Solve (91/4-21/8)*2/3/(5frac{3{8}-frac{2}{3}):11,3}+frac{frac{3}{5}*1,35:0,9}{0,72-frac{3}{25}}+0,1

$$\frac { ( 9 \frac { 1 } { 4 } - 2 \frac { 1 } { 8 } ) \cdot \frac { 2 } { 3 } } { ( 5 \frac { 3 } { 8 } - \frac { 2 } { 3 } ) : 11,3 } + \frac { \frac { 3 } { 5 } \cdot 1,35 : 0,9 } { 0,72 - \frac { 3 } { 25 } } + 0,1$$

Evaluate

$$13$$

Solution Steps

Multiply 9 and 4 to get 36.

$$\frac{\left(\frac{36+1}{4}-\frac{2\times 8+1}{8}\right)\times \frac{2}{3}}{\frac{\frac{5\times 8+3}{8}-\frac{2}{3}}{11,3}}+\frac{\frac{\frac{3}{5}\times 1,35}{0,9}}{0,72-\frac{3}{25}}+0,1$$

Add 36 and 1 to get 37.

$$\frac{\left(\frac{37}{4}-\frac{2\times 8+1}{8}\right)\times \frac{2}{3}}{\frac{\frac{5\times 8+3}{8}-\frac{2}{3}}{11,3}}+\frac{\frac{\frac{3}{5}\times 1,35}{0,9}}{0,72-\frac{3}{25}}+0,1$$

Multiply 2 and 8 to get 16.

$$\frac{\left(\frac{37}{4}-\frac{16+1}{8}\right)\times \frac{2}{3}}{\frac{\frac{5\times 8+3}{8}-\frac{2}{3}}{11,3}}+\frac{\frac{\frac{3}{5}\times 1,35}{0,9}}{0,72-\frac{3}{25}}+0,1$$

Add 16 and 1 to get 17.

$$\frac{\left(\frac{37}{4}-\frac{17}{8}\right)\times \frac{2}{3}}{\frac{\frac{5\times 8+3}{8}-\frac{2}{3}}{11,3}}+\frac{\frac{\frac{3}{5}\times 1,35}{0,9}}{0,72-\frac{3}{25}}+0,1$$

Least common multiple of 4 and 8 is 8. Convert \frac{37}{4} and \frac{17}{8} to fractions with denominator 8.

$$\frac{\left(\frac{74}{8}-\frac{17}{8}\right)\times \frac{2}{3}}{\frac{\frac{5\times 8+3}{8}-\frac{2}{3}}{11,3}}+\frac{\frac{\frac{3}{5}\times 1,35}{0,9}}{0,72-\frac{3}{25}}+0,1$$

Since \frac{74}{8} and \frac{17}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{74-17}{8}\times \frac{2}{3}}{\frac{\frac{5\times 8+3}{8}-\frac{2}{3}}{11,3}}+\frac{\frac{\frac{3}{5}\times 1,35}{0,9}}{0,72-\frac{3}{25}}+0,1$$

Subtract 17 from 74 to get 57.

$$\frac{\frac{57}{8}\times \frac{2}{3}}{\frac{\frac{5\times 8+3}{8}-\frac{2}{3}}{11,3}}+\frac{\frac{\frac{3}{5}\times 1,35}{0,9}}{0,72-\frac{3}{25}}+0,1$$

Multiply \frac{57}{8} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{57\times 2}{8\times 3}}{\frac{\frac{5\times 8+3}{8}-\frac{2}{3}}{11,3}}+\frac{\frac{\frac{3}{5}\times 1,35}{0,9}}{0,72-\frac{3}{25}}+0,1$$

Do the multiplications in the fraction \frac{57\times 2}{8\times 3}.

$$\frac{\frac{114}{24}}{\frac{\frac{5\times 8+3}{8}-\frac{2}{3}}{11,3}}+\frac{\frac{\frac{3}{5}\times 1,35}{0,9}}{0,72-\frac{3}{25}}+0,1$$

Reduce the fraction \frac{114}{24} to lowest terms by extracting and canceling out 6.

$$\frac{\frac{19}{4}}{\frac{\frac{5\times 8+3}{8}-\frac{2}{3}}{11,3}}+\frac{\frac{\frac{3}{5}\times 1,35}{0,9}}{0,72-\frac{3}{25}}+0,1$$

Multiply 5 and 8 to get 40.

$$\frac{\frac{19}{4}}{\frac{\frac{40+3}{8}-\frac{2}{3}}{11,3}}+\frac{\frac{\frac{3}{5}\times 1,35}{0,9}}{0,72-\frac{3}{25}}+0,1$$

Add 40 and 3 to get 43.

$$\frac{\frac{19}{4}}{\frac{\frac{43}{8}-\frac{2}{3}}{11,3}}+\frac{\frac{\frac{3}{5}\times 1,35}{0,9}}{0,72-\frac{3}{25}}+0,1$$

Least common multiple of 8 and 3 is 24. Convert \frac{43}{8} and \frac{2}{3} to fractions with denominator 24.

$$\frac{\frac{19}{4}}{\frac{\frac{129}{24}-\frac{16}{24}}{11,3}}+\frac{\frac{\frac{3}{5}\times 1,35}{0,9}}{0,72-\frac{3}{25}}+0,1$$

Since \frac{129}{24} and \frac{16}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{19}{4}}{\frac{\frac{129-16}{24}}{11,3}}+\frac{\frac{\frac{3}{5}\times 1,35}{0,9}}{0,72-\frac{3}{25}}+0,1$$

Subtract 16 from 129 to get 113.

$$\frac{\frac{19}{4}}{\frac{\frac{113}{24}}{11,3}}+\frac{\frac{\frac{3}{5}\times 1,35}{0,9}}{0,72-\frac{3}{25}}+0,1$$

Express \frac{\frac{113}{24}}{11,3} as a single fraction.

$$\frac{\frac{19}{4}}{\frac{113}{24\times 11,3}}+\frac{\frac{\frac{3}{5}\times 1,35}{0,9}}{0,72-\frac{3}{25}}+0,1$$

Multiply 24 and 11,3 to get 271,2.

$$\frac{\frac{19}{4}}{\frac{113}{271,2}}+\frac{\frac{\frac{3}{5}\times 1,35}{0,9}}{0,72-\frac{3}{25}}+0,1$$

Expand \frac{113}{271,2} by multiplying both numerator and the denominator by 10.

$$\frac{\frac{19}{4}}{\frac{1130}{2712}}+\frac{\frac{\frac{3}{5}\times 1,35}{0,9}}{0,72-\frac{3}{25}}+0,1$$

Reduce the fraction \frac{1130}{2712} to lowest terms by extracting and canceling out 226.

$$\frac{\frac{19}{4}}{\frac{5}{12}}+\frac{\frac{\frac{3}{5}\times 1,35}{0,9}}{0,72-\frac{3}{25}}+0,1$$

Divide \frac{19}{4} by \frac{5}{12} by multiplying \frac{19}{4} by the reciprocal of \frac{5}{12}.

$$\frac{19}{4}\times \frac{12}{5}+\frac{\frac{\frac{3}{5}\times 1,35}{0,9}}{0,72-\frac{3}{25}}+0,1$$

Multiply \frac{19}{4} times \frac{12}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{19\times 12}{4\times 5}+\frac{\frac{\frac{3}{5}\times 1,35}{0,9}}{0,72-\frac{3}{25}}+0,1$$

Do the multiplications in the fraction \frac{19\times 12}{4\times 5}.

$$\frac{228}{20}+\frac{\frac{\frac{3}{5}\times 1,35}{0,9}}{0,72-\frac{3}{25}}+0,1$$

Reduce the fraction \frac{228}{20} to lowest terms by extracting and canceling out 4.

$$\frac{57}{5}+\frac{\frac{\frac{3}{5}\times 1,35}{0,9}}{0,72-\frac{3}{25}}+0,1$$

Convert decimal number 1,35 to fraction \frac{135}{100}. Reduce the fraction \frac{135}{100} to lowest terms by extracting and canceling out 5.

$$\frac{57}{5}+\frac{\frac{\frac{3}{5}\times \frac{27}{20}}{0,9}}{0,72-\frac{3}{25}}+0,1$$

Multiply \frac{3}{5} times \frac{27}{20} by multiplying numerator times numerator and denominator times denominator.

$$\frac{57}{5}+\frac{\frac{\frac{3\times 27}{5\times 20}}{0,9}}{0,72-\frac{3}{25}}+0,1$$

Do the multiplications in the fraction \frac{3\times 27}{5\times 20}.

$$\frac{57}{5}+\frac{\frac{\frac{81}{100}}{0,9}}{0,72-\frac{3}{25}}+0,1$$

Express \frac{\frac{81}{100}}{0,9} as a single fraction.

$$\frac{57}{5}+\frac{\frac{81}{100\times 0,9}}{0,72-\frac{3}{25}}+0,1$$

Multiply 100 and 0,9 to get 90.

$$\frac{57}{5}+\frac{\frac{81}{90}}{0,72-\frac{3}{25}}+0,1$$

Reduce the fraction \frac{81}{90} to lowest terms by extracting and canceling out 9.

$$\frac{57}{5}+\frac{\frac{9}{10}}{0,72-\frac{3}{25}}+0,1$$

Convert decimal number 0,72 to fraction \frac{72}{100}. Reduce the fraction \frac{72}{100} to lowest terms by extracting and canceling out 4.

$$\frac{57}{5}+\frac{\frac{9}{10}}{\frac{18}{25}-\frac{3}{25}}+0,1$$

Since \frac{18}{25} and \frac{3}{25} have the same denominator, subtract them by subtracting their numerators.

$$\frac{57}{5}+\frac{\frac{9}{10}}{\frac{18-3}{25}}+0,1$$

Subtract 3 from 18 to get 15.

$$\frac{57}{5}+\frac{\frac{9}{10}}{\frac{15}{25}}+0,1$$

Reduce the fraction \frac{15}{25} to lowest terms by extracting and canceling out 5.

$$\frac{57}{5}+\frac{\frac{9}{10}}{\frac{3}{5}}+0,1$$

Divide \frac{9}{10} by \frac{3}{5} by multiplying \frac{9}{10} by the reciprocal of \frac{3}{5}.

$$\frac{57}{5}+\frac{9}{10}\times \frac{5}{3}+0,1$$

Multiply \frac{9}{10} times \frac{5}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{57}{5}+\frac{9\times 5}{10\times 3}+0,1$$

Do the multiplications in the fraction \frac{9\times 5}{10\times 3}.

$$\frac{57}{5}+\frac{45}{30}+0,1$$

Reduce the fraction \frac{45}{30} to lowest terms by extracting and canceling out 15.

$$\frac{57}{5}+\frac{3}{2}+0,1$$

Least common multiple of 5 and 2 is 10. Convert \frac{57}{5} and \frac{3}{2} to fractions with denominator 10.

$$\frac{114}{10}+\frac{15}{10}+0,1$$

Since \frac{114}{10} and \frac{15}{10} have the same denominator, add them by adding their numerators.

$$\frac{114+15}{10}+0,1$$

Add 114 and 15 to get 129.

$$\frac{129}{10}+0,1$$

Convert decimal number 0,1 to fraction \frac{1}{10}.

$$\frac{129}{10}+\frac{1}{10}$$

Since \frac{129}{10} and \frac{1}{10} have the same denominator, add them by adding their numerators.

$$\frac{129+1}{10}$$

Add 129 and 1 to get 130.

$$\frac{130}{10}$$

Divide 130 by 10 to get 13.

$$13$$

Factor

$$13$$