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

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

Evaluate

$$-\frac{3}{20}=-0.15$$

Solution Steps

Divide 3 by 3 to get 1.

$$\frac{\frac{1}{2}\times \frac{5}{4}-1}{2+\frac{\frac{2}{3}}{\frac{4}{3}}}$$

Multiply \frac{1}{2} times \frac{5}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{1\times 5}{2\times 4}-1}{2+\frac{\frac{2}{3}}{\frac{4}{3}}}$$

Do the multiplications in the fraction \frac{1\times 5}{2\times 4}.

$$\frac{\frac{5}{8}-1}{2+\frac{\frac{2}{3}}{\frac{4}{3}}}$$

Convert 1 to fraction \frac{8}{8}.

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

Since \frac{5}{8} and \frac{8}{8} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 8 from 5 to get -3.

$$\frac{-\frac{3}{8}}{2+\frac{\frac{2}{3}}{\frac{4}{3}}}$$

Divide \frac{2}{3} by \frac{4}{3} by multiplying \frac{2}{3} by the reciprocal of \frac{4}{3}.

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

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

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

Cancel out 3 in both numerator and denominator.

$$\frac{-\frac{3}{8}}{2+\frac{2}{4}}$$

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

$$\frac{-\frac{3}{8}}{2+\frac{1}{2}}$$

Convert 2 to fraction \frac{4}{2}.

$$\frac{-\frac{3}{8}}{\frac{4}{2}+\frac{1}{2}}$$

Since \frac{4}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

$$\frac{-\frac{3}{8}}{\frac{4+1}{2}}$$

Add 4 and 1 to get 5.

$$\frac{-\frac{3}{8}}{\frac{5}{2}}$$

Divide -\frac{3}{8} by \frac{5}{2} by multiplying -\frac{3}{8} by the reciprocal of \frac{5}{2}.

$$-\frac{3}{8}\times \frac{2}{5}$$

Multiply -\frac{3}{8} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-3\times 2}{8\times 5}$$

Do the multiplications in the fraction \frac{-3\times 2}{8\times 5}.

$$\frac{-6}{40}$$

Reduce the fraction \frac{-6}{40} to lowest terms by extracting and canceling out 2.

$$-\frac{3}{20}$$

Factor

$$-\frac{3}{20} = -0.15$$