Solve (3/10+1/2)*((13/8+1/2):3-frac{1}{4})*(2frac{1}{2}-(frac{3}{4}-(frac{1}{2}-frac{1}{2})))*frac{8}{72}=

$$( \frac { 3 } { 10 } + \frac { 1 } { 2 } ) \cdot ( ( 1 \frac { 3 } { 8 } + \frac { 1 } { 2 } ) : 3 - \frac { 1 } { 4 } ) \cdot ( 2 \frac { 1 } { 2 } - ( \frac { 3 } { 4 } - ( \frac { 1 } { 2 } - \frac { 1 } { 2 } ) ) ) \cdot \frac { 8 } { 72 } =$$

Evaluate

$$\frac{7}{120}\approx 0.058333333$$

Solution Steps

Least common multiple of 10 and 2 is 10. Convert \frac{3}{10} and \frac{1}{2} to fractions with denominator 10.

$$\left(\frac{3}{10}+\frac{5}{10}\right)\left(\frac{\frac{1\times 8+3}{8}+\frac{1}{2}}{3}-\frac{1}{4}\right)\left(\frac{2\times 2+1}{2}-\left(\frac{3}{4}-\left(\frac{1}{2}-\frac{1}{2}\right)\right)\right)\times \frac{8}{72}$$

Since \frac{3}{10} and \frac{5}{10} have the same denominator, add them by adding their numerators.

$$\frac{3+5}{10}\left(\frac{\frac{1\times 8+3}{8}+\frac{1}{2}}{3}-\frac{1}{4}\right)\left(\frac{2\times 2+1}{2}-\left(\frac{3}{4}-\left(\frac{1}{2}-\frac{1}{2}\right)\right)\right)\times \frac{8}{72}$$

Add 3 and 5 to get 8.

$$\frac{8}{10}\left(\frac{\frac{1\times 8+3}{8}+\frac{1}{2}}{3}-\frac{1}{4}\right)\left(\frac{2\times 2+1}{2}-\left(\frac{3}{4}-\left(\frac{1}{2}-\frac{1}{2}\right)\right)\right)\times \frac{8}{72}$$

Reduce the fraction \frac{8}{10} to lowest terms by extracting and canceling out 2.

$$\frac{4}{5}\left(\frac{\frac{1\times 8+3}{8}+\frac{1}{2}}{3}-\frac{1}{4}\right)\left(\frac{2\times 2+1}{2}-\left(\frac{3}{4}-\left(\frac{1}{2}-\frac{1}{2}\right)\right)\right)\times \frac{8}{72}$$

Multiply 1 and 8 to get 8.

$$\frac{4}{5}\left(\frac{\frac{8+3}{8}+\frac{1}{2}}{3}-\frac{1}{4}\right)\left(\frac{2\times 2+1}{2}-\left(\frac{3}{4}-\left(\frac{1}{2}-\frac{1}{2}\right)\right)\right)\times \frac{8}{72}$$

Add 8 and 3 to get 11.

$$\frac{4}{5}\left(\frac{\frac{11}{8}+\frac{1}{2}}{3}-\frac{1}{4}\right)\left(\frac{2\times 2+1}{2}-\left(\frac{3}{4}-\left(\frac{1}{2}-\frac{1}{2}\right)\right)\right)\times \frac{8}{72}$$

Least common multiple of 8 and 2 is 8. Convert \frac{11}{8} and \frac{1}{2} to fractions with denominator 8.

$$\frac{4}{5}\left(\frac{\frac{11}{8}+\frac{4}{8}}{3}-\frac{1}{4}\right)\left(\frac{2\times 2+1}{2}-\left(\frac{3}{4}-\left(\frac{1}{2}-\frac{1}{2}\right)\right)\right)\times \frac{8}{72}$$

Since \frac{11}{8} and \frac{4}{8} have the same denominator, add them by adding their numerators.

$$\frac{4}{5}\left(\frac{\frac{11+4}{8}}{3}-\frac{1}{4}\right)\left(\frac{2\times 2+1}{2}-\left(\frac{3}{4}-\left(\frac{1}{2}-\frac{1}{2}\right)\right)\right)\times \frac{8}{72}$$

Add 11 and 4 to get 15.

$$\frac{4}{5}\left(\frac{\frac{15}{8}}{3}-\frac{1}{4}\right)\left(\frac{2\times 2+1}{2}-\left(\frac{3}{4}-\left(\frac{1}{2}-\frac{1}{2}\right)\right)\right)\times \frac{8}{72}$$

Express \frac{\frac{15}{8}}{3} as a single fraction.

$$\frac{4}{5}\left(\frac{15}{8\times 3}-\frac{1}{4}\right)\left(\frac{2\times 2+1}{2}-\left(\frac{3}{4}-\left(\frac{1}{2}-\frac{1}{2}\right)\right)\right)\times \frac{8}{72}$$

Multiply 8 and 3 to get 24.

$$\frac{4}{5}\left(\frac{15}{24}-\frac{1}{4}\right)\left(\frac{2\times 2+1}{2}-\left(\frac{3}{4}-\left(\frac{1}{2}-\frac{1}{2}\right)\right)\right)\times \frac{8}{72}$$

Reduce the fraction \frac{15}{24} to lowest terms by extracting and canceling out 3.

$$\frac{4}{5}\left(\frac{5}{8}-\frac{1}{4}\right)\left(\frac{2\times 2+1}{2}-\left(\frac{3}{4}-\left(\frac{1}{2}-\frac{1}{2}\right)\right)\right)\times \frac{8}{72}$$

Least common multiple of 8 and 4 is 8. Convert \frac{5}{8} and \frac{1}{4} to fractions with denominator 8.

$$\frac{4}{5}\left(\frac{5}{8}-\frac{2}{8}\right)\left(\frac{2\times 2+1}{2}-\left(\frac{3}{4}-\left(\frac{1}{2}-\frac{1}{2}\right)\right)\right)\times \frac{8}{72}$$

Since \frac{5}{8} and \frac{2}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4}{5}\times \frac{5-2}{8}\left(\frac{2\times 2+1}{2}-\left(\frac{3}{4}-\left(\frac{1}{2}-\frac{1}{2}\right)\right)\right)\times \frac{8}{72}$$

Subtract 2 from 5 to get 3.

$$\frac{4}{5}\times \frac{3}{8}\left(\frac{2\times 2+1}{2}-\left(\frac{3}{4}-\left(\frac{1}{2}-\frac{1}{2}\right)\right)\right)\times \frac{8}{72}$$

Multiply \frac{4}{5} times \frac{3}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\times 3}{5\times 8}\left(\frac{2\times 2+1}{2}-\left(\frac{3}{4}-\left(\frac{1}{2}-\frac{1}{2}\right)\right)\right)\times \frac{8}{72}$$

Do the multiplications in the fraction \frac{4\times 3}{5\times 8}.

$$\frac{12}{40}\left(\frac{2\times 2+1}{2}-\left(\frac{3}{4}-\left(\frac{1}{2}-\frac{1}{2}\right)\right)\right)\times \frac{8}{72}$$

Reduce the fraction \frac{12}{40} to lowest terms by extracting and canceling out 4.

$$\frac{3}{10}\left(\frac{2\times 2+1}{2}-\left(\frac{3}{4}-\left(\frac{1}{2}-\frac{1}{2}\right)\right)\right)\times \frac{8}{72}$$

Multiply 2 and 2 to get 4.

$$\frac{3}{10}\left(\frac{4+1}{2}-\left(\frac{3}{4}-\left(\frac{1}{2}-\frac{1}{2}\right)\right)\right)\times \frac{8}{72}$$

Add 4 and 1 to get 5.

$$\frac{3}{10}\left(\frac{5}{2}-\left(\frac{3}{4}-\left(\frac{1}{2}-\frac{1}{2}\right)\right)\right)\times \frac{8}{72}$$

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

$$\frac{3}{10}\left(\frac{5}{2}-\left(\frac{3}{4}-0\right)\right)\times \frac{8}{72}$$

Subtract 0 from \frac{3}{4} to get \frac{3}{4}.

$$\frac{3}{10}\left(\frac{5}{2}-\frac{3}{4}\right)\times \frac{8}{72}$$

Least common multiple of 2 and 4 is 4. Convert \frac{5}{2} and \frac{3}{4} to fractions with denominator 4.

$$\frac{3}{10}\left(\frac{10}{4}-\frac{3}{4}\right)\times \frac{8}{72}$$

Since \frac{10}{4} and \frac{3}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{10}\times \frac{10-3}{4}\times \frac{8}{72}$$

Subtract 3 from 10 to get 7.

$$\frac{3}{10}\times \frac{7}{4}\times \frac{8}{72}$$

Multiply \frac{3}{10} times \frac{7}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 7}{10\times 4}\times \frac{8}{72}$$

Do the multiplications in the fraction \frac{3\times 7}{10\times 4}.

$$\frac{21}{40}\times \frac{8}{72}$$

Reduce the fraction \frac{8}{72} to lowest terms by extracting and canceling out 8.

$$\frac{21}{40}\times \frac{1}{9}$$

Multiply \frac{21}{40} times \frac{1}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{21\times 1}{40\times 9}$$

Do the multiplications in the fraction \frac{21\times 1}{40\times 9}.

$$\frac{21}{360}$$

Reduce the fraction \frac{21}{360} to lowest terms by extracting and canceling out 3.

$$\frac{7}{120}$$

Factor

$$\frac{7}{2 ^ {3} \cdot 3 \cdot 5} = 0.058333333333333334$$