Solve {1/4*8/5:[1/20+(9/8-frac{3}{4}:frac{5}{3})-frac{7}{10}+(frac{3}{5}+frac{1}{2})+frac{7}{8}]+frac{2}{5}:frac{1}{2}}-frac{1}{2}=

$$\{ \frac { 1 } { 4 } \cdot \frac { 8 } { 5 } : [ \frac { 1 } { 20 } + ( \frac { 9 } { 8 } - \frac { 3 } { 4 } : \frac { 5 } { 3 } ) - \frac { 7 } { 10 } + ( \frac { 3 } { 5 } + \frac { 1 } { 2 } ) + \frac { 7 } { 8 } ] + \frac { 2 } { 5 } : \frac { 1 } { 2 } \} - \frac { 1 } { 2 } =$$

Evaluate

$$\frac{1}{2}=0.5$$

Solution Steps

Multiply \frac{1}{4} times \frac{8}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{1\times 8}{4\times 5}}{\frac{1}{20}+\frac{9}{8}-\frac{\frac{3}{4}}{\frac{5}{3}}-\frac{7}{10}+\frac{3}{5}+\frac{1}{2}+\frac{7}{8}}+\frac{\frac{2}{5}}{\frac{1}{2}}-\frac{1}{2}$$

Do the multiplications in the fraction \frac{1\times 8}{4\times 5}.

$$\frac{\frac{8}{20}}{\frac{1}{20}+\frac{9}{8}-\frac{\frac{3}{4}}{\frac{5}{3}}-\frac{7}{10}+\frac{3}{5}+\frac{1}{2}+\frac{7}{8}}+\frac{\frac{2}{5}}{\frac{1}{2}}-\frac{1}{2}$$

Reduce the fraction \frac{8}{20} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{2}{5}}{\frac{1}{20}+\frac{9}{8}-\frac{\frac{3}{4}}{\frac{5}{3}}-\frac{7}{10}+\frac{3}{5}+\frac{1}{2}+\frac{7}{8}}+\frac{\frac{2}{5}}{\frac{1}{2}}-\frac{1}{2}$$

Least common multiple of 20 and 8 is 40. Convert \frac{1}{20} and \frac{9}{8} to fractions with denominator 40.

$$\frac{\frac{2}{5}}{\frac{2}{40}+\frac{45}{40}-\frac{\frac{3}{4}}{\frac{5}{3}}-\frac{7}{10}+\frac{3}{5}+\frac{1}{2}+\frac{7}{8}}+\frac{\frac{2}{5}}{\frac{1}{2}}-\frac{1}{2}$$

Since \frac{2}{40} and \frac{45}{40} have the same denominator, add them by adding their numerators.

$$\frac{\frac{2}{5}}{\frac{2+45}{40}-\frac{\frac{3}{4}}{\frac{5}{3}}-\frac{7}{10}+\frac{3}{5}+\frac{1}{2}+\frac{7}{8}}+\frac{\frac{2}{5}}{\frac{1}{2}}-\frac{1}{2}$$

Add 2 and 45 to get 47.

$$\frac{\frac{2}{5}}{\frac{47}{40}-\frac{\frac{3}{4}}{\frac{5}{3}}-\frac{7}{10}+\frac{3}{5}+\frac{1}{2}+\frac{7}{8}}+\frac{\frac{2}{5}}{\frac{1}{2}}-\frac{1}{2}$$

Divide \frac{3}{4} by \frac{5}{3} by multiplying \frac{3}{4} by the reciprocal of \frac{5}{3}.

$$\frac{\frac{2}{5}}{\frac{47}{40}-\frac{3}{4}\times \frac{3}{5}-\frac{7}{10}+\frac{3}{5}+\frac{1}{2}+\frac{7}{8}}+\frac{\frac{2}{5}}{\frac{1}{2}}-\frac{1}{2}$$

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

$$\frac{\frac{2}{5}}{\frac{47}{40}-\frac{3\times 3}{4\times 5}-\frac{7}{10}+\frac{3}{5}+\frac{1}{2}+\frac{7}{8}}+\frac{\frac{2}{5}}{\frac{1}{2}}-\frac{1}{2}$$

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

$$\frac{\frac{2}{5}}{\frac{47}{40}-\frac{9}{20}-\frac{7}{10}+\frac{3}{5}+\frac{1}{2}+\frac{7}{8}}+\frac{\frac{2}{5}}{\frac{1}{2}}-\frac{1}{2}$$

Least common multiple of 40 and 20 is 40. Convert \frac{47}{40} and \frac{9}{20} to fractions with denominator 40.

$$\frac{\frac{2}{5}}{\frac{47}{40}-\frac{18}{40}-\frac{7}{10}+\frac{3}{5}+\frac{1}{2}+\frac{7}{8}}+\frac{\frac{2}{5}}{\frac{1}{2}}-\frac{1}{2}$$

Since \frac{47}{40} and \frac{18}{40} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{2}{5}}{\frac{47-18}{40}-\frac{7}{10}+\frac{3}{5}+\frac{1}{2}+\frac{7}{8}}+\frac{\frac{2}{5}}{\frac{1}{2}}-\frac{1}{2}$$

Subtract 18 from 47 to get 29.

$$\frac{\frac{2}{5}}{\frac{29}{40}-\frac{7}{10}+\frac{3}{5}+\frac{1}{2}+\frac{7}{8}}+\frac{\frac{2}{5}}{\frac{1}{2}}-\frac{1}{2}$$

Least common multiple of 40 and 10 is 40. Convert \frac{29}{40} and \frac{7}{10} to fractions with denominator 40.

$$\frac{\frac{2}{5}}{\frac{29}{40}-\frac{28}{40}+\frac{3}{5}+\frac{1}{2}+\frac{7}{8}}+\frac{\frac{2}{5}}{\frac{1}{2}}-\frac{1}{2}$$

Since \frac{29}{40} and \frac{28}{40} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{2}{5}}{\frac{29-28}{40}+\frac{3}{5}+\frac{1}{2}+\frac{7}{8}}+\frac{\frac{2}{5}}{\frac{1}{2}}-\frac{1}{2}$$

Subtract 28 from 29 to get 1.

$$\frac{\frac{2}{5}}{\frac{1}{40}+\frac{3}{5}+\frac{1}{2}+\frac{7}{8}}+\frac{\frac{2}{5}}{\frac{1}{2}}-\frac{1}{2}$$

Least common multiple of 40 and 5 is 40. Convert \frac{1}{40} and \frac{3}{5} to fractions with denominator 40.

$$\frac{\frac{2}{5}}{\frac{1}{40}+\frac{24}{40}+\frac{1}{2}+\frac{7}{8}}+\frac{\frac{2}{5}}{\frac{1}{2}}-\frac{1}{2}$$

Since \frac{1}{40} and \frac{24}{40} have the same denominator, add them by adding their numerators.

$$\frac{\frac{2}{5}}{\frac{1+24}{40}+\frac{1}{2}+\frac{7}{8}}+\frac{\frac{2}{5}}{\frac{1}{2}}-\frac{1}{2}$$

Add 1 and 24 to get 25.

$$\frac{\frac{2}{5}}{\frac{25}{40}+\frac{1}{2}+\frac{7}{8}}+\frac{\frac{2}{5}}{\frac{1}{2}}-\frac{1}{2}$$

Reduce the fraction \frac{25}{40} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{2}{5}}{\frac{5}{8}+\frac{1}{2}+\frac{7}{8}}+\frac{\frac{2}{5}}{\frac{1}{2}}-\frac{1}{2}$$

Least common multiple of 8 and 2 is 8. Convert \frac{5}{8} and \frac{1}{2} to fractions with denominator 8.

$$\frac{\frac{2}{5}}{\frac{5}{8}+\frac{4}{8}+\frac{7}{8}}+\frac{\frac{2}{5}}{\frac{1}{2}}-\frac{1}{2}$$

Since \frac{5}{8} and \frac{4}{8} have the same denominator, add them by adding their numerators.

$$\frac{\frac{2}{5}}{\frac{5+4}{8}+\frac{7}{8}}+\frac{\frac{2}{5}}{\frac{1}{2}}-\frac{1}{2}$$

Add 5 and 4 to get 9.

$$\frac{\frac{2}{5}}{\frac{9}{8}+\frac{7}{8}}+\frac{\frac{2}{5}}{\frac{1}{2}}-\frac{1}{2}$$

Since \frac{9}{8} and \frac{7}{8} have the same denominator, add them by adding their numerators.

$$\frac{\frac{2}{5}}{\frac{9+7}{8}}+\frac{\frac{2}{5}}{\frac{1}{2}}-\frac{1}{2}$$

Add 9 and 7 to get 16.

$$\frac{\frac{2}{5}}{\frac{16}{8}}+\frac{\frac{2}{5}}{\frac{1}{2}}-\frac{1}{2}$$

Divide 16 by 8 to get 2.

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

Express \frac{\frac{2}{5}}{2} as a single fraction.

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

Cancel out 2 in both numerator and denominator.

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

Divide \frac{2}{5} by \frac{1}{2} by multiplying \frac{2}{5} by the reciprocal of \frac{1}{2}.

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

Express \frac{2}{5}\times 2 as a single fraction.

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

Multiply 2 and 2 to get 4.

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

Since \frac{1}{5} and \frac{4}{5} have the same denominator, add them by adding their numerators.

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

Add 1 and 4 to get 5.

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

Divide 5 by 5 to get 1.

$$1-\frac{1}{2}$$

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

$$\frac{2}{2}-\frac{1}{2}$$

Since \frac{2}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2-1}{2}$$

Subtract 1 from 2 to get 1.

$$\frac{1}{2}$$

Factor

$$\frac{1}{2} = 0.5$$