Solve -1^2+|-2-1|div6*(1/3-1/2)

$$- 1 ^ { 2 } + | - 2 - 1 | \div 6 \times ( \frac { 1 } { 3 } - \frac { 1 } { 2 } )$$

Evaluate

$$-\frac{13}{12}\approx -1.083333333$$

Solution Steps

Calculate 1 to the power of 2 and get 1.

$$-1+\frac{|-2-1|}{6}\left(\frac{1}{3}-\frac{1}{2}\right)$$

Subtract 1 from -2 to get -3.

$$-1+\frac{|-3|}{6}\left(\frac{1}{3}-\frac{1}{2}\right)$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -3 is 3.

$$-1+\frac{3}{6}\left(\frac{1}{3}-\frac{1}{2}\right)$$

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

$$-1+\frac{1}{2}\left(\frac{1}{3}-\frac{1}{2}\right)$$

Least common multiple of 3 and 2 is 6. Convert \frac{1}{3} and \frac{1}{2} to fractions with denominator 6.

$$-1+\frac{1}{2}\left(\frac{2}{6}-\frac{3}{6}\right)$$

Since \frac{2}{6} and \frac{3}{6} have the same denominator, subtract them by subtracting their numerators.

$$-1+\frac{1}{2}\times \frac{2-3}{6}$$

Subtract 3 from 2 to get -1.

$$-1+\frac{1}{2}\left(-\frac{1}{6}\right)$$

Multiply \frac{1}{2} times -\frac{1}{6} by multiplying numerator times numerator and denominator times denominator.

$$-1+\frac{1\left(-1\right)}{2\times 6}$$

Do the multiplications in the fraction \frac{1\left(-1\right)}{2\times 6}.

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

Fraction \frac{-1}{12} can be rewritten as -\frac{1}{12} by extracting the negative sign.

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

Convert -1 to fraction -\frac{12}{12}.

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

Since -\frac{12}{12} and \frac{1}{12} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 1 from -12 to get -13.

$$-\frac{13}{12}$$

Factor

$$-\frac{13}{12} = -1\frac{1}{12} = -1.0833333333333333$$