Evaluate (7/(12+9/(16-1)))-(51/(24-2))+11/(12-5/8)

$(\frac{7}{12 + \frac{9}{16 - 1}}) - (\frac{51}{24 - 2}) + \frac{11}{12 - \frac{5}{8}}$

Simplify each term.

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Subtract $1$ from $16$ .

$\frac{7}{12 + \frac{9}{15}} - (\frac{51}{24 - 2}) + \frac{11}{12 - \frac{5}{8}}$

Simplify the denominator.

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To write $12$ as a fraction with a common denominator, multiply by $\frac{15}{15}$ .

$\frac{7}{12 \cdot \frac{15}{15} + \frac{9}{15}} - (\frac{51}{24 - 2}) + \frac{11}{12 - \frac{5}{8}}$

Combine $12$ and $\frac{15}{15}$ .

$\frac{7}{\frac{12 \cdot 15}{15} + \frac{9}{15}} - (\frac{51}{24 - 2}) + \frac{11}{12 - \frac{5}{8}}$

Combine the numerators over the common denominator.

$\frac{7}{\frac{12 \cdot 15 + 9}{15}} - (\frac{51}{24 - 2}) + \frac{11}{12 - \frac{5}{8}}$

Simplify the numerator.

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Multiply $12$ by $15$ .

$\frac{7}{\frac{180 + 9}{15}} - (\frac{51}{24 - 2}) + \frac{11}{12 - \frac{5}{8}}$

Add $180$ and $9$ .

$\frac{7}{\frac{189}{15}} - (\frac{51}{24 - 2}) + \frac{11}{12 - \frac{5}{8}}$

Cancel the common factor of $189$ and $15$ .

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Factor $3$ out of $189$ .

$\frac{7}{\frac{3 (63)}{15}} - (\frac{51}{24 - 2}) + \frac{11}{12 - \frac{5}{8}}$

Cancel the common factors.

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Factor $3$ out of $15$ .

$\frac{7}{\frac{3 \cdot 63}{3 \cdot 5}} - (\frac{51}{24 - 2}) + \frac{11}{12 - \frac{5}{8}}$

Cancel the common factor.

$\frac{7}{\frac{3 \cdot 63}{3 \cdot 5}} - (\frac{51}{24 - 2}) + \frac{11}{12 - \frac{5}{8}}$

Rewrite the expression.

$\frac{7}{\frac{63}{5}} - (\frac{51}{24 - 2}) + \frac{11}{12 - \frac{5}{8}}$

Multiply the numerator by the reciprocal of the denominator.

$7 (\frac{5}{63}) - (\frac{51}{24 - 2}) + \frac{11}{12 - \frac{5}{8}}$

Cancel the common factor of $7$ .

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Factor $7$ out of $63$ .

$7 \frac{5}{7 (9)} - (\frac{51}{24 - 2}) + \frac{11}{12 - \frac{5}{8}}$

Cancel the common factor.

$7 \frac{5}{7 \cdot 9} - (\frac{51}{24 - 2}) + \frac{11}{12 - \frac{5}{8}}$

Rewrite the expression.

$\frac{5}{9} - (\frac{51}{24 - 2}) + \frac{11}{12 - \frac{5}{8}}$

Subtract $2$ from $24$ .

$\frac{5}{9} - \frac{51}{22} + \frac{11}{12 - \frac{5}{8}}$

Simplify the denominator.

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To write $12$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{5}{9} - \frac{51}{22} + \frac{11}{12 \cdot \frac{8}{8} - \frac{5}{8}}$

Combine $12$ and $\frac{8}{8}$ .

$\frac{5}{9} - \frac{51}{22} + \frac{11}{\frac{12 \cdot 8}{8} - \frac{5}{8}}$

Combine the numerators over the common denominator.

$\frac{5}{9} - \frac{51}{22} + \frac{11}{\frac{12 \cdot 8 - 5}{8}}$

Simplify the numerator.

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Multiply $12$ by $8$ .

$\frac{5}{9} - \frac{51}{22} + \frac{11}{\frac{96 - 5}{8}}$

Subtract $5$ from $96$ .

$\frac{5}{9} - \frac{51}{22} + \frac{11}{\frac{91}{8}}$

Multiply the numerator by the reciprocal of the denominator.

$\frac{5}{9} - \frac{51}{22} + 11 (\frac{8}{91})$

Multiply $11 (\frac{8}{91})$ .

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Combine $11$ and $\frac{8}{91}$ .

$\frac{5}{9} - \frac{51}{22} + \frac{11 \cdot 8}{91}$

Multiply $11$ by $8$ .

$\frac{5}{9} - \frac{51}{22} + \frac{88}{91}$

To write $\frac{5}{9}$ as a fraction with a common denominator, multiply by $\frac{22}{22}$ .

$\frac{5}{9} \cdot \frac{22}{22} - \frac{51}{22} + \frac{88}{91}$

To write $- \frac{51}{22}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{5}{9} \cdot \frac{22}{22} - \frac{51}{22} \cdot \frac{9}{9} + \frac{88}{91}$

Write each expression with a common denominator of $198$ , by multiplying each by an appropriate factor of $1$ .

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Multiply $\frac{5}{9}$ and $\frac{22}{22}$ .

$\frac{5 \cdot 22}{9 \cdot 22} - \frac{51}{22} \cdot \frac{9}{9} + \frac{88}{91}$

Multiply $9$ by $22$ .

$\frac{5 \cdot 22}{198} - \frac{51}{22} \cdot \frac{9}{9} + \frac{88}{91}$

Multiply $\frac{51}{22}$ and $\frac{9}{9}$ .

$\frac{5 \cdot 22}{198} - \frac{51 \cdot 9}{22 \cdot 9} + \frac{88}{91}$

Multiply $22$ by $9$ .

$\frac{5 \cdot 22}{198} - \frac{51 \cdot 9}{198} + \frac{88}{91}$

Combine the numerators over the common denominator.

$\frac{5 \cdot 22 - 51 \cdot 9}{198} + \frac{88}{91}$

Simplify the numerator.

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Multiply $5$ by $22$ .

$\frac{110 - 51 \cdot 9}{198} + \frac{88}{91}$

Multiply $- 51$ by $9$ .

$\frac{110 - 459}{198} + \frac{88}{91}$

Subtract $459$ from $110$ .

$\frac{- 349}{198} + \frac{88}{91}$

Move the negative in front of the fraction.

$- \frac{349}{198} + \frac{88}{91}$

To write $- \frac{349}{198}$ as a fraction with a common denominator, multiply by $\frac{91}{91}$ .

$- \frac{349}{198} \cdot \frac{91}{91} + \frac{88}{91}$

To write $\frac{88}{91}$ as a fraction with a common denominator, multiply by $\frac{198}{198}$ .

$- \frac{349}{198} \cdot \frac{91}{91} + \frac{88}{91} \cdot \frac{198}{198}$

Write each expression with a common denominator of $18018$ , by multiplying each by an appropriate factor of $1$ .

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Multiply $\frac{349}{198}$ and $\frac{91}{91}$ .

$- \frac{349 \cdot 91}{198 \cdot 91} + \frac{88}{91} \cdot \frac{198}{198}$

Multiply $198$ by $91$ .

$- \frac{349 \cdot 91}{18018} + \frac{88}{91} \cdot \frac{198}{198}$

Multiply $\frac{88}{91}$ and $\frac{198}{198}$ .

$- \frac{349 \cdot 91}{18018} + \frac{88 \cdot 198}{91 \cdot 198}$

Multiply $91$ by $198$ .

$- \frac{349 \cdot 91}{18018} + \frac{88 \cdot 198}{18018}$

Combine the numerators over the common denominator.

$\frac{- 349 \cdot 91 + 88 \cdot 198}{18018}$

Simplify the numerator.

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Multiply $- 349$ by $91$ .

$\frac{- 31759 + 88 \cdot 198}{18018}$

Multiply $88$ by $198$ .

$\frac{- 31759 + 17424}{18018}$

Add $- 31759$ and $17424$ .

$\frac{- 14335}{18018}$

Move the negative in front of the fraction.

$- \frac{14335}{18018}$

The result can be shown in multiple forms.

Exact Form:

$- \frac{14335}{18018}$

Decimal Form:

$- 0.7\overline{955932}$

Evaluate (7/(12+9/(16-1)))-(51/(24-2))+11/(12-5/8)

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