Solve -1/6+1/1-(-frac{1{4})}-1/12

$$- \frac { 1 } { 6 } + \frac { 1 } { 1 - ( - \frac { 1 } { 4 } ) } - \frac { 1 } { 12 }$$

Evaluate

$$\frac{11}{20}=0.55$$

Solution Steps

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

$$-\frac{1}{6}+\frac{1}{1+\frac{1}{4}}-\frac{1}{12}$$

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

$$-\frac{1}{6}+\frac{1}{\frac{4}{4}+\frac{1}{4}}-\frac{1}{12}$$

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

$$-\frac{1}{6}+\frac{1}{\frac{4+1}{4}}-\frac{1}{12}$$

Add 4 and 1 to get 5.

$$-\frac{1}{6}+\frac{1}{\frac{5}{4}}-\frac{1}{12}$$

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

$$-\frac{1}{6}+1\times \frac{4}{5}-\frac{1}{12}$$

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

$$-\frac{1}{6}+\frac{4}{5}-\frac{1}{12}$$

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

$$-\frac{5}{30}+\frac{24}{30}-\frac{1}{12}$$

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

$$\frac{-5+24}{30}-\frac{1}{12}$$

Add -5 and 24 to get 19.

$$\frac{19}{30}-\frac{1}{12}$$

Least common multiple of 30 and 12 is 60. Convert \frac{19}{30} and \frac{1}{12} to fractions with denominator 60.

$$\frac{38}{60}-\frac{5}{60}$$

Since \frac{38}{60} and \frac{5}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{38-5}{60}$$

Subtract 5 from 38 to get 33.

$$\frac{33}{60}$$

Reduce the fraction \frac{33}{60} to lowest terms by extracting and canceling out 3.

$$\frac{11}{20}$$

Factor

$$\frac{11}{2 ^ {2} \cdot 5} = 0.55$$