Evaluate 1/4+(12/5+3/2)*5/2+((73/12)÷6-73/72)÷(61/7-131/21)-11

$\frac{1}{4} + (\frac{12}{5} + \frac{3}{2}) \cdot \frac{5}{2} + (\frac{73}{12} \div 6 - \frac{73}{72}) \div (\frac{61}{7} - \frac{131}{21}) - 11$

Simplify each term.

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To write $\frac{12}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{1}{4} + (\frac{12}{5} \cdot \frac{2}{2} + \frac{3}{2}) \cdot \frac{5}{2} + (\frac{73}{12} \div 6 - \frac{73}{72}) \div (\frac{61}{7} - \frac{131}{21}) - 11$

To write $\frac{3}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{1}{4} + (\frac{12}{5} \cdot \frac{2}{2} + \frac{3}{2} \cdot \frac{5}{5}) \cdot \frac{5}{2} + (\frac{73}{12} \div 6 - \frac{73}{72}) \div (\frac{61}{7} - \frac{131}{21}) - 11$

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

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Multiply $\frac{12}{5}$ and $\frac{2}{2}$ .

$\frac{1}{4} + (\frac{12 \cdot 2}{5 \cdot 2} + \frac{3}{2} \cdot \frac{5}{5}) \cdot \frac{5}{2} + (\frac{73}{12} \div 6 - \frac{73}{72}) \div (\frac{61}{7} - \frac{131}{21}) - 11$

Multiply $5$ by $2$ .

$\frac{1}{4} + (\frac{12 \cdot 2}{10} + \frac{3}{2} \cdot \frac{5}{5}) \cdot \frac{5}{2} + (\frac{73}{12} \div 6 - \frac{73}{72}) \div (\frac{61}{7} - \frac{131}{21}) - 11$

Multiply $\frac{3}{2}$ and $\frac{5}{5}$ .

$\frac{1}{4} + (\frac{12 \cdot 2}{10} + \frac{3 \cdot 5}{2 \cdot 5}) \cdot \frac{5}{2} + (\frac{73}{12} \div 6 - \frac{73}{72}) \div (\frac{61}{7} - \frac{131}{21}) - 11$

Multiply $2$ by $5$ .

$\frac{1}{4} + (\frac{12 \cdot 2}{10} + \frac{3 \cdot 5}{10}) \cdot \frac{5}{2} + (\frac{73}{12} \div 6 - \frac{73}{72}) \div (\frac{61}{7} - \frac{131}{21}) - 11$

Combine the numerators over the common denominator.

$\frac{1}{4} + \frac{12 \cdot 2 + 3 \cdot 5}{10} \cdot \frac{5}{2} + (\frac{73}{12} \div 6 - \frac{73}{72}) \div (\frac{61}{7} - \frac{131}{21}) - 11$

Simplify the numerator.

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Multiply $12$ by $2$ .

$\frac{1}{4} + \frac{24 + 3 \cdot 5}{10} \cdot \frac{5}{2} + (\frac{73}{12} \div 6 - \frac{73}{72}) \div (\frac{61}{7} - \frac{131}{21}) - 11$

Multiply $3$ by $5$ .

$\frac{1}{4} + \frac{24 + 15}{10} \cdot \frac{5}{2} + (\frac{73}{12} \div 6 - \frac{73}{72}) \div (\frac{61}{7} - \frac{131}{21}) - 11$

Add $24$ and $15$ .

$\frac{1}{4} + \frac{39}{10} \cdot \frac{5}{2} + (\frac{73}{12} \div 6 - \frac{73}{72}) \div (\frac{61}{7} - \frac{131}{21}) - 11$

Cancel the common factor of $5$ .

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Factor $5$ out of $10$ .

$\frac{1}{4} + \frac{39}{5 (2)} \cdot \frac{5}{2} + (\frac{73}{12} \div 6 - \frac{73}{72}) \div (\frac{61}{7} - \frac{131}{21}) - 11$

Cancel the common factor.

$\frac{1}{4} + \frac{39}{5 \cdot 2} \cdot \frac{5}{2} + (\frac{73}{12} \div 6 - \frac{73}{72}) \div (\frac{61}{7} - \frac{131}{21}) - 11$

Rewrite the expression.

$\frac{1}{4} + \frac{39}{2} \cdot \frac{1}{2} + (\frac{73}{12} \div 6 - \frac{73}{72}) \div (\frac{61}{7} - \frac{131}{21}) - 11$

Multiply $\frac{39}{2}$ and $\frac{1}{2}$ .

$\frac{1}{4} + \frac{39}{2 \cdot 2} + (\frac{73}{12} \div 6 - \frac{73}{72}) \div (\frac{61}{7} - \frac{131}{21}) - 11$

Multiply $2$ by $2$ .

$\frac{1}{4} + \frac{39}{4} + (\frac{73}{12} \div 6 - \frac{73}{72}) \div (\frac{61}{7} - \frac{131}{21}) - 11$

Rewrite the division as a fraction.

$\frac{1}{4} + \frac{39}{4} + \frac{\frac{73}{12} \div 6 - \frac{73}{72}}{\frac{61}{7} - \frac{131}{21}} - 11$

Multiply the numerator and denominator of the complex fraction by $504$ .

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Multiply $\frac{\frac{73}{12} \div 6 - \frac{73}{72}}{\frac{61}{7} - \frac{131}{21}}$ by $\frac{504}{504}$ .

$\frac{1}{4} + \frac{39}{4} + \frac{504}{504} \cdot \frac{\frac{73}{12} \div 6 - \frac{73}{72}}{\frac{61}{7} - \frac{131}{21}} - 11$

Combine.

$\frac{1}{4} + \frac{39}{4} + \frac{504 (\frac{73}{12} \div 6 - \frac{73}{72})}{504 (\frac{61}{7} - \frac{131}{21})} - 11$

Apply the distributive property.

$\frac{1}{4} + \frac{39}{4} + \frac{504 \frac{73}{12} \div 6 + 504 (- \frac{73}{72})}{504 (\frac{61}{7}) + 504 (- \frac{131}{21})} - 11$

Simplify by cancelling.

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Cancel the common factor of $72$ .

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Move the leading negative in $- \frac{73}{72}$ into the numerator.

$\frac{1}{4} + \frac{39}{4} + \frac{504 \frac{73}{12} \div 6 + 504 (\frac{- 73}{72})}{504 (\frac{61}{7}) + 504 (- \frac{131}{21})} - 11$

Factor $72$ out of $504$ .

$\frac{1}{4} + \frac{39}{4} + \frac{504 \frac{73}{12} \div 6 + 72 (7) \frac{- 73}{72}}{504 (\frac{61}{7}) + 504 (- \frac{131}{21})} - 11$

Cancel the common factor.

$\frac{1}{4} + \frac{39}{4} + \frac{504 \frac{73}{12} \div 6 + 72 \cdot 7 \frac{- 73}{72}}{504 (\frac{61}{7}) + 504 (- \frac{131}{21})} - 11$

Rewrite the expression.

$\frac{1}{4} + \frac{39}{4} + \frac{504 \frac{73}{12} \div 6 + 7 \cdot - 73}{504 (\frac{61}{7}) + 504 (- \frac{131}{21})} - 11$

Multiply $7$ by $- 73$ .

$\frac{1}{4} + \frac{39}{4} + \frac{504 \frac{73}{12} \div 6 - 511}{504 (\frac{61}{7}) + 504 (- \frac{131}{21})} - 11$

Cancel the common factor of $7$ .

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Factor $7$ out of $504$ .

$\frac{1}{4} + \frac{39}{4} + \frac{504 \frac{73}{12} \div 6 - 511}{7 (72) \frac{61}{7} + 504 (- \frac{131}{21})} - 11$

Cancel the common factor.

$\frac{1}{4} + \frac{39}{4} + \frac{504 \frac{73}{12} \div 6 - 511}{7 \cdot 72 \frac{61}{7} + 504 (- \frac{131}{21})} - 11$

Rewrite the expression.

$\frac{1}{4} + \frac{39}{4} + \frac{504 \frac{73}{12} \div 6 - 511}{72 \cdot 61 + 504 (- \frac{131}{21})} - 11$

Multiply $72$ by $61$ .

$\frac{1}{4} + \frac{39}{4} + \frac{504 \frac{73}{12} \div 6 - 511}{4392 + 504 (- \frac{131}{21})} - 11$

Cancel the common factor of $21$ .

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Move the leading negative in $- \frac{131}{21}$ into the numerator.

$\frac{1}{4} + \frac{39}{4} + \frac{504 \frac{73}{12} \div 6 - 511}{4392 + 504 (\frac{- 131}{21})} - 11$

Factor $21$ out of $504$ .

$\frac{1}{4} + \frac{39}{4} + \frac{504 \frac{73}{12} \div 6 - 511}{4392 + 21 (24) \frac{- 131}{21}} - 11$

Cancel the common factor.

$\frac{1}{4} + \frac{39}{4} + \frac{504 \frac{73}{12} \div 6 - 511}{4392 + 21 \cdot 24 \frac{- 131}{21}} - 11$

Rewrite the expression.

$\frac{1}{4} + \frac{39}{4} + \frac{504 \frac{73}{12} \div 6 - 511}{4392 + 24 \cdot - 131} - 11$

Multiply $24$ by $- 131$ .

$\frac{1}{4} + \frac{39}{4} + \frac{504 \frac{73}{12} \div 6 - 511}{4392 - 3144} - 11$

Simplify the numerator.

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Rewrite the division as a fraction.

$\frac{1}{4} + \frac{39}{4} + \frac{504 \frac{\frac{73}{12}}{6} - 511}{4392 - 3144} - 11$

Cancel the common factor of $6$ .

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Factor $6$ out of $504$ .

$\frac{1}{4} + \frac{39}{4} + \frac{6 (84) \frac{\frac{73}{12}}{6} - 511}{4392 - 3144} - 11$

Cancel the common factor.

$\frac{1}{4} + \frac{39}{4} + \frac{6 \cdot 84 \frac{\frac{73}{12}}{6} - 511}{4392 - 3144} - 11$

Rewrite the expression.

$\frac{1}{4} + \frac{39}{4} + \frac{84 (\frac{73}{12}) - 511}{4392 - 3144} - 11$

Combine $84$ and $\frac{73}{12}$ .

$\frac{1}{4} + \frac{39}{4} + \frac{\frac{84 \cdot 73}{12} - 511}{4392 - 3144} - 11$

Multiply $84$ by $73$ .

$\frac{1}{4} + \frac{39}{4} + \frac{\frac{6132}{12} - 511}{4392 - 3144} - 11$

Divide $6132$ by $12$ .

$\frac{1}{4} + \frac{39}{4} + \frac{511 - 511}{4392 - 3144} - 11$

Subtract $511$ from $511$ .

$\frac{1}{4} + \frac{39}{4} + \frac{0}{4392 - 3144} - 11$

Subtract $3144$ from $4392$ .

$\frac{1}{4} + \frac{39}{4} + \frac{0}{1248} - 11$

Divide $0$ by $1248$ .

$\frac{1}{4} + \frac{39}{4} + 0 - 11$

Combine fractions.

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Combine fractions with similar denominators.

$- 11 + \frac{1 + 39}{4}$

Simplify the expression.

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Add $1$ and $39$ .

$- 11 + \frac{40}{4}$

Divide $40$ by $4$ .

$- 11 + 10$

Add $- 11$ and $10$ .

$- 1$

Evaluate 1/4+(12/5+3/2)*5/2+((73/12)÷6-73/72)÷(61/7-131/21)-11

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