Solve (3/5+0.425-0,05):0,1/30,5+frac{1{6}+31/3}+6frac{3/4+5frac{2}{4}}{26:3frac{5}{7}}-0,05

$$\frac { ( \frac { 3 } { 5 } + 0.425 - 0,05 ) : 0,1 } { 30,5 + \frac { 1 } { 6 } + 3 \frac { 1 } { 3 } } + \frac { 6 \frac { 3 } { 4 } + 5 \frac { 2 } { 4 } } { 26 : 3 \frac { 5 } { 7 } } - 0,05$$

Sort

$$\frac{277}{136},5$$

Solution Steps

Convert decimal number 0.425 to fraction \frac{425}{1000}. Reduce the fraction \frac{425}{1000} to lowest terms by extracting and canceling out 25.

$$sort(\frac{\frac{\frac{3}{5}+\frac{17}{40}-0.05}{0.1}}{30.5+\frac{1}{6}+\frac{3\times 3+1}{3}}+\frac{\frac{6\times 4+3}{4}+\frac{5\times 4+2}{4}}{\frac{26}{\frac{3\times 7+5}{7}}}-0,5)$$

Least common multiple of 5 and 40 is 40. Convert \frac{3}{5} and \frac{17}{40} to fractions with denominator 40.

$$sort(\frac{\frac{\frac{24}{40}+\frac{17}{40}-0.05}{0.1}}{30.5+\frac{1}{6}+\frac{3\times 3+1}{3}}+\frac{\frac{6\times 4+3}{4}+\frac{5\times 4+2}{4}}{\frac{26}{\frac{3\times 7+5}{7}}}-0,5)$$

Since \frac{24}{40} and \frac{17}{40} have the same denominator, add them by adding their numerators.

$$sort(\frac{\frac{\frac{24+17}{40}-0.05}{0.1}}{30.5+\frac{1}{6}+\frac{3\times 3+1}{3}}+\frac{\frac{6\times 4+3}{4}+\frac{5\times 4+2}{4}}{\frac{26}{\frac{3\times 7+5}{7}}}-0,5)$$

Add 24 and 17 to get 41.

$$sort(\frac{\frac{\frac{41}{40}-0.05}{0.1}}{30.5+\frac{1}{6}+\frac{3\times 3+1}{3}}+\frac{\frac{6\times 4+3}{4}+\frac{5\times 4+2}{4}}{\frac{26}{\frac{3\times 7+5}{7}}}-0,5)$$

Convert decimal number 0.05 to fraction \frac{5}{100}. Reduce the fraction \frac{5}{100} to lowest terms by extracting and canceling out 5.

$$sort(\frac{\frac{\frac{41}{40}-\frac{1}{20}}{0.1}}{30.5+\frac{1}{6}+\frac{3\times 3+1}{3}}+\frac{\frac{6\times 4+3}{4}+\frac{5\times 4+2}{4}}{\frac{26}{\frac{3\times 7+5}{7}}}-0,5)$$

Least common multiple of 40 and 20 is 40. Convert \frac{41}{40} and \frac{1}{20} to fractions with denominator 40.

$$sort(\frac{\frac{\frac{41}{40}-\frac{2}{40}}{0.1}}{30.5+\frac{1}{6}+\frac{3\times 3+1}{3}}+\frac{\frac{6\times 4+3}{4}+\frac{5\times 4+2}{4}}{\frac{26}{\frac{3\times 7+5}{7}}}-0,5)$$

Since \frac{41}{40} and \frac{2}{40} have the same denominator, subtract them by subtracting their numerators.

$$sort(\frac{\frac{\frac{41-2}{40}}{0.1}}{30.5+\frac{1}{6}+\frac{3\times 3+1}{3}}+\frac{\frac{6\times 4+3}{4}+\frac{5\times 4+2}{4}}{\frac{26}{\frac{3\times 7+5}{7}}}-0,5)$$

Subtract 2 from 41 to get 39.

$$sort(\frac{\frac{\frac{39}{40}}{0.1}}{30.5+\frac{1}{6}+\frac{3\times 3+1}{3}}+\frac{\frac{6\times 4+3}{4}+\frac{5\times 4+2}{4}}{\frac{26}{\frac{3\times 7+5}{7}}}-0,5)$$

Express \frac{\frac{39}{40}}{0.1} as a single fraction.

$$sort(\frac{\frac{39}{40\times 0.1}}{30.5+\frac{1}{6}+\frac{3\times 3+1}{3}}+\frac{\frac{6\times 4+3}{4}+\frac{5\times 4+2}{4}}{\frac{26}{\frac{3\times 7+5}{7}}}-0,5)$$

Multiply 40 and 0.1 to get 4.

$$sort(\frac{\frac{39}{4}}{30.5+\frac{1}{6}+\frac{3\times 3+1}{3}}+\frac{\frac{6\times 4+3}{4}+\frac{5\times 4+2}{4}}{\frac{26}{\frac{3\times 7+5}{7}}}-0,5)$$

Convert decimal number 30.5 to fraction \frac{305}{10}. Reduce the fraction \frac{305}{10} to lowest terms by extracting and canceling out 5.

$$sort(\frac{\frac{39}{4}}{\frac{61}{2}+\frac{1}{6}+\frac{3\times 3+1}{3}}+\frac{\frac{6\times 4+3}{4}+\frac{5\times 4+2}{4}}{\frac{26}{\frac{3\times 7+5}{7}}}-0,5)$$

Least common multiple of 2 and 6 is 6. Convert \frac{61}{2} and \frac{1}{6} to fractions with denominator 6.

$$sort(\frac{\frac{39}{4}}{\frac{183}{6}+\frac{1}{6}+\frac{3\times 3+1}{3}}+\frac{\frac{6\times 4+3}{4}+\frac{5\times 4+2}{4}}{\frac{26}{\frac{3\times 7+5}{7}}}-0,5)$$

Since \frac{183}{6} and \frac{1}{6} have the same denominator, add them by adding their numerators.

$$sort(\frac{\frac{39}{4}}{\frac{183+1}{6}+\frac{3\times 3+1}{3}}+\frac{\frac{6\times 4+3}{4}+\frac{5\times 4+2}{4}}{\frac{26}{\frac{3\times 7+5}{7}}}-0,5)$$

Add 183 and 1 to get 184.

$$sort(\frac{\frac{39}{4}}{\frac{184}{6}+\frac{3\times 3+1}{3}}+\frac{\frac{6\times 4+3}{4}+\frac{5\times 4+2}{4}}{\frac{26}{\frac{3\times 7+5}{7}}}-0,5)$$

Reduce the fraction \frac{184}{6} to lowest terms by extracting and canceling out 2.

$$sort(\frac{\frac{39}{4}}{\frac{92}{3}+\frac{3\times 3+1}{3}}+\frac{\frac{6\times 4+3}{4}+\frac{5\times 4+2}{4}}{\frac{26}{\frac{3\times 7+5}{7}}}-0,5)$$

Multiply 3 and 3 to get 9.

$$sort(\frac{\frac{39}{4}}{\frac{92}{3}+\frac{9+1}{3}}+\frac{\frac{6\times 4+3}{4}+\frac{5\times 4+2}{4}}{\frac{26}{\frac{3\times 7+5}{7}}}-0,5)$$

Add 9 and 1 to get 10.

$$sort(\frac{\frac{39}{4}}{\frac{92}{3}+\frac{10}{3}}+\frac{\frac{6\times 4+3}{4}+\frac{5\times 4+2}{4}}{\frac{26}{\frac{3\times 7+5}{7}}}-0,5)$$

Since \frac{92}{3} and \frac{10}{3} have the same denominator, add them by adding their numerators.

$$sort(\frac{\frac{39}{4}}{\frac{92+10}{3}}+\frac{\frac{6\times 4+3}{4}+\frac{5\times 4+2}{4}}{\frac{26}{\frac{3\times 7+5}{7}}}-0,5)$$

Add 92 and 10 to get 102.

$$sort(\frac{\frac{39}{4}}{\frac{102}{3}}+\frac{\frac{6\times 4+3}{4}+\frac{5\times 4+2}{4}}{\frac{26}{\frac{3\times 7+5}{7}}}-0,5)$$

Divide 102 by 3 to get 34.

$$sort(\frac{\frac{39}{4}}{34}+\frac{\frac{6\times 4+3}{4}+\frac{5\times 4+2}{4}}{\frac{26}{\frac{3\times 7+5}{7}}}-0,5)$$

Express \frac{\frac{39}{4}}{34} as a single fraction.

$$sort(\frac{39}{4\times 34}+\frac{\frac{6\times 4+3}{4}+\frac{5\times 4+2}{4}}{\frac{26}{\frac{3\times 7+5}{7}}}-0,5)$$

Multiply 4 and 34 to get 136.

$$sort(\frac{39}{136}+\frac{\frac{6\times 4+3}{4}+\frac{5\times 4+2}{4}}{\frac{26}{\frac{3\times 7+5}{7}}}-0,5)$$

Multiply 6 and 4 to get 24.

$$sort(\frac{39}{136}+\frac{\frac{24+3}{4}+\frac{5\times 4+2}{4}}{\frac{26}{\frac{3\times 7+5}{7}}}-0,5)$$

Add 24 and 3 to get 27.

$$sort(\frac{39}{136}+\frac{\frac{27}{4}+\frac{5\times 4+2}{4}}{\frac{26}{\frac{3\times 7+5}{7}}}-0,5)$$

Multiply 5 and 4 to get 20.

$$sort(\frac{39}{136}+\frac{\frac{27}{4}+\frac{20+2}{4}}{\frac{26}{\frac{3\times 7+5}{7}}}-0,5)$$

Add 20 and 2 to get 22.

$$sort(\frac{39}{136}+\frac{\frac{27}{4}+\frac{22}{4}}{\frac{26}{\frac{3\times 7+5}{7}}}-0,5)$$

Since \frac{27}{4} and \frac{22}{4} have the same denominator, add them by adding their numerators.

$$sort(\frac{39}{136}+\frac{\frac{27+22}{4}}{\frac{26}{\frac{3\times 7+5}{7}}}-0,5)$$

Add 27 and 22 to get 49.

$$sort(\frac{39}{136}+\frac{\frac{49}{4}}{\frac{26}{\frac{3\times 7+5}{7}}}-0,5)$$

Divide 26 by \frac{3\times 7+5}{7} by multiplying 26 by the reciprocal of \frac{3\times 7+5}{7}.

$$sort(\frac{39}{136}+\frac{\frac{49}{4}}{\frac{26\times 7}{3\times 7+5}}-0,5)$$

Multiply 26 and 7 to get 182.

$$sort(\frac{39}{136}+\frac{\frac{49}{4}}{\frac{182}{3\times 7+5}}-0,5)$$

Multiply 3 and 7 to get 21.

$$sort(\frac{39}{136}+\frac{\frac{49}{4}}{\frac{182}{21+5}}-0,5)$$

Add 21 and 5 to get 26.

$$sort(\frac{39}{136}+\frac{\frac{49}{4}}{\frac{182}{26}}-0,5)$$

Divide 182 by 26 to get 7.

$$sort(\frac{39}{136}+\frac{\frac{49}{4}}{7}-0,5)$$

Express \frac{\frac{49}{4}}{7} as a single fraction.

$$sort(\frac{39}{136}+\frac{49}{4\times 7}-0,5)$$

Multiply 4 and 7 to get 28.

$$sort(\frac{39}{136}+\frac{49}{28}-0,5)$$

Reduce the fraction \frac{49}{28} to lowest terms by extracting and canceling out 7.

$$sort(\frac{39}{136}+\frac{7}{4}-0,5)$$

Least common multiple of 136 and 4 is 136. Convert \frac{39}{136} and \frac{7}{4} to fractions with denominator 136.

$$sort(\frac{39}{136}+\frac{238}{136}-0,5)$$

Since \frac{39}{136} and \frac{238}{136} have the same denominator, add them by adding their numerators.

$$sort(\frac{39+238}{136}-0,5)$$

Add 39 and 238 to get 277.

$$sort(\frac{277}{136}-0,5)$$

Subtract 0 from \frac{277}{136} to get \frac{277}{136}.

$$sort(\frac{277}{136},5)$$

Convert decimal numbers in the list \frac{277}{136},5 to fractions.

$$\frac{277}{136},5$$

Evaluate

$$\frac{277}{136},5$$