Solve 4/9-(-6div3/2)+(-4/3*1/2)-(-1)

$$\frac { 4 } { 9 } - ( - 6 \div \frac { 3 } { 2 } ) + ( - \frac { 4 } { 3 } \times \frac { 1 } { 2 } ) - ( - 1 )$$

Evaluate

$$\frac{43}{9}\approx 4.777777778$$

Solution Steps

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

$$\frac{4}{9}-\left(-6\times \frac{2}{3}\right)-\frac{4}{3}\times \frac{1}{2}-\left(-1\right)$$

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

$$\frac{4}{9}-\frac{-6\times 2}{3}-\frac{4}{3}\times \frac{1}{2}-\left(-1\right)$$

Multiply -6 and 2 to get -12.

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

Divide -12 by 3 to get -4.

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

The opposite of -4 is 4.

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

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

$$\frac{4}{9}+\frac{36}{9}-\frac{4}{3}\times \frac{1}{2}-\left(-1\right)$$

Since \frac{4}{9} and \frac{36}{9} have the same denominator, add them by adding their numerators.

$$\frac{4+36}{9}-\frac{4}{3}\times \frac{1}{2}-\left(-1\right)$$

Add 4 and 36 to get 40.

$$\frac{40}{9}-\frac{4}{3}\times \frac{1}{2}-\left(-1\right)$$

Multiply -\frac{4}{3} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{40}{9}+\frac{-4}{3\times 2}-\left(-1\right)$$

Do the multiplications in the fraction \frac{-4}{3\times 2}.

$$\frac{40}{9}+\frac{-4}{6}-\left(-1\right)$$

Reduce the fraction \frac{-4}{6} to lowest terms by extracting and canceling out 2.

$$\frac{40}{9}-\frac{2}{3}-\left(-1\right)$$

Least common multiple of 9 and 3 is 9. Convert \frac{40}{9} and \frac{2}{3} to fractions with denominator 9.

$$\frac{40}{9}-\frac{6}{9}-\left(-1\right)$$

Since \frac{40}{9} and \frac{6}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{40-6}{9}-\left(-1\right)$$

Subtract 6 from 40 to get 34.

$$\frac{34}{9}-\left(-1\right)$$

The opposite of -1 is 1.

$$\frac{34}{9}+1$$

Convert 1 to fraction \frac{9}{9}.

$$\frac{34}{9}+\frac{9}{9}$$

Since \frac{34}{9} and \frac{9}{9} have the same denominator, add them by adding their numerators.

$$\frac{34+9}{9}$$

Add 34 and 9 to get 43.

$$\frac{43}{9}$$

Factor

$$\frac{43}{3 ^ {2}} = 4\frac{7}{9} = 4.777777777777778$$