Solve [1/6+2-(3/5+2/3)]-1/5*(frac{5*frac{1}{2}-frac{7}{3}}{2})

$$[ \frac { 1 } { 6 } + 2 - ( \frac { 3 } { 5 } + \frac { 2 } { 3 } ) ] - \frac { 1 } { 5 } \cdot ( \frac { 5 \cdot \frac { 1 } { 2 } - \frac { 7 } { 3 } } { 2 } )$$

Evaluate

$$\frac{53}{60}\approx 0.883333333$$

Solution Steps

Convert 2 to fraction \frac{12}{6}.

$$\frac{1}{6}+\frac{12}{6}-\left(\frac{3}{5}+\frac{2}{3}\right)-\frac{1}{5}\times \frac{5\times \frac{1}{2}-\frac{7}{3}}{2}$$

Since \frac{1}{6} and \frac{12}{6} have the same denominator, add them by adding their numerators.

$$\frac{1+12}{6}-\left(\frac{3}{5}+\frac{2}{3}\right)-\frac{1}{5}\times \frac{5\times \frac{1}{2}-\frac{7}{3}}{2}$$

Add 1 and 12 to get 13.

$$\frac{13}{6}-\left(\frac{3}{5}+\frac{2}{3}\right)-\frac{1}{5}\times \frac{5\times \frac{1}{2}-\frac{7}{3}}{2}$$

Least common multiple of 5 and 3 is 15. Convert \frac{3}{5} and \frac{2}{3} to fractions with denominator 15.

$$\frac{13}{6}-\left(\frac{9}{15}+\frac{10}{15}\right)-\frac{1}{5}\times \frac{5\times \frac{1}{2}-\frac{7}{3}}{2}$$

Since \frac{9}{15} and \frac{10}{15} have the same denominator, add them by adding their numerators.

$$\frac{13}{6}-\frac{9+10}{15}-\frac{1}{5}\times \frac{5\times \frac{1}{2}-\frac{7}{3}}{2}$$

Add 9 and 10 to get 19.

$$\frac{13}{6}-\frac{19}{15}-\frac{1}{5}\times \frac{5\times \frac{1}{2}-\frac{7}{3}}{2}$$

Least common multiple of 6 and 15 is 30. Convert \frac{13}{6} and \frac{19}{15} to fractions with denominator 30.

$$\frac{65}{30}-\frac{38}{30}-\frac{1}{5}\times \frac{5\times \frac{1}{2}-\frac{7}{3}}{2}$$

Since \frac{65}{30} and \frac{38}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{65-38}{30}-\frac{1}{5}\times \frac{5\times \frac{1}{2}-\frac{7}{3}}{2}$$

Subtract 38 from 65 to get 27.

$$\frac{27}{30}-\frac{1}{5}\times \frac{5\times \frac{1}{2}-\frac{7}{3}}{2}$$

Reduce the fraction \frac{27}{30} to lowest terms by extracting and canceling out 3.

$$\frac{9}{10}-\frac{1}{5}\times \frac{5\times \frac{1}{2}-\frac{7}{3}}{2}$$

Multiply 5 and \frac{1}{2} to get \frac{5}{2}.

$$\frac{9}{10}-\frac{1}{5}\times \frac{\frac{5}{2}-\frac{7}{3}}{2}$$

Least common multiple of 2 and 3 is 6. Convert \frac{5}{2} and \frac{7}{3} to fractions with denominator 6.

$$\frac{9}{10}-\frac{1}{5}\times \frac{\frac{15}{6}-\frac{14}{6}}{2}$$

Since \frac{15}{6} and \frac{14}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9}{10}-\frac{1}{5}\times \frac{\frac{15-14}{6}}{2}$$

Subtract 14 from 15 to get 1.

$$\frac{9}{10}-\frac{1}{5}\times \frac{\frac{1}{6}}{2}$$

Express \frac{\frac{1}{6}}{2} as a single fraction.

$$\frac{9}{10}-\frac{1}{5}\times \frac{1}{6\times 2}$$

Multiply 6 and 2 to get 12.

$$\frac{9}{10}-\frac{1}{5}\times \frac{1}{12}$$

Multiply \frac{1}{5} times \frac{1}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9}{10}-\frac{1\times 1}{5\times 12}$$

Do the multiplications in the fraction \frac{1\times 1}{5\times 12}.

$$\frac{9}{10}-\frac{1}{60}$$

Least common multiple of 10 and 60 is 60. Convert \frac{9}{10} and \frac{1}{60} to fractions with denominator 60.

$$\frac{54}{60}-\frac{1}{60}$$

Since \frac{54}{60} and \frac{1}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{54-1}{60}$$

Subtract 1 from 54 to get 53.

$$\frac{53}{60}$$

Factor

$$\frac{53}{2 ^ {2} \cdot 3 \cdot 5} = 0.8833333333333333$$