Solve 2-1/3/8+frac{5/6/3}{(5divfrac{1}{8})*(frac{1}{5}divfrac{1}{10})}

$$\frac { \frac { 2 - \frac { 1 } { 3 } } { 8 } + \frac { \frac { 5 } { 6 } } { 3 } } { ( 5 \div \frac { 1 } { 8 } ) \cdot ( \frac { 1 } { 5 } \div \frac { 1 } { 10 } ) }$$

Evaluate

$$\frac{7}{1152}\approx 0.006076389$$

Solution Steps

Convert 2 to fraction \frac{6}{3}.

$$\frac{\frac{\frac{6}{3}-\frac{1}{3}}{8}+\frac{\frac{5}{6}}{3}}{\frac{5}{\frac{1}{8}}\times \frac{\frac{1}{5}}{\frac{1}{10}}}$$

Since \frac{6}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{\frac{6-1}{3}}{8}+\frac{\frac{5}{6}}{3}}{\frac{5}{\frac{1}{8}}\times \frac{\frac{1}{5}}{\frac{1}{10}}}$$

Subtract 1 from 6 to get 5.

$$\frac{\frac{\frac{5}{3}}{8}+\frac{\frac{5}{6}}{3}}{\frac{5}{\frac{1}{8}}\times \frac{\frac{1}{5}}{\frac{1}{10}}}$$

Express \frac{\frac{5}{3}}{8} as a single fraction.

$$\frac{\frac{5}{3\times 8}+\frac{\frac{5}{6}}{3}}{\frac{5}{\frac{1}{8}}\times \frac{\frac{1}{5}}{\frac{1}{10}}}$$

Multiply 3 and 8 to get 24.

$$\frac{\frac{5}{24}+\frac{\frac{5}{6}}{3}}{\frac{5}{\frac{1}{8}}\times \frac{\frac{1}{5}}{\frac{1}{10}}}$$

Express \frac{\frac{5}{6}}{3} as a single fraction.

$$\frac{\frac{5}{24}+\frac{5}{6\times 3}}{\frac{5}{\frac{1}{8}}\times \frac{\frac{1}{5}}{\frac{1}{10}}}$$

Multiply 6 and 3 to get 18.

$$\frac{\frac{5}{24}+\frac{5}{18}}{\frac{5}{\frac{1}{8}}\times \frac{\frac{1}{5}}{\frac{1}{10}}}$$

Least common multiple of 24 and 18 is 72. Convert \frac{5}{24} and \frac{5}{18} to fractions with denominator 72.

$$\frac{\frac{15}{72}+\frac{20}{72}}{\frac{5}{\frac{1}{8}}\times \frac{\frac{1}{5}}{\frac{1}{10}}}$$

Since \frac{15}{72} and \frac{20}{72} have the same denominator, add them by adding their numerators.

$$\frac{\frac{15+20}{72}}{\frac{5}{\frac{1}{8}}\times \frac{\frac{1}{5}}{\frac{1}{10}}}$$

Add 15 and 20 to get 35.

$$\frac{\frac{35}{72}}{\frac{5}{\frac{1}{8}}\times \frac{\frac{1}{5}}{\frac{1}{10}}}$$

Divide 5 by \frac{1}{8} by multiplying 5 by the reciprocal of \frac{1}{8}.

$$\frac{\frac{35}{72}}{5\times 8\times \frac{\frac{1}{5}}{\frac{1}{10}}}$$

Multiply 5 and 8 to get 40.

$$\frac{\frac{35}{72}}{40\times \frac{\frac{1}{5}}{\frac{1}{10}}}$$

Divide \frac{1}{5} by \frac{1}{10} by multiplying \frac{1}{5} by the reciprocal of \frac{1}{10}.

$$\frac{\frac{35}{72}}{40\times \frac{1}{5}\times 10}$$

Multiply \frac{1}{5} and 10 to get \frac{10}{5}.

$$\frac{\frac{35}{72}}{40\times \frac{10}{5}}$$

Divide 10 by 5 to get 2.

$$\frac{\frac{35}{72}}{40\times 2}$$

Multiply 40 and 2 to get 80.

$$\frac{\frac{35}{72}}{80}$$

Express \frac{\frac{35}{72}}{80} as a single fraction.

$$\frac{35}{72\times 80}$$

Multiply 72 and 80 to get 5760.

$$\frac{35}{5760}$$

Reduce the fraction \frac{35}{5760} to lowest terms by extracting and canceling out 5.

$$\frac{7}{1152}$$

Factor

$$\frac{7}{2 ^ {7} \cdot 3 ^ {2}} = 0.006076388888888889$$