Solve 2-2/3/4/5+3-1/3/4/3/frac{4-1/4{1/2}+frac{5-1/5}{24}}*(frac{7}{20}*frac{11}{2})

$$\frac { \frac { 2 - \frac { 2 } { 3 } } { 4 / 5 } + \frac { 3 - 1 / 3 } { 4 / 3 } } { \frac { 4 - 1 / 4 } { 1 / 2 } + \frac { 5 - 1 / 5 } { 24 } } \times ( \frac { 7 } { 20 } \times \frac { 11 } { 2 } )$$

Evaluate

$$\frac{11}{12}\approx 0.916666667$$

Solution Steps

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

$$\frac{\frac{\frac{6}{3}-\frac{2}{3}}{\frac{4}{5}}+\frac{3-\frac{1}{3}}{\frac{4}{3}}}{\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

Since \frac{6}{3} and \frac{2}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{\frac{6-2}{3}}{\frac{4}{5}}+\frac{3-\frac{1}{3}}{\frac{4}{3}}}{\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

Subtract 2 from 6 to get 4.

$$\frac{\frac{\frac{4}{3}}{\frac{4}{5}}+\frac{3-\frac{1}{3}}{\frac{4}{3}}}{\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

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

$$\frac{\frac{4}{3}\times \frac{5}{4}+\frac{3-\frac{1}{3}}{\frac{4}{3}}}{\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

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

$$\frac{\frac{4\times 5}{3\times 4}+\frac{3-\frac{1}{3}}{\frac{4}{3}}}{\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

Cancel out 4 in both numerator and denominator.

$$\frac{\frac{5}{3}+\frac{3-\frac{1}{3}}{\frac{4}{3}}}{\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

Convert 3 to fraction \frac{9}{3}.

$$\frac{\frac{5}{3}+\frac{\frac{9}{3}-\frac{1}{3}}{\frac{4}{3}}}{\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

Since \frac{9}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5}{3}+\frac{\frac{9-1}{3}}{\frac{4}{3}}}{\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

Subtract 1 from 9 to get 8.

$$\frac{\frac{5}{3}+\frac{\frac{8}{3}}{\frac{4}{3}}}{\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

Divide \frac{8}{3} by \frac{4}{3} by multiplying \frac{8}{3} by the reciprocal of \frac{4}{3}.

$$\frac{\frac{5}{3}+\frac{8}{3}\times \frac{3}{4}}{\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

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

$$\frac{\frac{5}{3}+\frac{8\times 3}{3\times 4}}{\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

Cancel out 3 in both numerator and denominator.

$$\frac{\frac{5}{3}+\frac{8}{4}}{\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

Divide 8 by 4 to get 2.

$$\frac{\frac{5}{3}+2}{\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

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

$$\frac{\frac{5}{3}+\frac{6}{3}}{\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

Since \frac{5}{3} and \frac{6}{3} have the same denominator, add them by adding their numerators.

$$\frac{\frac{5+6}{3}}{\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

Add 5 and 6 to get 11.

$$\frac{\frac{11}{3}}{\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

Convert 4 to fraction \frac{16}{4}.

$$\frac{\frac{11}{3}}{\frac{\frac{16}{4}-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

Since \frac{16}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{11}{3}}{\frac{\frac{16-1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

Subtract 1 from 16 to get 15.

$$\frac{\frac{11}{3}}{\frac{\frac{15}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

Divide \frac{15}{4} by \frac{1}{2} by multiplying \frac{15}{4} by the reciprocal of \frac{1}{2}.

$$\frac{\frac{11}{3}}{\frac{15}{4}\times 2+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

Express \frac{15}{4}\times 2 as a single fraction.

$$\frac{\frac{11}{3}}{\frac{15\times 2}{4}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

Multiply 15 and 2 to get 30.

$$\frac{\frac{11}{3}}{\frac{30}{4}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

Reduce the fraction \frac{30}{4} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{11}{3}}{\frac{15}{2}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

Convert 5 to fraction \frac{25}{5}.

$$\frac{\frac{11}{3}}{\frac{15}{2}+\frac{\frac{25}{5}-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

Since \frac{25}{5} and \frac{1}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{11}{3}}{\frac{15}{2}+\frac{\frac{25-1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

Subtract 1 from 25 to get 24.

$$\frac{\frac{11}{3}}{\frac{15}{2}+\frac{\frac{24}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

Express \frac{\frac{24}{5}}{24} as a single fraction.

$$\frac{\frac{11}{3}}{\frac{15}{2}+\frac{24}{5\times 24}}\times \frac{7}{20}\times \frac{11}{2}$$

Cancel out 24 in both numerator and denominator.

$$\frac{\frac{11}{3}}{\frac{15}{2}+\frac{1}{5}}\times \frac{7}{20}\times \frac{11}{2}$$

Least common multiple of 2 and 5 is 10. Convert \frac{15}{2} and \frac{1}{5} to fractions with denominator 10.

$$\frac{\frac{11}{3}}{\frac{75}{10}+\frac{2}{10}}\times \frac{7}{20}\times \frac{11}{2}$$

Since \frac{75}{10} and \frac{2}{10} have the same denominator, add them by adding their numerators.

$$\frac{\frac{11}{3}}{\frac{75+2}{10}}\times \frac{7}{20}\times \frac{11}{2}$$

Add 75 and 2 to get 77.

$$\frac{\frac{11}{3}}{\frac{77}{10}}\times \frac{7}{20}\times \frac{11}{2}$$

Divide \frac{11}{3} by \frac{77}{10} by multiplying \frac{11}{3} by the reciprocal of \frac{77}{10}.

$$\frac{11}{3}\times \frac{10}{77}\times \frac{7}{20}\times \frac{11}{2}$$

Multiply \frac{11}{3} times \frac{10}{77} by multiplying numerator times numerator and denominator times denominator.

$$\frac{11\times 10}{3\times 77}\times \frac{7}{20}\times \frac{11}{2}$$

Do the multiplications in the fraction \frac{11\times 10}{3\times 77}.

$$\frac{110}{231}\times \frac{7}{20}\times \frac{11}{2}$$

Reduce the fraction \frac{110}{231} to lowest terms by extracting and canceling out 11.

$$\frac{10}{21}\times \frac{7}{20}\times \frac{11}{2}$$

Multiply \frac{10}{21} times \frac{7}{20} by multiplying numerator times numerator and denominator times denominator.

$$\frac{10\times 7}{21\times 20}\times \frac{11}{2}$$

Do the multiplications in the fraction \frac{10\times 7}{21\times 20}.

$$\frac{70}{420}\times \frac{11}{2}$$

Reduce the fraction \frac{70}{420} to lowest terms by extracting and canceling out 70.

$$\frac{1}{6}\times \frac{11}{2}$$

Multiply \frac{1}{6} times \frac{11}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 11}{6\times 2}$$

Do the multiplications in the fraction \frac{1\times 11}{6\times 2}.

$$\frac{11}{12}$$

Factor

$$\frac{11}{2 ^ {2} \cdot 3} = 0.9166666666666666$$