Solve 91/2:1,9-41/5/2,32*frac{15{29}+4/5}+frac{(6+7frac{1}{2}):15}{(1frac{7}{15}+frac{1}{3})*5}

$$\frac { 9 \frac { 1 } { 2 } : 1,9 - 4 \frac { 1 } { 5 } } { 2,32 \cdot \frac { 15 } { 29 } + \frac { 4 } { 5 } } + \frac { ( 6 + 7 \frac { 1 } { 2 } ) : 15 } { ( 1 \frac { 7 } { 15 } + \frac { 1 } { 3 } ) \cdot 5 }$$

Evaluate

$$0,5$$

Solution Steps

Express \frac{\frac{9\times 2+1}{2}}{1,9} as a single fraction.

$$\frac{\frac{9\times 2+1}{2\times 1,9}-\frac{4\times 5+1}{5}}{2,32\times \frac{15}{29}+\frac{4}{5}}+\frac{\frac{6+\frac{7\times 2+1}{2}}{15}}{\left(\frac{1\times 15+7}{15}+\frac{1}{3}\right)\times 5}$$

Multiply 9 and 2 to get 18.

$$\frac{\frac{18+1}{2\times 1,9}-\frac{4\times 5+1}{5}}{2,32\times \frac{15}{29}+\frac{4}{5}}+\frac{\frac{6+\frac{7\times 2+1}{2}}{15}}{\left(\frac{1\times 15+7}{15}+\frac{1}{3}\right)\times 5}$$

Add 18 and 1 to get 19.

$$\frac{\frac{19}{2\times 1,9}-\frac{4\times 5+1}{5}}{2,32\times \frac{15}{29}+\frac{4}{5}}+\frac{\frac{6+\frac{7\times 2+1}{2}}{15}}{\left(\frac{1\times 15+7}{15}+\frac{1}{3}\right)\times 5}$$

Multiply 2 and 1,9 to get 3,8.

$$\frac{\frac{19}{3,8}-\frac{4\times 5+1}{5}}{2,32\times \frac{15}{29}+\frac{4}{5}}+\frac{\frac{6+\frac{7\times 2+1}{2}}{15}}{\left(\frac{1\times 15+7}{15}+\frac{1}{3}\right)\times 5}$$

Expand \frac{19}{3,8} by multiplying both numerator and the denominator by 10.

$$\frac{\frac{190}{38}-\frac{4\times 5+1}{5}}{2,32\times \frac{15}{29}+\frac{4}{5}}+\frac{\frac{6+\frac{7\times 2+1}{2}}{15}}{\left(\frac{1\times 15+7}{15}+\frac{1}{3}\right)\times 5}$$

Divide 190 by 38 to get 5.

$$\frac{5-\frac{4\times 5+1}{5}}{2,32\times \frac{15}{29}+\frac{4}{5}}+\frac{\frac{6+\frac{7\times 2+1}{2}}{15}}{\left(\frac{1\times 15+7}{15}+\frac{1}{3}\right)\times 5}$$

Multiply 4 and 5 to get 20.

$$\frac{5-\frac{20+1}{5}}{2,32\times \frac{15}{29}+\frac{4}{5}}+\frac{\frac{6+\frac{7\times 2+1}{2}}{15}}{\left(\frac{1\times 15+7}{15}+\frac{1}{3}\right)\times 5}$$

Add 20 and 1 to get 21.

$$\frac{5-\frac{21}{5}}{2,32\times \frac{15}{29}+\frac{4}{5}}+\frac{\frac{6+\frac{7\times 2+1}{2}}{15}}{\left(\frac{1\times 15+7}{15}+\frac{1}{3}\right)\times 5}$$

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

$$\frac{\frac{25}{5}-\frac{21}{5}}{2,32\times \frac{15}{29}+\frac{4}{5}}+\frac{\frac{6+\frac{7\times 2+1}{2}}{15}}{\left(\frac{1\times 15+7}{15}+\frac{1}{3}\right)\times 5}$$

Since \frac{25}{5} and \frac{21}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{25-21}{5}}{2,32\times \frac{15}{29}+\frac{4}{5}}+\frac{\frac{6+\frac{7\times 2+1}{2}}{15}}{\left(\frac{1\times 15+7}{15}+\frac{1}{3}\right)\times 5}$$

Subtract 21 from 25 to get 4.

$$\frac{\frac{4}{5}}{2,32\times \frac{15}{29}+\frac{4}{5}}+\frac{\frac{6+\frac{7\times 2+1}{2}}{15}}{\left(\frac{1\times 15+7}{15}+\frac{1}{3}\right)\times 5}$$

Convert decimal number 2,32 to fraction \frac{232}{100}. Reduce the fraction \frac{232}{100} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{4}{5}}{\frac{58}{25}\times \frac{15}{29}+\frac{4}{5}}+\frac{\frac{6+\frac{7\times 2+1}{2}}{15}}{\left(\frac{1\times 15+7}{15}+\frac{1}{3}\right)\times 5}$$

Multiply \frac{58}{25} times \frac{15}{29} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{4}{5}}{\frac{58\times 15}{25\times 29}+\frac{4}{5}}+\frac{\frac{6+\frac{7\times 2+1}{2}}{15}}{\left(\frac{1\times 15+7}{15}+\frac{1}{3}\right)\times 5}$$

Do the multiplications in the fraction \frac{58\times 15}{25\times 29}.

$$\frac{\frac{4}{5}}{\frac{870}{725}+\frac{4}{5}}+\frac{\frac{6+\frac{7\times 2+1}{2}}{15}}{\left(\frac{1\times 15+7}{15}+\frac{1}{3}\right)\times 5}$$

Reduce the fraction \frac{870}{725} to lowest terms by extracting and canceling out 145.

$$\frac{\frac{4}{5}}{\frac{6}{5}+\frac{4}{5}}+\frac{\frac{6+\frac{7\times 2+1}{2}}{15}}{\left(\frac{1\times 15+7}{15}+\frac{1}{3}\right)\times 5}$$

Since \frac{6}{5} and \frac{4}{5} have the same denominator, add them by adding their numerators.

$$\frac{\frac{4}{5}}{\frac{6+4}{5}}+\frac{\frac{6+\frac{7\times 2+1}{2}}{15}}{\left(\frac{1\times 15+7}{15}+\frac{1}{3}\right)\times 5}$$

Add 6 and 4 to get 10.

$$\frac{\frac{4}{5}}{\frac{10}{5}}+\frac{\frac{6+\frac{7\times 2+1}{2}}{15}}{\left(\frac{1\times 15+7}{15}+\frac{1}{3}\right)\times 5}$$

Divide 10 by 5 to get 2.

$$\frac{\frac{4}{5}}{2}+\frac{\frac{6+\frac{7\times 2+1}{2}}{15}}{\left(\frac{1\times 15+7}{15}+\frac{1}{3}\right)\times 5}$$

Express \frac{\frac{4}{5}}{2} as a single fraction.

$$\frac{4}{5\times 2}+\frac{\frac{6+\frac{7\times 2+1}{2}}{15}}{\left(\frac{1\times 15+7}{15}+\frac{1}{3}\right)\times 5}$$

Multiply 5 and 2 to get 10.

$$\frac{4}{10}+\frac{\frac{6+\frac{7\times 2+1}{2}}{15}}{\left(\frac{1\times 15+7}{15}+\frac{1}{3}\right)\times 5}$$

Reduce the fraction \frac{4}{10} to lowest terms by extracting and canceling out 2.

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

Multiply 7 and 2 to get 14.

$$\frac{2}{5}+\frac{\frac{6+\frac{14+1}{2}}{15}}{\left(\frac{1\times 15+7}{15}+\frac{1}{3}\right)\times 5}$$

Add 14 and 1 to get 15.

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

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

$$\frac{2}{5}+\frac{\frac{\frac{12}{2}+\frac{15}{2}}{15}}{\left(\frac{1\times 15+7}{15}+\frac{1}{3}\right)\times 5}$$

Since \frac{12}{2} and \frac{15}{2} have the same denominator, add them by adding their numerators.

$$\frac{2}{5}+\frac{\frac{\frac{12+15}{2}}{15}}{\left(\frac{1\times 15+7}{15}+\frac{1}{3}\right)\times 5}$$

Add 12 and 15 to get 27.

$$\frac{2}{5}+\frac{\frac{\frac{27}{2}}{15}}{\left(\frac{1\times 15+7}{15}+\frac{1}{3}\right)\times 5}$$

Express \frac{\frac{27}{2}}{15} as a single fraction.

$$\frac{2}{5}+\frac{\frac{27}{2\times 15}}{\left(\frac{1\times 15+7}{15}+\frac{1}{3}\right)\times 5}$$

Multiply 2 and 15 to get 30.

$$\frac{2}{5}+\frac{\frac{27}{30}}{\left(\frac{1\times 15+7}{15}+\frac{1}{3}\right)\times 5}$$

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

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

Multiply 1 and 15 to get 15.

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

Add 15 and 7 to get 22.

$$\frac{2}{5}+\frac{\frac{9}{10}}{\left(\frac{22}{15}+\frac{1}{3}\right)\times 5}$$

Least common multiple of 15 and 3 is 15. Convert \frac{22}{15} and \frac{1}{3} to fractions with denominator 15.

$$\frac{2}{5}+\frac{\frac{9}{10}}{\left(\frac{22}{15}+\frac{5}{15}\right)\times 5}$$

Since \frac{22}{15} and \frac{5}{15} have the same denominator, add them by adding their numerators.

$$\frac{2}{5}+\frac{\frac{9}{10}}{\frac{22+5}{15}\times 5}$$

Add 22 and 5 to get 27.

$$\frac{2}{5}+\frac{\frac{9}{10}}{\frac{27}{15}\times 5}$$

Reduce the fraction \frac{27}{15} to lowest terms by extracting and canceling out 3.

$$\frac{2}{5}+\frac{\frac{9}{10}}{\frac{9}{5}\times 5}$$

Cancel out 5 and 5.

$$\frac{2}{5}+\frac{\frac{9}{10}}{9}$$

Express \frac{\frac{9}{10}}{9} as a single fraction.

$$\frac{2}{5}+\frac{9}{10\times 9}$$

Cancel out 9 in both numerator and denominator.

$$\frac{2}{5}+\frac{1}{10}$$

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

$$\frac{4}{10}+\frac{1}{10}$$

Since \frac{4}{10} and \frac{1}{10} have the same denominator, add them by adding their numerators.

$$\frac{4+1}{10}$$

Add 4 and 1 to get 5.

$$\frac{5}{10}$$

Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

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

Factor

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