Solve -1div(-|-2|)-1/3*[2-(-|-3|)div1/3]

$$- 1 \div ( - | - 2 | ) - \frac { 1 } { 3 } \times [ 2 - ( - | - 3 | ) \div \frac { 1 } { 3 } ]$$

Evaluate

$$-\frac{19}{6}\approx -3.166666667$$

Solution Steps

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -2 is 2.

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

Fraction \frac{-1}{-2} can be simplified to \frac{1}{2} by removing the negative sign from both the numerator and the denominator.

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

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.

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

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

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

Multiply -3 and 3 to get -9.

$$\frac{1}{2}-\frac{1}{3}\left(2-\left(-9\right)\right)$$

The opposite of -9 is 9.

$$\frac{1}{2}-\frac{1}{3}\left(2+9\right)$$

Add 2 and 9 to get 11.

$$\frac{1}{2}-\frac{1}{3}\times 11$$

Multiply \frac{1}{3} and 11 to get \frac{11}{3}.

$$\frac{1}{2}-\frac{11}{3}$$

Least common multiple of 2 and 3 is 6. Convert \frac{1}{2} and \frac{11}{3} to fractions with denominator 6.

$$\frac{3}{6}-\frac{22}{6}$$

Since \frac{3}{6} and \frac{22}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3-22}{6}$$

Subtract 22 from 3 to get -19.

$$-\frac{19}{6}$$

Factor

$$-\frac{19}{6} = -3\frac{1}{6} = -3.1666666666666665$$