Solve 1/3-(-1/3+1/12)+(-3)=

$$\frac { 1 } { 3 } - ( - \frac { 1 } { 3 } + \frac { 1 } { 12 } ) + ( - 3 ) =$$

Evaluate

$$-\frac{29}{12}\approx -2.416666667$$

Solution Steps

Least common multiple of 3 and 12 is 12. Convert -\frac{1}{3} and \frac{1}{12} to fractions with denominator 12.

$$\frac{1}{3}-\left(-\frac{4}{12}+\frac{1}{12}\right)-3$$

Since -\frac{4}{12} and \frac{1}{12} have the same denominator, add them by adding their numerators.

$$\frac{1}{3}-\frac{-4+1}{12}-3$$

Add -4 and 1 to get -3.

$$\frac{1}{3}-\frac{-3}{12}-3$$

Reduce the fraction \frac{-3}{12} to lowest terms by extracting and canceling out 3.

$$\frac{1}{3}-\left(-\frac{1}{4}\right)-3$$

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

$$\frac{1}{3}+\frac{1}{4}-3$$

Least common multiple of 3 and 4 is 12. Convert \frac{1}{3} and \frac{1}{4} to fractions with denominator 12.

$$\frac{4}{12}+\frac{3}{12}-3$$

Since \frac{4}{12} and \frac{3}{12} have the same denominator, add them by adding their numerators.

$$\frac{4+3}{12}-3$$

Add 4 and 3 to get 7.

$$\frac{7}{12}-3$$

Convert 3 to fraction \frac{36}{12}.

$$\frac{7}{12}-\frac{36}{12}$$

Since \frac{7}{12} and \frac{36}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7-36}{12}$$

Subtract 36 from 7 to get -29.

$$-\frac{29}{12}$$

Factor

$$-\frac{29}{12} = -2\frac{5}{12} = -2.4166666666666665$$