Solve {l}{1+2(5-0,5+2div1/3-7)}{1+2,5(3/4-1/6)-2+1/3}

$$\left. \begin{array} { l } { 1 + 2 ( 5 - 0,5 + 2 \div \frac { 1 } { 3 } - 7 ) } \\ { 1 + 2,5 ( \frac { 3 } { 4 } - \frac { 1 } { 6 } ) - 2 + \frac { 1 } { 3 } } \end{array} \right.$$

Sort

$$\frac{19}{24};8$$

Solution Steps

Subtract 0,5 from 5 to get 4,5.

$$sort(1+2\left(4,5+\frac{2}{\frac{1}{3}}-7\right);1+2,5\left(\frac{3}{4}-\frac{1}{6}\right)-2+\frac{1}{3})$$

Divide 2 by \frac{1}{3} by multiplying 2 by the reciprocal of \frac{1}{3}.

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

Multiply 2 and 3 to get 6.

$$sort(1+2\left(4,5+6-7\right);1+2,5\left(\frac{3}{4}-\frac{1}{6}\right)-2+\frac{1}{3})$$

Add 4,5 and 6 to get 10,5.

$$sort(1+2\left(10,5-7\right);1+2,5\left(\frac{3}{4}-\frac{1}{6}\right)-2+\frac{1}{3})$$

Subtract 7 from 10,5 to get 3,5.

$$sort(1+2\times 3,5;1+2,5\left(\frac{3}{4}-\frac{1}{6}\right)-2+\frac{1}{3})$$

Multiply 2 and 3,5 to get 7.

$$sort(1+7;1+2,5\left(\frac{3}{4}-\frac{1}{6}\right)-2+\frac{1}{3})$$

Add 1 and 7 to get 8.

$$sort(8;1+2,5\left(\frac{3}{4}-\frac{1}{6}\right)-2+\frac{1}{3})$$

Least common multiple of 4 and 6 is 12. Convert \frac{3}{4} and \frac{1}{6} to fractions with denominator 12.

$$sort(8;1+2,5\left(\frac{9}{12}-\frac{2}{12}\right)-2+\frac{1}{3})$$

Since \frac{9}{12} and \frac{2}{12} have the same denominator, subtract them by subtracting their numerators.

$$sort(8;1+2,5\times \frac{9-2}{12}-2+\frac{1}{3})$$

Subtract 2 from 9 to get 7.

$$sort(8;1+2,5\times \frac{7}{12}-2+\frac{1}{3})$$

Convert decimal number 2,5 to fraction \frac{25}{10}. Reduce the fraction \frac{25}{10} to lowest terms by extracting and canceling out 5.

$$sort(8;1+\frac{5}{2}\times \frac{7}{12}-2+\frac{1}{3})$$

Multiply \frac{5}{2} times \frac{7}{12} by multiplying numerator times numerator and denominator times denominator.

$$sort(8;1+\frac{5\times 7}{2\times 12}-2+\frac{1}{3})$$

Do the multiplications in the fraction \frac{5\times 7}{2\times 12}.

$$sort(8;1+\frac{35}{24}-2+\frac{1}{3})$$

Convert 1 to fraction \frac{24}{24}.

$$sort(8;\frac{24}{24}+\frac{35}{24}-2+\frac{1}{3})$$

Since \frac{24}{24} and \frac{35}{24} have the same denominator, add them by adding their numerators.

$$sort(8;\frac{24+35}{24}-2+\frac{1}{3})$$

Add 24 and 35 to get 59.

$$sort(8;\frac{59}{24}-2+\frac{1}{3})$$

Convert 2 to fraction \frac{48}{24}.

$$sort(8;\frac{59}{24}-\frac{48}{24}+\frac{1}{3})$$

Since \frac{59}{24} and \frac{48}{24} have the same denominator, subtract them by subtracting their numerators.

$$sort(8;\frac{59-48}{24}+\frac{1}{3})$$

Subtract 48 from 59 to get 11.

$$sort(8;\frac{11}{24}+\frac{1}{3})$$

Least common multiple of 24 and 3 is 24. Convert \frac{11}{24} and \frac{1}{3} to fractions with denominator 24.

$$sort(8;\frac{11}{24}+\frac{8}{24})$$

Since \frac{11}{24} and \frac{8}{24} have the same denominator, add them by adding their numerators.

$$sort(8;\frac{11+8}{24})$$

Add 11 and 8 to get 19.

$$sort(8;\frac{19}{24})$$

Convert decimal numbers in the list 8;\frac{19}{24} to fractions.

$$8;\frac{19}{24}$$

To sort the list, start from a single element 8.

$$8$$

Insert \frac{19}{24} to the appropriate location in the new list.

$$\frac{19}{24};8$$

Evaluate

$$8,\ \frac{19}{24}$$