Solve (-3)div21/4*(-2/3)+4-2*(-1/3)

$$( - 3 ) \div 2 \frac { 1 } { 4 } \times ( - \frac { 2 } { 3 } ) + 4 - 2 \times ( - \frac { 1 } { 3 } )$$

Evaluate

$$\frac{50}{9}\approx 5.555555556$$

Solution Steps

Divide -3 by \frac{2\times 4+1}{4} by multiplying -3 by the reciprocal of \frac{2\times 4+1}{4}.

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

Multiply -3 and 4 to get -12.

$$\frac{-12}{2\times 4+1}\left(-\frac{2}{3}\right)+4-2\left(-\frac{1}{3}\right)$$

Multiply 2 and 4 to get 8.

$$\frac{-12}{8+1}\left(-\frac{2}{3}\right)+4-2\left(-\frac{1}{3}\right)$$

Add 8 and 1 to get 9.

$$\frac{-12}{9}\left(-\frac{2}{3}\right)+4-2\left(-\frac{1}{3}\right)$$

Reduce the fraction \frac{-12}{9} to lowest terms by extracting and canceling out 3.

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

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

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

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

$$\frac{8}{9}+4-2\left(-\frac{1}{3}\right)$$

Convert 4 to fraction \frac{36}{9}.

$$\frac{8}{9}+\frac{36}{9}-2\left(-\frac{1}{3}\right)$$

Since \frac{8}{9} and \frac{36}{9} have the same denominator, add them by adding their numerators.

$$\frac{8+36}{9}-2\left(-\frac{1}{3}\right)$$

Add 8 and 36 to get 44.

$$\frac{44}{9}-2\left(-\frac{1}{3}\right)$$

Express 2\left(-\frac{1}{3}\right) as a single fraction.

$$\frac{44}{9}-\frac{2\left(-1\right)}{3}$$

Multiply 2 and -1 to get -2.

$$\frac{44}{9}-\frac{-2}{3}$$

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

$$\frac{44}{9}-\left(-\frac{2}{3}\right)$$

The opposite of -\frac{2}{3} is \frac{2}{3}.

$$\frac{44}{9}+\frac{2}{3}$$

Least common multiple of 9 and 3 is 9. Convert \frac{44}{9} and \frac{2}{3} to fractions with denominator 9.

$$\frac{44}{9}+\frac{6}{9}$$

Since \frac{44}{9} and \frac{6}{9} have the same denominator, add them by adding their numerators.

$$\frac{44+6}{9}$$

Add 44 and 6 to get 50.

$$\frac{50}{9}$$

Factor

$$\frac{2 \cdot 5 ^ {2}}{3 ^ {2}} = 5\frac{5}{9} = 5.555555555555555$$