Solve 2[(+1/2-5/4+2/3):(+6/5)]*(+frac{8}{5})}+frac{3}{4}-frac{2}{3}+frac{1}{1}*(+frac{9}{4})-frac{2}{1}=

$$2 [ ( + \frac { 1 } { 2 } - \frac { 5 } { 4 } + \frac { 2 } { 3 } ) : ( + \frac { 6 } { 5 } ) ] \cdot ( + \frac { 8 } { 5 } ) \} + \frac { 3 } { 4 } - \frac { 2 } { 3 } + \frac { 1 } { 1 } \cdot ( + \frac { 9 } { 4 } ) - \frac { 2 } { 1 } =$$

Evaluate

$$-\frac{2}{9}\approx -0.222222222$$

Solution Steps

Least common multiple of 2 and 4 is 4. Convert \frac{1}{2} and \frac{5}{4} to fractions with denominator 4.

$$2\times \frac{\frac{2}{4}-\frac{5}{4}+\frac{2}{3}}{\frac{6}{5}}\times \frac{8}{5}$$

Since \frac{2}{4} and \frac{5}{4} have the same denominator, subtract them by subtracting their numerators.

$$2\times \frac{\frac{2-5}{4}+\frac{2}{3}}{\frac{6}{5}}\times \frac{8}{5}$$

Subtract 5 from 2 to get -3.

$$2\times \frac{-\frac{3}{4}+\frac{2}{3}}{\frac{6}{5}}\times \frac{8}{5}$$

Least common multiple of 4 and 3 is 12. Convert -\frac{3}{4} and \frac{2}{3} to fractions with denominator 12.

$$2\times \frac{-\frac{9}{12}+\frac{8}{12}}{\frac{6}{5}}\times \frac{8}{5}$$

Since -\frac{9}{12} and \frac{8}{12} have the same denominator, add them by adding their numerators.

$$2\times \frac{\frac{-9+8}{12}}{\frac{6}{5}}\times \frac{8}{5}$$

Add -9 and 8 to get -1.

$$2\times \frac{-\frac{1}{12}}{\frac{6}{5}}\times \frac{8}{5}$$

Divide -\frac{1}{12} by \frac{6}{5} by multiplying -\frac{1}{12} by the reciprocal of \frac{6}{5}.

$$2\left(-\frac{1}{12}\right)\times \frac{5}{6}\times \frac{8}{5}$$

Multiply -\frac{1}{12} times \frac{5}{6} by multiplying numerator times numerator and denominator times denominator.

$$2\times \frac{-5}{12\times 6}\times \frac{8}{5}$$

Do the multiplications in the fraction \frac{-5}{12\times 6}.

$$2\times \frac{-5}{72}\times \frac{8}{5}$$

Fraction \frac{-5}{72} can be rewritten as -\frac{5}{72} by extracting the negative sign.

$$2\left(-\frac{5}{72}\right)\times \frac{8}{5}$$

Express 2\left(-\frac{5}{72}\right) as a single fraction.

$$\frac{2\left(-5\right)}{72}\times \frac{8}{5}$$

Multiply 2 and -5 to get -10.

$$\frac{-10}{72}\times \frac{8}{5}$$

Reduce the fraction \frac{-10}{72} to lowest terms by extracting and canceling out 2.

$$-\frac{5}{36}\times \frac{8}{5}$$

Multiply -\frac{5}{36} times \frac{8}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-5\times 8}{36\times 5}$$

Do the multiplications in the fraction \frac{-5\times 8}{36\times 5}.

$$\frac{-40}{180}$$

Reduce the fraction \frac{-40}{180} to lowest terms by extracting and canceling out 20.

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

Factor

$$-\frac{2}{9} = -0.2222222222222222$$