Solve (2-3/2)-1/2+(5/3-3/5)*frac{3}{8}:(2+frac{1}{2})

$$( 2 - \frac { 3 } { 2 } ) - \frac { 1 } { 2 } + ( \frac { 5 } { 3 } - \frac { 3 } { 5 } ) \times \frac { 3 } { 8 } : ( 2 + \frac { 1 } { 2 } )$$

Evaluate

$$\frac{4}{25}=0.16$$

Solution Steps

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

$$\frac{4}{2}-\frac{3}{2}-\frac{1}{2}+\frac{\left(\frac{5}{3}-\frac{3}{5}\right)\times \frac{3}{8}}{2+\frac{1}{2}}$$

Since \frac{4}{2} and \frac{3}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4-3}{2}-\frac{1}{2}+\frac{\left(\frac{5}{3}-\frac{3}{5}\right)\times \frac{3}{8}}{2+\frac{1}{2}}$$

Subtract 3 from 4 to get 1.

$$\frac{1}{2}-\frac{1}{2}+\frac{\left(\frac{5}{3}-\frac{3}{5}\right)\times \frac{3}{8}}{2+\frac{1}{2}}$$

Subtract \frac{1}{2} from \frac{1}{2} to get 0.

$$\frac{\left(\frac{5}{3}-\frac{3}{5}\right)\times \frac{3}{8}}{2+\frac{1}{2}}$$

Least common multiple of 3 and 5 is 15. Convert \frac{5}{3} and \frac{3}{5} to fractions with denominator 15.

$$\frac{\left(\frac{25}{15}-\frac{9}{15}\right)\times \frac{3}{8}}{2+\frac{1}{2}}$$

Since \frac{25}{15} and \frac{9}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{25-9}{15}\times \frac{3}{8}}{2+\frac{1}{2}}$$

Subtract 9 from 25 to get 16.

$$\frac{\frac{16}{15}\times \frac{3}{8}}{2+\frac{1}{2}}$$

Multiply \frac{16}{15} times \frac{3}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{16\times 3}{15\times 8}}{2+\frac{1}{2}}$$

Do the multiplications in the fraction \frac{16\times 3}{15\times 8}.

$$\frac{\frac{48}{120}}{2+\frac{1}{2}}$$

Reduce the fraction \frac{48}{120} to lowest terms by extracting and canceling out 24.

$$\frac{\frac{2}{5}}{2+\frac{1}{2}}$$

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

$$\frac{\frac{2}{5}}{\frac{4}{2}+\frac{1}{2}}$$

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

$$\frac{\frac{2}{5}}{\frac{4+1}{2}}$$

Add 4 and 1 to get 5.

$$\frac{\frac{2}{5}}{\frac{5}{2}}$$

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

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

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

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

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

$$\frac{4}{25}$$

Factor

$$\frac{2 ^ {2}}{5 ^ {2}} = 0.16$$