Solve [(2/5)(4/3)-(1/3+2)]/1+[3(frac{1{2})]}=

$$\frac { [ ( \frac { 2 } { 5 } ) ( \frac { 4 } { 3 } ) - ( \frac { 1 } { 3 } + 2 ) ] } { 1 + [ 3 ( \frac { 1 } { 2 } ) ] } =$$

Evaluate

$$-\frac{18}{25}=-0.72$$

Solution Steps

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

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

Do the multiplications in the fraction \frac{2\times 4}{5\times 3}.

$$\frac{\frac{8}{15}-\left(\frac{1}{3}+2\right)}{1+3\times \frac{1}{2}}$$

Convert 2 to fraction \frac{6}{3}.

$$\frac{\frac{8}{15}-\left(\frac{1}{3}+\frac{6}{3}\right)}{1+3\times \frac{1}{2}}$$

Since \frac{1}{3} and \frac{6}{3} have the same denominator, add them by adding their numerators.

$$\frac{\frac{8}{15}-\frac{1+6}{3}}{1+3\times \frac{1}{2}}$$

Add 1 and 6 to get 7.

$$\frac{\frac{8}{15}-\frac{7}{3}}{1+3\times \frac{1}{2}}$$

Least common multiple of 15 and 3 is 15. Convert \frac{8}{15} and \frac{7}{3} to fractions with denominator 15.

$$\frac{\frac{8}{15}-\frac{35}{15}}{1+3\times \frac{1}{2}}$$

Since \frac{8}{15} and \frac{35}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{8-35}{15}}{1+3\times \frac{1}{2}}$$

Subtract 35 from 8 to get -27.

$$\frac{\frac{-27}{15}}{1+3\times \frac{1}{2}}$$

Reduce the fraction \frac{-27}{15} to lowest terms by extracting and canceling out 3.

$$\frac{-\frac{9}{5}}{1+3\times \frac{1}{2}}$$

Multiply 3 and \frac{1}{2} to get \frac{3}{2}.

$$\frac{-\frac{9}{5}}{1+\frac{3}{2}}$$

Convert 1 to fraction \frac{2}{2}.

$$\frac{-\frac{9}{5}}{\frac{2}{2}+\frac{3}{2}}$$

Since \frac{2}{2} and \frac{3}{2} have the same denominator, add them by adding their numerators.

$$\frac{-\frac{9}{5}}{\frac{2+3}{2}}$$

Add 2 and 3 to get 5.

$$\frac{-\frac{9}{5}}{\frac{5}{2}}$$

Divide -\frac{9}{5} by \frac{5}{2} by multiplying -\frac{9}{5} by the reciprocal of \frac{5}{2}.

$$-\frac{9}{5}\times \frac{2}{5}$$

Multiply -\frac{9}{5} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-9\times 2}{5\times 5}$$

Do the multiplications in the fraction \frac{-9\times 2}{5\times 5}.

$$\frac{-18}{25}$$

Fraction \frac{-18}{25} can be rewritten as -\frac{18}{25} by extracting the negative sign.

$$-\frac{18}{25}$$

Factor

$$-\frac{18}{25} = -0.72$$