Solve -1/6+frac{1/1-(-frac{1{4})}-7/12}{(4-5/frac{2{7}-1})*(-1)}

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

Evaluate

$$-\frac{1}{220}\approx -0.004545455$$

Solution Steps

The opposite of -\frac{1}{4} is \frac{1}{4}.

$$\frac{-\frac{1}{6}+\frac{1}{1+\frac{1}{4}}-\frac{7}{12}}{\left(4-\frac{5}{\frac{2}{7}-1}\right)\left(-1\right)}$$

Convert 1 to fraction \frac{4}{4}.

$$\frac{-\frac{1}{6}+\frac{1}{\frac{4}{4}+\frac{1}{4}}-\frac{7}{12}}{\left(4-\frac{5}{\frac{2}{7}-1}\right)\left(-1\right)}$$

Since \frac{4}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

$$\frac{-\frac{1}{6}+\frac{1}{\frac{4+1}{4}}-\frac{7}{12}}{\left(4-\frac{5}{\frac{2}{7}-1}\right)\left(-1\right)}$$

Add 4 and 1 to get 5.

$$\frac{-\frac{1}{6}+\frac{1}{\frac{5}{4}}-\frac{7}{12}}{\left(4-\frac{5}{\frac{2}{7}-1}\right)\left(-1\right)}$$

Divide 1 by \frac{5}{4} by multiplying 1 by the reciprocal of \frac{5}{4}.

$$\frac{-\frac{1}{6}+1\times \frac{4}{5}-\frac{7}{12}}{\left(4-\frac{5}{\frac{2}{7}-1}\right)\left(-1\right)}$$

Multiply 1 and \frac{4}{5} to get \frac{4}{5}.

$$\frac{-\frac{1}{6}+\frac{4}{5}-\frac{7}{12}}{\left(4-\frac{5}{\frac{2}{7}-1}\right)\left(-1\right)}$$

Least common multiple of 6 and 5 is 30. Convert -\frac{1}{6} and \frac{4}{5} to fractions with denominator 30.

$$\frac{-\frac{5}{30}+\frac{24}{30}-\frac{7}{12}}{\left(4-\frac{5}{\frac{2}{7}-1}\right)\left(-1\right)}$$

Since -\frac{5}{30} and \frac{24}{30} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-5+24}{30}-\frac{7}{12}}{\left(4-\frac{5}{\frac{2}{7}-1}\right)\left(-1\right)}$$

Add -5 and 24 to get 19.

$$\frac{\frac{19}{30}-\frac{7}{12}}{\left(4-\frac{5}{\frac{2}{7}-1}\right)\left(-1\right)}$$

Least common multiple of 30 and 12 is 60. Convert \frac{19}{30} and \frac{7}{12} to fractions with denominator 60.

$$\frac{\frac{38}{60}-\frac{35}{60}}{\left(4-\frac{5}{\frac{2}{7}-1}\right)\left(-1\right)}$$

Since \frac{38}{60} and \frac{35}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{38-35}{60}}{\left(4-\frac{5}{\frac{2}{7}-1}\right)\left(-1\right)}$$

Subtract 35 from 38 to get 3.

$$\frac{\frac{3}{60}}{\left(4-\frac{5}{\frac{2}{7}-1}\right)\left(-1\right)}$$

Reduce the fraction \frac{3}{60} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{1}{20}}{\left(4-\frac{5}{\frac{2}{7}-1}\right)\left(-1\right)}$$

Convert 1 to fraction \frac{7}{7}.

$$\frac{\frac{1}{20}}{\left(4-\frac{5}{\frac{2}{7}-\frac{7}{7}}\right)\left(-1\right)}$$

Since \frac{2}{7} and \frac{7}{7} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1}{20}}{\left(4-\frac{5}{\frac{2-7}{7}}\right)\left(-1\right)}$$

Subtract 7 from 2 to get -5.

$$\frac{\frac{1}{20}}{\left(4-\frac{5}{-\frac{5}{7}}\right)\left(-1\right)}$$

Divide 5 by -\frac{5}{7} by multiplying 5 by the reciprocal of -\frac{5}{7}.

$$\frac{\frac{1}{20}}{\left(4-5\left(-\frac{7}{5}\right)\right)\left(-1\right)}$$

Cancel out 5 and 5.

$$\frac{\frac{1}{20}}{\left(4-\left(-7\right)\right)\left(-1\right)}$$

The opposite of -7 is 7.

$$\frac{\frac{1}{20}}{\left(4+7\right)\left(-1\right)}$$

Add 4 and 7 to get 11.

$$\frac{\frac{1}{20}}{11\left(-1\right)}$$

Multiply 11 and -1 to get -11.

$$\frac{\frac{1}{20}}{-11}$$

Express \frac{\frac{1}{20}}{-11} as a single fraction.

$$\frac{1}{20\left(-11\right)}$$

Multiply 20 and -11 to get -220.

$$\frac{1}{-220}$$

Fraction \frac{1}{-220} can be rewritten as -\frac{1}{220} by extracting the negative sign.

$$-\frac{1}{220}$$

Factor

$$-\frac{1}{220} = -0.004545454545454545$$