Solve {l}{1,8*6-(3,4:0,2-(2,4*30-(0,12:4-5,2)))}{4,8:4-(0,75:1/2-(31/2*20-(3/8:0,75-0,5)))}

$$\left. \begin{array} { l } { 1,8 \cdot 6 - ( 3,4 : 0,2 - ( 2,4 \cdot 30 - ( 0,12 : 4 - 5,2 ) ) ) } \\ { 4,8 : 4 - ( 0,75 : \frac { 1 } { 2 } - ( 3 \frac { 1 } { 2 } \cdot 20 - ( \frac { 3 } { 8 } : 0,75 - 0,5 ) ) ) } \end{array} \right.$$

Sort

$$69,7;70,97$$

Solution Steps

Multiply 1,8 and 6 to get 10,8.

$$sort(10,8-\left(\frac{3,4}{0,2}-\left(2,4\times 30-\left(\frac{0,12}{4}-5,2\right)\right)\right);\frac{4,8}{4}-\left(\frac{0,75}{\frac{1}{2}}-\left(\frac{3\times 2+1}{2}\times 20-\left(\frac{\frac{3}{8}}{0,75}-0,5\right)\right)\right))$$

Expand \frac{3,4}{0,2} by multiplying both numerator and the denominator by 10.

$$sort(10,8-\left(\frac{34}{2}-\left(2,4\times 30-\left(\frac{0,12}{4}-5,2\right)\right)\right);\frac{4,8}{4}-\left(\frac{0,75}{\frac{1}{2}}-\left(\frac{3\times 2+1}{2}\times 20-\left(\frac{\frac{3}{8}}{0,75}-0,5\right)\right)\right))$$

Divide 34 by 2 to get 17.

$$sort(10,8-\left(17-\left(2,4\times 30-\left(\frac{0,12}{4}-5,2\right)\right)\right);\frac{4,8}{4}-\left(\frac{0,75}{\frac{1}{2}}-\left(\frac{3\times 2+1}{2}\times 20-\left(\frac{\frac{3}{8}}{0,75}-0,5\right)\right)\right))$$

Multiply 2,4 and 30 to get 72.

$$sort(10,8-\left(17-\left(72-\left(\frac{0,12}{4}-5,2\right)\right)\right);\frac{4,8}{4}-\left(\frac{0,75}{\frac{1}{2}}-\left(\frac{3\times 2+1}{2}\times 20-\left(\frac{\frac{3}{8}}{0,75}-0,5\right)\right)\right))$$

Expand \frac{0,12}{4} by multiplying both numerator and the denominator by 100.

$$sort(10,8-\left(17-\left(72-\left(\frac{12}{400}-5,2\right)\right)\right);\frac{4,8}{4}-\left(\frac{0,75}{\frac{1}{2}}-\left(\frac{3\times 2+1}{2}\times 20-\left(\frac{\frac{3}{8}}{0,75}-0,5\right)\right)\right))$$

Reduce the fraction \frac{12}{400} to lowest terms by extracting and canceling out 4.

$$sort(10,8-\left(17-\left(72-\left(\frac{3}{100}-5,2\right)\right)\right);\frac{4,8}{4}-\left(\frac{0,75}{\frac{1}{2}}-\left(\frac{3\times 2+1}{2}\times 20-\left(\frac{\frac{3}{8}}{0,75}-0,5\right)\right)\right))$$

Convert decimal number 5,2 to fraction \frac{52}{10}. Reduce the fraction \frac{52}{10} to lowest terms by extracting and canceling out 2.

$$sort(10,8-\left(17-\left(72-\left(\frac{3}{100}-\frac{26}{5}\right)\right)\right);\frac{4,8}{4}-\left(\frac{0,75}{\frac{1}{2}}-\left(\frac{3\times 2+1}{2}\times 20-\left(\frac{\frac{3}{8}}{0,75}-0,5\right)\right)\right))$$

Least common multiple of 100 and 5 is 100. Convert \frac{3}{100} and \frac{26}{5} to fractions with denominator 100.

$$sort(10,8-\left(17-\left(72-\left(\frac{3}{100}-\frac{520}{100}\right)\right)\right);\frac{4,8}{4}-\left(\frac{0,75}{\frac{1}{2}}-\left(\frac{3\times 2+1}{2}\times 20-\left(\frac{\frac{3}{8}}{0,75}-0,5\right)\right)\right))$$

Since \frac{3}{100} and \frac{520}{100} have the same denominator, subtract them by subtracting their numerators.

$$sort(10,8-\left(17-\left(72-\frac{3-520}{100}\right)\right);\frac{4,8}{4}-\left(\frac{0,75}{\frac{1}{2}}-\left(\frac{3\times 2+1}{2}\times 20-\left(\frac{\frac{3}{8}}{0,75}-0,5\right)\right)\right))$$

Subtract 520 from 3 to get -517.

$$sort(10,8-\left(17-\left(72-\left(-\frac{517}{100}\right)\right)\right);\frac{4,8}{4}-\left(\frac{0,75}{\frac{1}{2}}-\left(\frac{3\times 2+1}{2}\times 20-\left(\frac{\frac{3}{8}}{0,75}-0,5\right)\right)\right))$$

The opposite of -\frac{517}{100} is \frac{517}{100}.

$$sort(10,8-\left(17-\left(72+\frac{517}{100}\right)\right);\frac{4,8}{4}-\left(\frac{0,75}{\frac{1}{2}}-\left(\frac{3\times 2+1}{2}\times 20-\left(\frac{\frac{3}{8}}{0,75}-0,5\right)\right)\right))$$

Convert 72 to fraction \frac{7200}{100}.

$$sort(10,8-\left(17-\left(\frac{7200}{100}+\frac{517}{100}\right)\right);\frac{4,8}{4}-\left(\frac{0,75}{\frac{1}{2}}-\left(\frac{3\times 2+1}{2}\times 20-\left(\frac{\frac{3}{8}}{0,75}-0,5\right)\right)\right))$$

Since \frac{7200}{100} and \frac{517}{100} have the same denominator, add them by adding their numerators.

$$sort(10,8-\left(17-\frac{7200+517}{100}\right);\frac{4,8}{4}-\left(\frac{0,75}{\frac{1}{2}}-\left(\frac{3\times 2+1}{2}\times 20-\left(\frac{\frac{3}{8}}{0,75}-0,5\right)\right)\right))$$

Add 7200 and 517 to get 7717.

$$sort(10,8-\left(17-\frac{7717}{100}\right);\frac{4,8}{4}-\left(\frac{0,75}{\frac{1}{2}}-\left(\frac{3\times 2+1}{2}\times 20-\left(\frac{\frac{3}{8}}{0,75}-0,5\right)\right)\right))$$

Convert 17 to fraction \frac{1700}{100}.

$$sort(10,8-\left(\frac{1700}{100}-\frac{7717}{100}\right);\frac{4,8}{4}-\left(\frac{0,75}{\frac{1}{2}}-\left(\frac{3\times 2+1}{2}\times 20-\left(\frac{\frac{3}{8}}{0,75}-0,5\right)\right)\right))$$

Since \frac{1700}{100} and \frac{7717}{100} have the same denominator, subtract them by subtracting their numerators.

$$sort(10,8-\frac{1700-7717}{100};\frac{4,8}{4}-\left(\frac{0,75}{\frac{1}{2}}-\left(\frac{3\times 2+1}{2}\times 20-\left(\frac{\frac{3}{8}}{0,75}-0,5\right)\right)\right))$$

Subtract 7717 from 1700 to get -6017.

$$sort(10,8-\left(-\frac{6017}{100}\right);\frac{4,8}{4}-\left(\frac{0,75}{\frac{1}{2}}-\left(\frac{3\times 2+1}{2}\times 20-\left(\frac{\frac{3}{8}}{0,75}-0,5\right)\right)\right))$$

The opposite of -\frac{6017}{100} is \frac{6017}{100}.

$$sort(10,8+\frac{6017}{100};\frac{4,8}{4}-\left(\frac{0,75}{\frac{1}{2}}-\left(\frac{3\times 2+1}{2}\times 20-\left(\frac{\frac{3}{8}}{0,75}-0,5\right)\right)\right))$$

Convert decimal number 10,8 to fraction \frac{108}{10}. Reduce the fraction \frac{108}{10} to lowest terms by extracting and canceling out 2.

$$sort(\frac{54}{5}+\frac{6017}{100};\frac{4,8}{4}-\left(\frac{0,75}{\frac{1}{2}}-\left(\frac{3\times 2+1}{2}\times 20-\left(\frac{\frac{3}{8}}{0,75}-0,5\right)\right)\right))$$

Least common multiple of 5 and 100 is 100. Convert \frac{54}{5} and \frac{6017}{100} to fractions with denominator 100.

$$sort(\frac{1080}{100}+\frac{6017}{100};\frac{4,8}{4}-\left(\frac{0,75}{\frac{1}{2}}-\left(\frac{3\times 2+1}{2}\times 20-\left(\frac{\frac{3}{8}}{0,75}-0,5\right)\right)\right))$$

Since \frac{1080}{100} and \frac{6017}{100} have the same denominator, add them by adding their numerators.

$$sort(\frac{1080+6017}{100};\frac{4,8}{4}-\left(\frac{0,75}{\frac{1}{2}}-\left(\frac{3\times 2+1}{2}\times 20-\left(\frac{\frac{3}{8}}{0,75}-0,5\right)\right)\right))$$

Add 1080 and 6017 to get 7097.

$$sort(\frac{7097}{100};\frac{4,8}{4}-\left(\frac{0,75}{\frac{1}{2}}-\left(\frac{3\times 2+1}{2}\times 20-\left(\frac{\frac{3}{8}}{0,75}-0,5\right)\right)\right))$$

Expand \frac{4,8}{4} by multiplying both numerator and the denominator by 10.

$$sort(\frac{7097}{100};\frac{48}{40}-\left(\frac{0,75}{\frac{1}{2}}-\left(\frac{3\times 2+1}{2}\times 20-\left(\frac{\frac{3}{8}}{0,75}-0,5\right)\right)\right))$$

Reduce the fraction \frac{48}{40} to lowest terms by extracting and canceling out 8.

$$sort(\frac{7097}{100};\frac{6}{5}-\left(\frac{0,75}{\frac{1}{2}}-\left(\frac{3\times 2+1}{2}\times 20-\left(\frac{\frac{3}{8}}{0,75}-0,5\right)\right)\right))$$

Divide 0,75 by \frac{1}{2} by multiplying 0,75 by the reciprocal of \frac{1}{2}.

$$sort(\frac{7097}{100};\frac{6}{5}-\left(0,75\times 2-\left(\frac{3\times 2+1}{2}\times 20-\left(\frac{\frac{3}{8}}{0,75}-0,5\right)\right)\right))$$

Multiply 0,75 and 2 to get 1,5.

$$sort(\frac{7097}{100};\frac{6}{5}-\left(1,5-\left(\frac{3\times 2+1}{2}\times 20-\left(\frac{\frac{3}{8}}{0,75}-0,5\right)\right)\right))$$

Multiply 3 and 2 to get 6.

$$sort(\frac{7097}{100};\frac{6}{5}-\left(1,5-\left(\frac{6+1}{2}\times 20-\left(\frac{\frac{3}{8}}{0,75}-0,5\right)\right)\right))$$

Add 6 and 1 to get 7.

$$sort(\frac{7097}{100};\frac{6}{5}-\left(1,5-\left(\frac{7}{2}\times 20-\left(\frac{\frac{3}{8}}{0,75}-0,5\right)\right)\right))$$

Express \frac{7}{2}\times 20 as a single fraction.

$$sort(\frac{7097}{100};\frac{6}{5}-\left(1,5-\left(\frac{7\times 20}{2}-\left(\frac{\frac{3}{8}}{0,75}-0,5\right)\right)\right))$$

Multiply 7 and 20 to get 140.

$$sort(\frac{7097}{100};\frac{6}{5}-\left(1,5-\left(\frac{140}{2}-\left(\frac{\frac{3}{8}}{0,75}-0,5\right)\right)\right))$$

Divide 140 by 2 to get 70.

$$sort(\frac{7097}{100};\frac{6}{5}-\left(1,5-\left(70-\left(\frac{\frac{3}{8}}{0,75}-0,5\right)\right)\right))$$

Express \frac{\frac{3}{8}}{0,75} as a single fraction.

$$sort(\frac{7097}{100};\frac{6}{5}-\left(1,5-\left(70-\left(\frac{3}{8\times 0,75}-0,5\right)\right)\right))$$

Multiply 8 and 0,75 to get 6.

$$sort(\frac{7097}{100};\frac{6}{5}-\left(1,5-\left(70-\left(\frac{3}{6}-0,5\right)\right)\right))$$

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

$$sort(\frac{7097}{100};\frac{6}{5}-\left(1,5-\left(70-\left(\frac{1}{2}-0,5\right)\right)\right))$$

Subtract 0,5 from \frac{1}{2} to get 0.

$$sort(\frac{7097}{100};\frac{6}{5}-\left(1,5-\left(70-0\right)\right))$$

Subtract 0 from 70 to get 70.

$$sort(\frac{7097}{100};\frac{6}{5}-\left(1,5-70\right))$$

Subtract 70 from 1,5 to get -68,5.

$$sort(\frac{7097}{100};\frac{6}{5}-\left(-68,5\right))$$

The opposite of -68,5 is 68,5.

$$sort(\frac{7097}{100};\frac{6}{5}+68,5)$$

Convert decimal number 68,5 to fraction \frac{685}{10}. Reduce the fraction \frac{685}{10} to lowest terms by extracting and canceling out 5.

$$sort(\frac{7097}{100};\frac{6}{5}+\frac{137}{2})$$

Least common multiple of 5 and 2 is 10. Convert \frac{6}{5} and \frac{137}{2} to fractions with denominator 10.

$$sort(\frac{7097}{100};\frac{12}{10}+\frac{685}{10})$$

Since \frac{12}{10} and \frac{685}{10} have the same denominator, add them by adding their numerators.

$$sort(\frac{7097}{100};\frac{12+685}{10})$$

Add 12 and 685 to get 697.

$$sort(\frac{7097}{100};\frac{697}{10})$$

Least common denominator of the numbers in the list \frac{7097}{100};\frac{697}{10} is 100. Convert numbers in the list to fractions with denominator 100.

$$\frac{7097}{100};\frac{6970}{100}$$

To sort the list, start from a single element \frac{7097}{100}.

$$\frac{7097}{100}$$

Insert \frac{6970}{100} to the appropriate location in the new list.

$$\frac{6970}{100};\frac{7097}{100}$$

Replace the obtained fractions with the initial values.

$$\frac{697}{10};\frac{7097}{100}$$

Evaluate

$$70,97,\ 69,7$$