Solve 4+4/3(-5/2)3+2:2/3-2(1/2-frac{2}{3})

$$4 + \frac { 4 } { 3 } ( - \frac { 5 } { 2 } ) 3 + 2 : \frac { 2 } { 3 } - 2 ( \frac { 1 } { 2 } - \frac { 2 } { 3 } )$$

Evaluate

$$-\frac{8}{3}\approx -2.666666667$$

Solution Steps

Multiply \frac{4}{3} times -\frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$4+\frac{4\left(-5\right)}{3\times 2}\times 3+\frac{2}{\frac{2}{3}}-2\left(\frac{1}{2}-\frac{2}{3}\right)$$

Do the multiplications in the fraction \frac{4\left(-5\right)}{3\times 2}.

$$4+\frac{-20}{6}\times 3+\frac{2}{\frac{2}{3}}-2\left(\frac{1}{2}-\frac{2}{3}\right)$$

Reduce the fraction \frac{-20}{6} to lowest terms by extracting and canceling out 2.

$$4-\frac{10}{3}\times 3+\frac{2}{\frac{2}{3}}-2\left(\frac{1}{2}-\frac{2}{3}\right)$$

Cancel out 3 and 3.

$$4-10+\frac{2}{\frac{2}{3}}-2\left(\frac{1}{2}-\frac{2}{3}\right)$$

Subtract 10 from 4 to get -6.

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

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

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

Cancel out 2 and 2.

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

Add -6 and 3 to get -3.

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

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

$$-3-2\left(\frac{3}{6}-\frac{4}{6}\right)$$

Since \frac{3}{6} and \frac{4}{6} have the same denominator, subtract them by subtracting their numerators.

$$-3-2\times \frac{3-4}{6}$$

Subtract 4 from 3 to get -1.

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

Express 2\left(-\frac{1}{6}\right) as a single fraction.

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

Multiply 2 and -1 to get -2.

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

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

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

The opposite of -\frac{1}{3} is \frac{1}{3}.

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

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

$$-\frac{9}{3}+\frac{1}{3}$$

Since -\frac{9}{3} and \frac{1}{3} have the same denominator, add them by adding their numerators.

$$\frac{-9+1}{3}$$

Add -9 and 1 to get -8.

$$-\frac{8}{3}$$

Factor

$$-\frac{8}{3} = -2\frac{2}{3} = -2.6666666666666665$$