Basic Math Examples

\frac{(9 - \frac{43}{8}) (4 \frac{5}{12} - 4 \div 2 \frac{2}{3} + (0.3 - 0.5 \div 4) \cdot \frac{4}{7})}{\frac{1}{24} + 0.25 \div 13 \frac{1}{3}}

$\frac{(9 - \frac{43}{8}) (4 \frac{5}{12} - 4 \div 2 \frac{2}{3} + (0.3 - 0.5 \div 4) \cdot \frac{4}{7})}{\frac{1}{24} + 0.25 \div 13 \frac{1}{3}}$

Step 1

Convert

$4 \frac{5}{12}$ to an improper fraction.

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Step 1.1

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

$\frac{(9 - \frac{43}{8}) (4 + \frac{5}{12} - 4 \div 2 \frac{2}{3} + (0.3 - 0.5 \div 4) \cdot \frac{4}{7})}{\frac{1}{24} + 0.25 \div 13 \frac{1}{3}}$

Step 1.2

Add

$4$ and

$\frac{5}{12}$ .

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Step 1.2.1

To write

$4$ as a fraction with a common denominator, multiply by

$\frac{12}{12}$ .

$\frac{(9 - \frac{43}{8}) (4 \cdot \frac{12}{12} + \frac{5}{12} - 4 \div 2 \frac{2}{3} + (0.3 - 0.5 \div 4) \cdot \frac{4}{7})}{\frac{1}{24} + 0.25 \div 13 \frac{1}{3}}$

Step 1.2.2

Combine

$4$ and

$\frac{12}{12}$ .

$\frac{(9 - \frac{43}{8}) (\frac{4 \cdot 12}{12} + \frac{5}{12} - 4 \div 2 \frac{2}{3} + (0.3 - 0.5 \div 4) \cdot \frac{4}{7})}{\frac{1}{24} + 0.25 \div 13 \frac{1}{3}}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{(9 - \frac{43}{8}) (\frac{4 \cdot 12 + 5}{12} - 4 \div 2 \frac{2}{3} + (0.3 - 0.5 \div 4) \cdot \frac{4}{7})}{\frac{1}{24} + 0.25 \div 13 \frac{1}{3}}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

$4$ by

$12$ .

$\frac{(9 - \frac{43}{8}) (\frac{48 + 5}{12} - 4 \div 2 \frac{2}{3} + (0.3 - 0.5 \div 4) \cdot \frac{4}{7})}{\frac{1}{24} + 0.25 \div 13 \frac{1}{3}}$

Step 1.2.4.2

Add

$48$ and

$5$ .

$\frac{(9 - \frac{43}{8}) (\frac{53}{12} - 4 \div 2 \frac{2}{3} + (0.3 - 0.5 \div 4) \cdot \frac{4}{7})}{\frac{1}{24} + 0.25 \div 13 \frac{1}{3}}$

Step 2

Convert

$2 \frac{2}{3}$ to an improper fraction.

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Step 2.1

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

$\frac{(9 - \frac{43}{8}) (\frac{53}{12} - 4 \div (2 + \frac{2}{3}) + (0.3 - 0.5 \div 4) \cdot \frac{4}{7})}{\frac{1}{24} + 0.25 \div 13 \frac{1}{3}}$

Step 2.2

Add

$2$ and

$\frac{2}{3}$ .

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Step 2.2.1

To write

$2$ as a fraction with a common denominator, multiply by

$\frac{3}{3}$ .

$\frac{(9 - \frac{43}{8}) (\frac{53}{12} - 4 \div (2 \cdot \frac{3}{3} + \frac{2}{3}) + (0.3 - 0.5 \div 4) \cdot \frac{4}{7})}{\frac{1}{24} + 0.25 \div 13 \frac{1}{3}}$

Step 2.2.2

Combine

$2$ and

$\frac{3}{3}$ .

$\frac{(9 - \frac{43}{8}) (\frac{53}{12} - 4 \div (\frac{2 \cdot 3}{3} + \frac{2}{3}) + (0.3 - 0.5 \div 4) \cdot \frac{4}{7})}{\frac{1}{24} + 0.25 \div 13 \frac{1}{3}}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{(9 - \frac{43}{8}) (\frac{53}{12} - 4 \div \frac{2 \cdot 3 + 2}{3} + (0.3 - 0.5 \div 4) \cdot \frac{4}{7})}{\frac{1}{24} + 0.25 \div 13 \frac{1}{3}}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

$2$ by

$3$ .

$\frac{(9 - \frac{43}{8}) (\frac{53}{12} - 4 \div \frac{6 + 2}{3} + (0.3 - 0.5 \div 4) \cdot \frac{4}{7})}{\frac{1}{24} + 0.25 \div 13 \frac{1}{3}}$

Step 2.2.4.2

Add

$6$ and

$2$ .

$\frac{(9 - \frac{43}{8}) (\frac{53}{12} - 4 \div \frac{8}{3} + (0.3 - 0.5 \div 4) \cdot \frac{4}{7})}{\frac{1}{24} + 0.25 \div 13 \frac{1}{3}}$

Step 3

Convert

$13 \frac{1}{3}$ to an improper fraction.

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Step 3.1

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

$\frac{(9 - \frac{43}{8}) (\frac{53}{12} - 4 \div \frac{8}{3} + (0.3 - 0.5 \div 4) \cdot \frac{4}{7})}{\frac{1}{24} + 0.25 \div (13 + \frac{1}{3})}$

Step 3.2

Add

$13$ and

$\frac{1}{3}$ .

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Step 3.2.1

To write

$13$ as a fraction with a common denominator, multiply by

$\frac{3}{3}$ .

$\frac{(9 - \frac{43}{8}) (\frac{53}{12} - 4 \div \frac{8}{3} + (0.3 - 0.5 \div 4) \cdot \frac{4}{7})}{\frac{1}{24} + 0.25 \div (13 \cdot \frac{3}{3} + \frac{1}{3})}$

Step 3.2.2

Combine

$13$ and

$\frac{3}{3}$ .

$\frac{(9 - \frac{43}{8}) (\frac{53}{12} - 4 \div \frac{8}{3} + (0.3 - 0.5 \div 4) \cdot \frac{4}{7})}{\frac{1}{24} + 0.25 \div (\frac{13 \cdot 3}{3} + \frac{1}{3})}$

Step 3.2.3

Combine the numerators over the common denominator.

$\frac{(9 - \frac{43}{8}) (\frac{53}{12} - 4 \div \frac{8}{3} + (0.3 - 0.5 \div 4) \cdot \frac{4}{7})}{\frac{1}{24} + 0.25 \div \frac{13 \cdot 3 + 1}{3}}$

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply

$13$ by

$3$ .

$\frac{(9 - \frac{43}{8}) (\frac{53}{12} - 4 \div \frac{8}{3} + (0.3 - 0.5 \div 4) \cdot \frac{4}{7})}{\frac{1}{24} + 0.25 \div \frac{39 + 1}{3}}$

Step 3.2.4.2

Add

$39$ and

$1$ .

$\frac{(9 - \frac{43}{8}) (\frac{53}{12} - 4 \div \frac{8}{3} + (0.3 - 0.5 \div 4) \cdot \frac{4}{7})}{\frac{1}{24} + 0.25 \div \frac{40}{3}}$

Step 4

Simplify the numerator.

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Step 4.1

To write

$9$ as a fraction with a common denominator, multiply by

$\frac{8}{8}$ .

$\frac{(9 \cdot \frac{8}{8} - \frac{43}{8}) (\frac{53}{12} - 4 \div \frac{8}{3} + (0.3 - 0.5 \div 4) \cdot \frac{4}{7})}{\frac{1}{24} + 0.25 \div \frac{40}{3}}$

Step 4.2

Combine

$9$ and

$\frac{8}{8}$ .

$\frac{(\frac{9 \cdot 8}{8} - \frac{43}{8}) (\frac{53}{12} - 4 \div \frac{8}{3} + (0.3 - 0.5 \div 4) \cdot \frac{4}{7})}{\frac{1}{24} + 0.25 \div \frac{40}{3}}$

Step 4.3

Combine the numerators over the common denominator.

$\frac{\frac{9 \cdot 8 - 43}{8} (\frac{53}{12} - 4 \div \frac{8}{3} + (0.3 - 0.5 \div 4) \cdot \frac{4}{7})}{\frac{1}{24} + 0.25 \div \frac{40}{3}}$

Step 4.4

Simplify the numerator.

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Step 4.4.1

Multiply

$9$ by

$8$ .

$\frac{\frac{72 - 43}{8} (\frac{53}{12} - 4 \div \frac{8}{3} + (0.3 - 0.5 \div 4) \cdot \frac{4}{7})}{\frac{1}{24} + 0.25 \div \frac{40}{3}}$

Step 4.4.2

Subtract

$43$ from

$72$ .

$\frac{\frac{29}{8} (\frac{53}{12} - 4 \div \frac{8}{3} + (0.3 - 0.5 \div 4) \cdot \frac{4}{7})}{\frac{1}{24} + 0.25 \div \frac{40}{3}}$

Step 4.5

To divide by a fraction, multiply by its reciprocal.

$\frac{\frac{29}{8} (\frac{53}{12} - (4 (\frac{3}{8})) + (0.3 - 0.5 \div 4) \cdot \frac{4}{7})}{\frac{1}{24} + 0.25 \div \frac{40}{3}}$

Step 4.6

Cancel the common factor of

$4$ .

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Step 4.6.1

Factor

$4$ out of

$8$ .

$\frac{\frac{29}{8} (\frac{53}{12} - (4 \frac{3}{4 (2)}) + (0.3 - 0.5 \div 4) \cdot \frac{4}{7})}{\frac{1}{24} + 0.25 \div \frac{40}{3}}$

Step 4.6.2

Cancel the common factor.

$\frac{\frac{29}{8} (\frac{53}{12} - (4 \frac{3}{4 \cdot 2}) + (0.3 - 0.5 \div 4) \cdot \frac{4}{7})}{\frac{1}{24} + 0.25 \div \frac{40}{3}}$

Step 4.6.3

Rewrite the expression.

$\frac{\frac{29}{8} (\frac{53}{12} - \frac{3}{2} + (0.3 - 0.5 \div 4) \cdot \frac{4}{7})}{\frac{1}{24} + 0.25 \div \frac{40}{3}}$

Step 4.7

Simplify each term.

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Step 4.7.1

Divide

$0.5$ by

$4$ .

$\frac{\frac{29}{8} (\frac{53}{12} - \frac{3}{2} + (0.3 - 1 \cdot 0.125) \cdot \frac{4}{7})}{\frac{1}{24} + 0.25 \div \frac{40}{3}}$

Step 4.7.2

Multiply

$- 1$ by

$0.125$ .

$\frac{\frac{29}{8} (\frac{53}{12} - \frac{3}{2} + (0.3 - 0.125) \cdot \frac{4}{7})}{\frac{1}{24} + 0.25 \div \frac{40}{3}}$

Step 4.8

Subtract

$0.125$ from

$0.3$ .

$\frac{\frac{29}{8} (\frac{53}{12} - \frac{3}{2} + 0.175 \cdot \frac{4}{7})}{\frac{1}{24} + 0.25 \div \frac{40}{3}}$

Step 4.9

Cancel the common factor of

$0.175$ .

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Step 4.9.1

Factor

$0.175$ out of

$7$ .

$\frac{\frac{29}{8} (\frac{53}{12} - \frac{3}{2} + 0.175 \cdot \frac{4}{0.175 (40)})}{\frac{1}{24} + 0.25 \div \frac{40}{3}}$

Step 4.9.2

Cancel the common factor.

$\frac{\frac{29}{8} (\frac{53}{12} - \frac{3}{2} + 0.175 \cdot \frac{4}{0.175 \cdot 40})}{\frac{1}{24} + 0.25 \div \frac{40}{3}}$

Step 4.9.3

Rewrite the expression.

$\frac{\frac{29}{8} (\frac{53}{12} - \frac{3}{2} + \frac{4}{40})}{\frac{1}{24} + 0.25 \div \frac{40}{3}}$

Step 4.10

Cancel the common factor of

$4$ and

$40$ .

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Step 4.10.1

Factor

$4$ out of

$4$ .

$\frac{\frac{29}{8} (\frac{53}{12} - \frac{3}{2} + \frac{4 (1)}{40})}{\frac{1}{24} + 0.25 \div \frac{40}{3}}$

Step 4.10.2

Cancel the common factors.

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Step 4.10.2.1

Factor

$4$ out of

$40$ .

$\frac{\frac{29}{8} (\frac{53}{12} - \frac{3}{2} + \frac{4 \cdot 1}{4 \cdot 10})}{\frac{1}{24} + 0.25 \div \frac{40}{3}}$

Step 4.10.2.2

Cancel the common factor.

$\frac{\frac{29}{8} (\frac{53}{12} - \frac{3}{2} + \frac{4 \cdot 1}{4 \cdot 10})}{\frac{1}{24} + 0.25 \div \frac{40}{3}}$

Step 4.10.2.3

Rewrite the expression.

$\frac{\frac{29}{8} (\frac{53}{12} - \frac{3}{2} + \frac{1}{10})}{\frac{1}{24} + 0.25 \div \frac{40}{3}}$

Step 4.11

To write

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

$\frac{6}{6}$ .

$\frac{\frac{29}{8} (\frac{53}{12} - \frac{3}{2} \cdot \frac{6}{6} + \frac{1}{10})}{\frac{1}{24} + 0.25 \div \frac{40}{3}}$

Step 4.12

Write each expression with a common denominator of

$12$ , by multiplying each by an appropriate factor of

$1$ .

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Step 4.12.1

Multiply

$\frac{3}{2}$ by

$\frac{6}{6}$ .

$\frac{\frac{29}{8} (\frac{53}{12} - \frac{3 \cdot 6}{2 \cdot 6} + \frac{1}{10})}{\frac{1}{24} + 0.25 \div \frac{40}{3}}$

Step 4.12.2

Multiply

$2$ by

$6$ .

$\frac{\frac{29}{8} (\frac{53}{12} - \frac{3 \cdot 6}{12} + \frac{1}{10})}{\frac{1}{24} + 0.25 \div \frac{40}{3}}$

Step 4.13

Combine the numerators over the common denominator.

$\frac{\frac{29}{8} (\frac{53 - 3 \cdot 6}{12} + \frac{1}{10})}{\frac{1}{24} + 0.25 \div \frac{40}{3}}$

Step 4.14

Simplify the numerator.

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Step 4.14.1

Multiply

$- 3$ by

$6$ .

$\frac{\frac{29}{8} (\frac{53 - 18}{12} + \frac{1}{10})}{\frac{1}{24} + 0.25 \div \frac{40}{3}}$

Step 4.14.2

Subtract

$18$ from

$53$ .

$\frac{\frac{29}{8} (\frac{35}{12} + \frac{1}{10})}{\frac{1}{24} + 0.25 \div \frac{40}{3}}$

Step 4.15

To write

$\frac{35}{12}$ as a fraction with a common denominator, multiply by

$\frac{5}{5}$ .

$\frac{\frac{29}{8} (\frac{35}{12} \cdot \frac{5}{5} + \frac{1}{10})}{\frac{1}{24} + 0.25 \div \frac{40}{3}}$

Step 4.16

To write

$\frac{1}{10}$ as a fraction with a common denominator, multiply by

$\frac{6}{6}$ .

$\frac{\frac{29}{8} (\frac{35}{12} \cdot \frac{5}{5} + \frac{1}{10} \cdot \frac{6}{6})}{\frac{1}{24} + 0.25 \div \frac{40}{3}}$

Step 4.17

Write each expression with a common denominator of

$60$ , by multiplying each by an appropriate factor of

$1$ .

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Step 4.17.1

Multiply

$\frac{35}{12}$ by

$\frac{5}{5}$ .

$\frac{\frac{29}{8} (\frac{35 \cdot 5}{12 \cdot 5} + \frac{1}{10} \cdot \frac{6}{6})}{\frac{1}{24} + 0.25 \div \frac{40}{3}}$

Step 4.17.2

Multiply

$12$ by

$5$ .

$\frac{\frac{29}{8} (\frac{35 \cdot 5}{60} + \frac{1}{10} \cdot \frac{6}{6})}{\frac{1}{24} + 0.25 \div \frac{40}{3}}$

Step 4.17.3

Multiply

$\frac{1}{10}$ by

$\frac{6}{6}$ .

$\frac{\frac{29}{8} (\frac{35 \cdot 5}{60} + \frac{6}{10 \cdot 6})}{\frac{1}{24} + 0.25 \div \frac{40}{3}}$

Step 4.17.4

Multiply

$10$ by

$6$ .

$\frac{\frac{29}{8} (\frac{35 \cdot 5}{60} + \frac{6}{60})}{\frac{1}{24} + 0.25 \div \frac{40}{3}}$

Step 4.18

Combine the numerators over the common denominator.

$\frac{\frac{29}{8} \cdot \frac{35 \cdot 5 + 6}{60}}{\frac{1}{24} + 0.25 \div \frac{40}{3}}$

Step 4.19

Simplify the numerator.

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Step 4.19.1

Multiply

$35$ by

$5$ .

$\frac{\frac{29}{8} \cdot \frac{175 + 6}{60}}{\frac{1}{24} + 0.25 \div \frac{40}{3}}$

Step 4.19.2

Add

$175$ and

$6$ .

$\frac{\frac{29}{8} \cdot \frac{181}{60}}{\frac{1}{24} + 0.25 \div \frac{40}{3}}$

Step 5

Simplify the denominator.

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Step 5.1

To write

$\frac{1}{24}$ as a fraction with a common denominator, multiply by

$\frac{\frac{40}{3}}{\frac{40}{3}}$ .

$\frac{\frac{29}{8} \cdot \frac{181}{60}}{\frac{1}{24} \cdot \frac{\frac{40}{3}}{\frac{40}{3}} + 0.25 \div \frac{40}{3}}$

Step 5.2

To write

$0.25 \div \frac{40}{3}$ as a fraction with a common denominator, multiply by

$\frac{24}{24}$ .

$\frac{\frac{29}{8} \cdot \frac{181}{60}}{\frac{1}{24} \cdot \frac{\frac{40}{3}}{\frac{40}{3}} + 0.25 \div \frac{40}{3} \cdot \frac{24}{24}}$

Step 5.3

Write each expression with a common denominator of

$24 (\frac{40}{3})$ , by multiplying each by an appropriate factor of

$1$ .

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Step 5.3.1

Multiply

$\frac{1}{24}$ by

$\frac{\frac{40}{3}}{\frac{40}{3}}$ .

$\frac{\frac{29}{8} \cdot \frac{181}{60}}{\frac{\frac{40}{3}}{24 (\frac{40}{3})} + 0.25 \div \frac{40}{3} \cdot \frac{24}{24}}$

Step 5.3.2

Combine

$24$ and

$\frac{40}{3}$ .

$\frac{\frac{29}{8} \cdot \frac{181}{60}}{\frac{\frac{40}{3}}{\frac{24 \cdot 40}{3}} + 0.25 \div \frac{40}{3} \cdot \frac{24}{24}}$

Step 5.3.3

Multiply

$0.25 \div \frac{40}{3}$ by

$\frac{24}{24}$ .

$\frac{\frac{29}{8} \cdot \frac{181}{60}}{\frac{\frac{40}{3}}{\frac{24 \cdot 40}{3}} + \frac{0.25 \cdot 24}{\frac{40}{3} \cdot 24}}$

Step 5.3.4

Combine

$\frac{40}{3}$ and

$24$ .

$\frac{\frac{29}{8} \cdot \frac{181}{60}}{\frac{\frac{40}{3}}{\frac{24 \cdot 40}{3}} + \frac{0.25 \cdot 24}{\frac{40 \cdot 24}{3}}}$

Step 5.3.5

Reorder terms.

$\frac{\frac{29}{8} \cdot \frac{181}{60}}{\frac{\frac{40}{3}}{\frac{24 \cdot 40}{3}} + \frac{0.25 \cdot 24}{\frac{24 \cdot 40}{3}}}$

Step 5.4

Combine the numerators over the common denominator.

$\frac{\frac{29}{8} \cdot \frac{181}{60}}{\frac{\frac{40}{3} + 0.25 \cdot 24}{\frac{24 \cdot 40}{3}}}$

Step 5.5

Rewrite

$\frac{\frac{40}{3} + 0.25 \cdot 24}{\frac{24 \cdot 40}{3}}$ in a factored form.

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Step 5.5.1

Multiply

$0.25$ by

$24$ .

$\frac{\frac{29}{8} \cdot \frac{181}{60}}{\frac{\frac{40}{3} + 6}{\frac{24 \cdot 40}{3}}}$

Step 5.5.2

To write

$6$ as a fraction with a common denominator, multiply by

$\frac{3}{3}$ .

$\frac{\frac{29}{8} \cdot \frac{181}{60}}{\frac{\frac{40}{3} + 6 \cdot \frac{3}{3}}{\frac{24 \cdot 40}{3}}}$

Step 5.5.3

Combine

$6$ and

$\frac{3}{3}$ .

$\frac{\frac{29}{8} \cdot \frac{181}{60}}{\frac{\frac{40}{3} + \frac{6 \cdot 3}{3}}{\frac{24 \cdot 40}{3}}}$

Step 5.5.4

Combine the numerators over the common denominator.

$\frac{\frac{29}{8} \cdot \frac{181}{60}}{\frac{\frac{40 + 6 \cdot 3}{3}}{\frac{24 \cdot 40}{3}}}$

Step 5.5.5

Simplify the numerator.

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Step 5.5.5.1

Multiply

$6$ by

$3$ .

$\frac{\frac{29}{8} \cdot \frac{181}{60}}{\frac{\frac{40 + 18}{3}}{\frac{24 \cdot 40}{3}}}$

Step 5.5.5.2

Add

$40$ and

$18$ .

$\frac{\frac{29}{8} \cdot \frac{181}{60}}{\frac{\frac{58}{3}}{\frac{24 \cdot 40}{3}}}$

Step 5.5.6

Cancel the common factor of

$58$ and

$3$ .

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Step 5.5.6.1

Rewrite

$58$ as

$1 (58)$ .

$\frac{\frac{29}{8} \cdot \frac{181}{60}}{\frac{\frac{1 (58)}{3}}{\frac{24 \cdot 40}{3}}}$

Step 5.5.6.2

Cancel the common factors.

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Step 5.5.6.2.1

Rewrite

$3$ as

$1 (3)$ .

$\frac{\frac{29}{8} \cdot \frac{181}{60}}{\frac{\frac{1 \cdot 58}{1 \cdot 3}}{\frac{24 \cdot 40}{3}}}$

Step 5.5.6.2.2

Cancel the common factor.

$\frac{\frac{29}{8} \cdot \frac{181}{60}}{\frac{\frac{1 \cdot 58}{1 \cdot 3}}{\frac{24 \cdot 40}{3}}}$

Step 5.5.6.2.3

Rewrite the expression.

$\frac{\frac{29}{8} \cdot \frac{181}{60}}{\frac{\frac{58}{3}}{\frac{24 \cdot 40}{3}}}$

Step 5.5.7

Reduce the expression by cancelling the common factors.

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Step 5.5.7.1

Reduce the expression

$\frac{24 \cdot 40}{3}$ by cancelling the common factors.

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Step 5.5.7.1.1

Factor

$3$ out of

$24 \cdot 40$ .

$\frac{\frac{29}{8} \cdot \frac{181}{60}}{\frac{\frac{58}{3}}{\frac{3 (8 \cdot 40)}{3}}}$

Step 5.5.7.1.2

Factor

$3$ out of

$3$ .

$\frac{\frac{29}{8} \cdot \frac{181}{60}}{\frac{\frac{58}{3}}{\frac{3 (8 \cdot 40)}{3 (1)}}}$

Step 5.5.7.1.3

Cancel the common factor.

$\frac{\frac{29}{8} \cdot \frac{181}{60}}{\frac{\frac{58}{3}}{\frac{3 (8 \cdot 40)}{3 \cdot 1}}}$

Step 5.5.7.1.4

Rewrite the expression.

$\frac{\frac{29}{8} \cdot \frac{181}{60}}{\frac{\frac{58}{3}}{\frac{8 \cdot 40}{1}}}$

Step 5.5.7.2

Divide

$8 \cdot 40$ by

$1$ .

$\frac{\frac{29}{8} \cdot \frac{181}{60}}{\frac{\frac{58}{3}}{8 \cdot 40}}$

Step 5.6

Multiply the numerator by the reciprocal of the denominator.

$\frac{\frac{29}{8} \cdot \frac{181}{60}}{\frac{58}{3} \cdot \frac{1}{8 \cdot 40}}$

Step 5.7

Multiply

$8$ by

$40$ .

$\frac{\frac{29}{8} \cdot \frac{181}{60}}{\frac{58}{3} \cdot \frac{1}{320}}$

Step 5.8

Cancel the common factor of

$2$ .

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Step 5.8.1

Factor

$2$ out of

$58$ .

$\frac{\frac{29}{8} \cdot \frac{181}{60}}{\frac{2 (29)}{3} \cdot \frac{1}{320}}$

Step 5.8.2

Factor

$2$ out of

$320$ .

$\frac{\frac{29}{8} \cdot \frac{181}{60}}{\frac{2 \cdot 29}{3} \cdot \frac{1}{2 \cdot 160}}$

Step 5.8.3

Cancel the common factor.

$\frac{\frac{29}{8} \cdot \frac{181}{60}}{\frac{2 \cdot 29}{3} \cdot \frac{1}{2 \cdot 160}}$

Step 5.8.4

Rewrite the expression.

$\frac{\frac{29}{8} \cdot \frac{181}{60}}{\frac{29}{3} \cdot \frac{1}{160}}$

Step 5.9

Multiply

$\frac{29}{3}$ by

$\frac{1}{160}$ .

$\frac{\frac{29}{8} \cdot \frac{181}{60}}{\frac{29}{3 \cdot 160}}$

Step 5.10

Multiply

$3$ by

$160$ .

$\frac{\frac{29}{8} \cdot \frac{181}{60}}{\frac{29}{480}}$

Step 6

Combine fractions.

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Step 6.1

Multiply

$\frac{29}{8}$ by

$\frac{181}{60}$ .

$\frac{\frac{29 \cdot 181}{8 \cdot 60}}{\frac{29}{480}}$

Step 6.2

Multiply.

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Step 6.2.1

Multiply

$29$ by

$181$ .

$\frac{\frac{5249}{8 \cdot 60}}{\frac{29}{480}}$

Step 6.2.2

Multiply

$8$ by

$60$ .

$\frac{\frac{5249}{480}}{\frac{29}{480}}$

Step 7

Multiply the numerator by the reciprocal of the denominator.

$\frac{5249}{480} \cdot \frac{480}{29}$

Step 8

Cancel the common factor of

$29$ .

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Step 8.1

Factor

$29$ out of

$5249$ .

$\frac{29 (181)}{480} \cdot \frac{480}{29}$

Step 8.2

Cancel the common factor.

$\frac{29 \cdot 181}{480} \cdot \frac{480}{29}$

Step 8.3

Rewrite the expression.

$\frac{181}{480} \cdot 480$

Step 9

Cancel the common factor of

$480$ .

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Step 9.1

Cancel the common factor.

$\frac{181}{480} \cdot 480$

Step 9.2

Rewrite the expression.

$181$