Solve -3+[1/2*8/3-(-2/3:1/6)]=

$$- 3 + [ \frac { 1 } { 2 } \cdot \frac { 8 } { 3 } - ( - \frac { 2 } { 3 } : \frac { 1 } { 6 } ) ] =$$

Evaluate

$$\frac{7}{3}\approx 2.333333333$$

Solution Steps

Multiply \frac{1}{2} times \frac{8}{3} by multiplying numerator times numerator and denominator times denominator.

$$-3+\frac{1\times 8}{2\times 3}-\frac{-\frac{2}{3}}{\frac{1}{6}}$$

Do the multiplications in the fraction \frac{1\times 8}{2\times 3}.

$$-3+\frac{8}{6}-\frac{-\frac{2}{3}}{\frac{1}{6}}$$

Reduce the fraction \frac{8}{6} to lowest terms by extracting and canceling out 2.

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

Convert -3 to fraction -\frac{9}{3}.

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

Since -\frac{9}{3} and \frac{4}{3} have the same denominator, add them by adding their numerators.

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

Add -9 and 4 to get -5.

$$-\frac{5}{3}-\frac{-\frac{2}{3}}{\frac{1}{6}}$$

Divide -\frac{2}{3} by \frac{1}{6} by multiplying -\frac{2}{3} by the reciprocal of \frac{1}{6}.

$$-\frac{5}{3}-\left(-\frac{2}{3}\times 6\right)$$

Express -\frac{2}{3}\times 6 as a single fraction.

$$-\frac{5}{3}-\frac{-2\times 6}{3}$$

Multiply -2 and 6 to get -12.

$$-\frac{5}{3}-\frac{-12}{3}$$

Divide -12 by 3 to get -4.

$$-\frac{5}{3}-\left(-4\right)$$

The opposite of -4 is 4.

$$-\frac{5}{3}+4$$

Convert 4 to fraction \frac{12}{3}.

$$-\frac{5}{3}+\frac{12}{3}$$

Since -\frac{5}{3} and \frac{12}{3} have the same denominator, add them by adding their numerators.

$$\frac{-5+12}{3}$$

Add -5 and 12 to get 7.

$$\frac{7}{3}$$

Factor

$$\frac{7}{3} = 2\frac{1}{3} = 2.3333333333333335$$