Solve 2/3[-6+12.2-(-11/3)]

$$\frac { 2 } { 3 } [ - 6 + 12.2 - ( - 1 \frac { 1 } { 3 } ) ]$$

Evaluate

$$\frac{226}{45}\approx 5.022222222$$

Solution Steps

Add -6 and 12.2 to get 6.2.

$$\frac{2}{3}\left(6.2-\left(-\frac{1\times 3+1}{3}\right)\right)$$

Multiply 1 and 3 to get 3.

$$\frac{2}{3}\left(6.2-\left(-\frac{3+1}{3}\right)\right)$$

Add 3 and 1 to get 4.

$$\frac{2}{3}\left(6.2-\left(-\frac{4}{3}\right)\right)$$

The opposite of -\frac{4}{3} is \frac{4}{3}.

$$\frac{2}{3}\left(6.2+\frac{4}{3}\right)$$

Convert decimal number 6.2 to fraction \frac{62}{10}. Reduce the fraction \frac{62}{10} to lowest terms by extracting and canceling out 2.

$$\frac{2}{3}\left(\frac{31}{5}+\frac{4}{3}\right)$$

Least common multiple of 5 and 3 is 15. Convert \frac{31}{5} and \frac{4}{3} to fractions with denominator 15.

$$\frac{2}{3}\left(\frac{93}{15}+\frac{20}{15}\right)$$

Since \frac{93}{15} and \frac{20}{15} have the same denominator, add them by adding their numerators.

$$\frac{2}{3}\times \frac{93+20}{15}$$

Add 93 and 20 to get 113.

$$\frac{2}{3}\times \frac{113}{15}$$

Multiply \frac{2}{3} times \frac{113}{15} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\times 113}{3\times 15}$$

Do the multiplications in the fraction \frac{2\times 113}{3\times 15}.

$$\frac{226}{45}$$

Factor

$$\frac{2 \cdot 113}{5 \cdot 3 ^ {2}} = 5\frac{1}{45} = 5.022222222222222$$