

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Step 1.1

A mixed number is an addition of its whole and fractional parts.

$(2 + \frac{1}{5}) \cdot 1 \frac{3}{22} - {(9 \frac{1}{5} \div 2 \frac{4}{23})}^{5 \frac{4}{3}}$

Step 1.2

Add $2$ and $\frac{1}{5}$ .

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Step 1.2.1

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

$(2 \cdot \frac{5}{5} + \frac{1}{5}) \cdot 1 \frac{3}{22} - {(9 \frac{1}{5} \div 2 \frac{4}{23})}^{5 \frac{4}{3}}$

Step 1.2.2

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

$(\frac{2 \cdot 5}{5} + \frac{1}{5}) \cdot 1 \frac{3}{22} - {(9 \frac{1}{5} \div 2 \frac{4}{23})}^{5 \frac{4}{3}}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{2 \cdot 5 + 1}{5} \cdot 1 \frac{3}{22} - {(9 \frac{1}{5} \div 2 \frac{4}{23})}^{5 \frac{4}{3}}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $2$ by $5$ .

$\frac{10 + 1}{5} \cdot 1 \frac{3}{22} - {(9 \frac{1}{5} \div 2 \frac{4}{23})}^{5 \frac{4}{3}}$

Step 1.2.4.2

Add $10$ and $1$ .

$\frac{11}{5} \cdot 1 \frac{3}{22} - {(9 \frac{1}{5} \div 2 \frac{4}{23})}^{5 \frac{4}{3}}$

Step 2

Convert $1 \frac{3}{22}$ to an improper fraction.

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Step 2.1

A mixed number is an addition of its whole and fractional parts.

$\frac{11}{5} \cdot (1 + \frac{3}{22}) - {(9 \frac{1}{5} \div 2 \frac{4}{23})}^{5 \frac{4}{3}}$

Step 2.2

Add $1$ and $\frac{3}{22}$ .

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Step 2.2.1

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

$\frac{11}{5} \cdot (\frac{22}{22} + \frac{3}{22}) - {(9 \frac{1}{5} \div 2 \frac{4}{23})}^{5 \frac{4}{3}}$

Step 2.2.2

Combine the numerators over the common denominator.

$\frac{11}{5} \cdot \frac{22 + 3}{22} - {(9 \frac{1}{5} \div 2 \frac{4}{23})}^{5 \frac{4}{3}}$

Step 2.2.3

Add $22$ and $3$ .

$\frac{11}{5} \cdot \frac{25}{22} - {(9 \frac{1}{5} \div 2 \frac{4}{23})}^{5 \frac{4}{3}}$

Step 3

Convert $9 \frac{1}{5}$ to an improper fraction.

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Step 3.1

A mixed number is an addition of its whole and fractional parts.

$\frac{11}{5} \cdot \frac{25}{22} - {((9 + \frac{1}{5}) \div 2 \frac{4}{23})}^{5 \frac{4}{3}}$

Step 3.2

Add $9$ and $\frac{1}{5}$ .

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Step 3.2.1

To write $9$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{11}{5} \cdot \frac{25}{22} - {((9 \cdot \frac{5}{5} + \frac{1}{5}) \div 2 \frac{4}{23})}^{5 \frac{4}{3}}$

Step 3.2.2

Combine $9$ and $\frac{5}{5}$ .

$\frac{11}{5} \cdot \frac{25}{22} - {((\frac{9 \cdot 5}{5} + \frac{1}{5}) \div 2 \frac{4}{23})}^{5 \frac{4}{3}}$

Step 3.2.3

Combine the numerators over the common denominator.

$\frac{11}{5} \cdot \frac{25}{22} - {(\frac{9 \cdot 5 + 1}{5} \div 2 \frac{4}{23})}^{5 \frac{4}{3}}$

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply $9$ by $5$ .

$\frac{11}{5} \cdot \frac{25}{22} - {(\frac{45 + 1}{5} \div 2 \frac{4}{23})}^{5 \frac{4}{3}}$

Step 3.2.4.2

Add $45$ and $1$ .

$\frac{11}{5} \cdot \frac{25}{22} - {(\frac{46}{5} \div 2 \frac{4}{23})}^{5 \frac{4}{3}}$

Step 4

Convert $2 \frac{4}{23}$ to an improper fraction.

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Step 4.1

A mixed number is an addition of its whole and fractional parts.

$\frac{11}{5} \cdot \frac{25}{22} - {(\frac{46}{5} \div (2 + \frac{4}{23}))}^{5 \frac{4}{3}}$

Step 4.2

Add $2$ and $\frac{4}{23}$ .

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Step 4.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{23}{23}$ .

$\frac{11}{5} \cdot \frac{25}{22} - {(\frac{46}{5} \div (2 \cdot \frac{23}{23} + \frac{4}{23}))}^{5 \frac{4}{3}}$

Step 4.2.2

Combine $2$ and $\frac{23}{23}$ .

$\frac{11}{5} \cdot \frac{25}{22} - {(\frac{46}{5} \div (\frac{2 \cdot 23}{23} + \frac{4}{23}))}^{5 \frac{4}{3}}$

Step 4.2.3

Combine the numerators over the common denominator.

$\frac{11}{5} \cdot \frac{25}{22} - {(\frac{46}{5} \div \frac{2 \cdot 23 + 4}{23})}^{5 \frac{4}{3}}$

Step 4.2.4

Simplify the numerator.

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Step 4.2.4.1

Multiply $2$ by $23$ .

$\frac{11}{5} \cdot \frac{25}{22} - {(\frac{46}{5} \div \frac{46 + 4}{23})}^{5 \frac{4}{3}}$

Step 4.2.4.2

Add $46$ and $4$ .

$\frac{11}{5} \cdot \frac{25}{22} - {(\frac{46}{5} \div \frac{50}{23})}^{5 \frac{4}{3}}$

Step 5

Convert $5 \frac{4}{3}$ to an improper fraction.

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Step 5.1

A mixed number is an addition of its whole and fractional parts.

$\frac{11}{5} \cdot \frac{25}{22} - {(\frac{46}{5} \div \frac{50}{23})}^{5 + \frac{4}{3}}$

Step 5.2

Add $5$ and $\frac{4}{3}$ .

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Step 5.2.1

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

$\frac{11}{5} \cdot \frac{25}{22} - {(\frac{46}{5} \div \frac{50}{23})}^{5 \cdot \frac{3}{3} + \frac{4}{3}}$

Step 5.2.2

Combine $5$ and $\frac{3}{3}$ .

$\frac{11}{5} \cdot \frac{25}{22} - {(\frac{46}{5} \div \frac{50}{23})}^{\frac{5 \cdot 3}{3} + \frac{4}{3}}$

Step 5.2.3

Combine the numerators over the common denominator.

$\frac{11}{5} \cdot \frac{25}{22} - {(\frac{46}{5} \div \frac{50}{23})}^{\frac{5 \cdot 3 + 4}{3}}$

Step 5.2.4

Simplify the numerator.

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Step 5.2.4.1

Multiply $5$ by $3$ .

$\frac{11}{5} \cdot \frac{25}{22} - {(\frac{46}{5} \div \frac{50}{23})}^{\frac{15 + 4}{3}}$

Step 5.2.4.2

Add $15$ and $4$ .

$\frac{11}{5} \cdot \frac{25}{22} - {(\frac{46}{5} \div \frac{50}{23})}^{\frac{19}{3}}$

Step 6

Simplify each term.

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Step 6.1

Cancel the common factor of $11$ .

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Step 6.1.1

Factor $11$ out of $22$ .

$\frac{11}{5} \cdot \frac{25}{11 (2)} - {(\frac{46}{5} \div \frac{50}{23})}^{\frac{19}{3}}$

Step 6.1.2

Cancel the common factor.

$\frac{11}{5} \cdot \frac{25}{11 \cdot 2} - {(\frac{46}{5} \div \frac{50}{23})}^{\frac{19}{3}}$

Step 6.1.3

Rewrite the expression.

$\frac{1}{5} \cdot \frac{25}{2} - {(\frac{46}{5} \div \frac{50}{23})}^{\frac{19}{3}}$

Step 6.2

Cancel the common factor of $5$ .

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Step 6.2.1

Factor $5$ out of $25$ .

$\frac{1}{5} \cdot \frac{5 (5)}{2} - {(\frac{46}{5} \div \frac{50}{23})}^{\frac{19}{3}}$

Step 6.2.2

Cancel the common factor.

$\frac{1}{5} \cdot \frac{5 \cdot 5}{2} - {(\frac{46}{5} \div \frac{50}{23})}^{\frac{19}{3}}$

Step 6.2.3

Rewrite the expression.

$\frac{5}{2} - {(\frac{46}{5} \div \frac{50}{23})}^{\frac{19}{3}}$

Step 6.3

To divide by a fraction, multiply by its reciprocal.

$\frac{5}{2} - {(\frac{46}{5} \cdot \frac{23}{50})}^{\frac{19}{3}}$

Step 6.4

Cancel the common factor of $2$ .

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Step 6.4.1

Factor $2$ out of $46$ .

$\frac{5}{2} - {(\frac{2 (23)}{5} \cdot \frac{23}{50})}^{\frac{19}{3}}$

Step 6.4.2

Factor $2$ out of $50$ .

$\frac{5}{2} - {(\frac{2 \cdot 23}{5} \cdot \frac{23}{2 \cdot 25})}^{\frac{19}{3}}$

Step 6.4.3

Cancel the common factor.

$\frac{5}{2} - {(\frac{2 \cdot 23}{5} \cdot \frac{23}{2 \cdot 25})}^{\frac{19}{3}}$

Step 6.4.4

Rewrite the expression.

$\frac{5}{2} - {(\frac{23}{5} \cdot \frac{23}{25})}^{\frac{19}{3}}$

Step 6.5

Multiply $\frac{23}{5}$ by $\frac{23}{25}$ .

$\frac{5}{2} - {(\frac{23 \cdot 23}{5 \cdot 25})}^{\frac{19}{3}}$

Step 6.6

Multiply $23$ by $23$ .

$\frac{5}{2} - {(\frac{529}{5 \cdot 25})}^{\frac{19}{3}}$

Step 6.7

Multiply $5$ by $25$ .

$\frac{5}{2} - {(\frac{529}{125})}^{\frac{19}{3}}$

Step 6.8

Apply the product rule to $\frac{529}{125}$ .

$\frac{5}{2} - \frac{529^{\frac{19}{3}}}{125^{\frac{19}{3}}}$

Step 6.9

Simplify the denominator.

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Step 6.9.1

Rewrite $125$ as $5^{3}$ .

$\frac{5}{2} - \frac{529^{\frac{19}{3}}}{{(5^{3})}^{\frac{19}{3}}}$

Step 6.9.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{5}{2} - \frac{529^{\frac{19}{3}}}{5^{3 (\frac{19}{3})}}$

Step 6.9.3

Cancel the common factor of $3$ .

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Step 6.9.3.1

Cancel the common factor.

$\frac{5}{2} - \frac{529^{\frac{19}{3}}}{5^{3 (\frac{19}{3})}}$

Step 6.9.3.2

Rewrite the expression.

$\frac{5}{2} - \frac{529^{\frac{19}{3}}}{5^{19}}$

Step 6.9.4

Raise $5$ to the power of $19$ .

$\frac{5}{2} - \frac{529^{\frac{19}{3}}}{19073486328125}$

Step 7

To write $\frac{5}{2}$ as a fraction with a common denominator, multiply by $\frac{19073486328125}{19073486328125}$ .

$\frac{5}{2} \cdot \frac{19073486328125}{19073486328125} - \frac{529^{\frac{19}{3}}}{19073486328125}$

Step 8

To write $- \frac{529^{\frac{19}{3}}}{19073486328125}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{5}{2} \cdot \frac{19073486328125}{19073486328125} - \frac{529^{\frac{19}{3}}}{19073486328125} \cdot \frac{2}{2}$

Step 9

Write each expression with a common denominator of $38146972656250$ , by multiplying each by an appropriate factor of $1$ .

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Step 9.1

Multiply $\frac{5}{2}$ by $\frac{19073486328125}{19073486328125}$ .

$\frac{5 \cdot 19073486328125}{2 \cdot 19073486328125} - \frac{529^{\frac{19}{3}}}{19073486328125} \cdot \frac{2}{2}$

Step 9.2

Multiply $2$ by $19073486328125$ .

$\frac{5 \cdot 19073486328125}{38146972656250} - \frac{529^{\frac{19}{3}}}{19073486328125} \cdot \frac{2}{2}$

Step 9.3

Multiply $\frac{529^{\frac{19}{3}}}{19073486328125}$ by $\frac{2}{2}$ .

$\frac{5 \cdot 19073486328125}{38146972656250} - \frac{529^{\frac{19}{3}} \cdot 2}{19073486328125 \cdot 2}$

Step 9.4

Multiply $19073486328125$ by $2$ .

$\frac{5 \cdot 19073486328125}{38146972656250} - \frac{529^{\frac{19}{3}} \cdot 2}{38146972656250}$

Step 10

Combine the numerators over the common denominator.

$\frac{5 \cdot 19073486328125 - 529^{\frac{19}{3}} \cdot 2}{38146972656250}$

Step 11

Simplify the numerator.

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Step 11.1

Multiply $5$ by $19073486328125$ .

$\frac{95367431640625 - 529^{\frac{19}{3}} \cdot 2}{38146972656250}$

Step 11.2

Divide $19$ by $3$ .

$\frac{95367431640625 - 529^{6.\overline{3}} \cdot 2}{38146972656250}$

Step 11.3

Raise $529$ to the power of $6.\overline{3}$ .

$\frac{95367431640625 - 1 \cdot 177236265095204000 \cdot 2}{38146972656250}$

Step 11.4

Multiply $- 1$ by $177236265095204000$ .

$\frac{95367431640625 - 177236265095204000 \cdot 2}{38146972656250}$

Step 11.5

Multiply $- 177236265095204000$ by $2$ .

$\frac{95367431640625 - 354472530190408000}{38146972656250}$

Step 11.6

Subtract $354472530190408000$ from $95367431640625$ .

$\frac{- 354377162758767375}{38146972656250}$

Step 12

Cancel the common factor of $- 354377162758767375$ and $38146972656250$ .

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Step 12.1

Factor $125$ out of $- 354377162758767375$ .

$\frac{125 (- 2835017302070139)}{38146972656250}$

Step 12.2

Cancel the common factors.

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Step 12.2.1

Factor $125$ out of $38146972656250$ .

$\frac{125 \cdot - 2835017302070139}{125 \cdot 305175781250}$

Step 12.2.2

Cancel the common factor.

$\frac{125 \cdot - 2835017302070139}{125 \cdot 305175781250}$

Step 12.2.3

Rewrite the expression.

$\frac{- 2835017302070139}{305175781250}$

Step 13

Move the negative in front of the fraction.

$- \frac{2835017302070139}{305175781250}$

Step 14

The result can be shown in multiple forms.

Exact Form:

$- \frac{2835017302070139}{305175781250}$

Decimal Form:

$- 9289.78469542 \dots$