Solve -|1/1+frac{1{2+3}}-3-2/1+frac{2{9-5}}+6-7/4|

$$- | \frac { 1 } { 1 + \frac { 1 } { 2 + 3 } } - \frac { 3 - 2 } { 1 + \frac { 2 } { 9 - 5 } } + \frac { 6 - 7 } { 4 } |$$

Evaluate

$$-\frac{1}{12}\approx -0.083333333$$

Solution Steps

Add 2 and 3 to get 5.

$$-|\frac{1}{1+\frac{1}{5}}-\frac{3-2}{1+\frac{2}{9-5}}+\frac{6-7}{4}|$$

Convert 1 to fraction \frac{5}{5}.

$$-|\frac{1}{\frac{5}{5}+\frac{1}{5}}-\frac{3-2}{1+\frac{2}{9-5}}+\frac{6-7}{4}|$$

Since \frac{5}{5} and \frac{1}{5} have the same denominator, add them by adding their numerators.

$$-|\frac{1}{\frac{5+1}{5}}-\frac{3-2}{1+\frac{2}{9-5}}+\frac{6-7}{4}|$$

Add 5 and 1 to get 6.

$$-|\frac{1}{\frac{6}{5}}-\frac{3-2}{1+\frac{2}{9-5}}+\frac{6-7}{4}|$$

Divide 1 by \frac{6}{5} by multiplying 1 by the reciprocal of \frac{6}{5}.

$$-|1\times \frac{5}{6}-\frac{3-2}{1+\frac{2}{9-5}}+\frac{6-7}{4}|$$

Multiply 1 and \frac{5}{6} to get \frac{5}{6}.

$$-|\frac{5}{6}-\frac{3-2}{1+\frac{2}{9-5}}+\frac{6-7}{4}|$$

Subtract 2 from 3 to get 1.

$$-|\frac{5}{6}-\frac{1}{1+\frac{2}{9-5}}+\frac{6-7}{4}|$$

Subtract 5 from 9 to get 4.

$$-|\frac{5}{6}-\frac{1}{1+\frac{2}{4}}+\frac{6-7}{4}|$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$-|\frac{5}{6}-\frac{1}{1+\frac{1}{2}}+\frac{6-7}{4}|$$

Convert 1 to fraction \frac{2}{2}.

$$-|\frac{5}{6}-\frac{1}{\frac{2}{2}+\frac{1}{2}}+\frac{6-7}{4}|$$

Since \frac{2}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

$$-|\frac{5}{6}-\frac{1}{\frac{2+1}{2}}+\frac{6-7}{4}|$$

Add 2 and 1 to get 3.

$$-|\frac{5}{6}-\frac{1}{\frac{3}{2}}+\frac{6-7}{4}|$$

Divide 1 by \frac{3}{2} by multiplying 1 by the reciprocal of \frac{3}{2}.

$$-|\frac{5}{6}-1\times \frac{2}{3}+\frac{6-7}{4}|$$

Multiply 1 and \frac{2}{3} to get \frac{2}{3}.

$$-|\frac{5}{6}-\frac{2}{3}+\frac{6-7}{4}|$$

Least common multiple of 6 and 3 is 6. Convert \frac{5}{6} and \frac{2}{3} to fractions with denominator 6.

$$-|\frac{5}{6}-\frac{4}{6}+\frac{6-7}{4}|$$

Since \frac{5}{6} and \frac{4}{6} have the same denominator, subtract them by subtracting their numerators.

$$-|\frac{5-4}{6}+\frac{6-7}{4}|$$

Subtract 4 from 5 to get 1.

$$-|\frac{1}{6}+\frac{6-7}{4}|$$

Subtract 7 from 6 to get -1.

$$-|\frac{1}{6}+\frac{-1}{4}|$$

Fraction \frac{-1}{4} can be rewritten as -\frac{1}{4} by extracting the negative sign.

$$-|\frac{1}{6}-\frac{1}{4}|$$

Least common multiple of 6 and 4 is 12. Convert \frac{1}{6} and \frac{1}{4} to fractions with denominator 12.

$$-|\frac{2}{12}-\frac{3}{12}|$$

Since \frac{2}{12} and \frac{3}{12} have the same denominator, subtract them by subtracting their numerators.

$$-|\frac{2-3}{12}|$$

Subtract 3 from 2 to get -1.

$$-|-\frac{1}{12}|$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{1}{12} is \frac{1}{12}.

$$-\frac{1}{12}$$

Factor

$$-\frac{1}{12} = -0.08333333333333333$$