Solve {c}{(1-1/2)div(3/4-5/8)}{1/2}

$$\left. \begin{array} { c } { ( 1 - \frac { 1 } { 2 } ) \div ( \frac { 3 } { 4 } - \frac { 5 } { 8 } ) } \\ { 1 / 2 } \end{array} \right.$$

Sort

$$\frac{1}{2},4$$

Solution Steps

Convert 1 to fraction \frac{2}{2}.

$$sort(\frac{\frac{2}{2}-\frac{1}{2}}{\frac{3}{4}-\frac{5}{8}},\frac{1}{2})$$

Since \frac{2}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

$$sort(\frac{\frac{2-1}{2}}{\frac{3}{4}-\frac{5}{8}},\frac{1}{2})$$

Subtract 1 from 2 to get 1.

$$sort(\frac{\frac{1}{2}}{\frac{3}{4}-\frac{5}{8}},\frac{1}{2})$$

Least common multiple of 4 and 8 is 8. Convert \frac{3}{4} and \frac{5}{8} to fractions with denominator 8.

$$sort(\frac{\frac{1}{2}}{\frac{6}{8}-\frac{5}{8}},\frac{1}{2})$$

Since \frac{6}{8} and \frac{5}{8} have the same denominator, subtract them by subtracting their numerators.

$$sort(\frac{\frac{1}{2}}{\frac{6-5}{8}},\frac{1}{2})$$

Subtract 5 from 6 to get 1.

$$sort(\frac{\frac{1}{2}}{\frac{1}{8}},\frac{1}{2})$$

Divide \frac{1}{2} by \frac{1}{8} by multiplying \frac{1}{2} by the reciprocal of \frac{1}{8}.

$$sort(\frac{1}{2}\times 8,\frac{1}{2})$$

Multiply \frac{1}{2} and 8 to get \frac{8}{2}.

$$sort(\frac{8}{2},\frac{1}{2})$$

Divide 8 by 2 to get 4.

$$sort(4,\frac{1}{2})$$

Convert decimal numbers in the list 4,\frac{1}{2} to fractions.

$$4,\frac{1}{2}$$

To sort the list, start from a single element 4.

$$4$$

Insert \frac{1}{2} to the appropriate location in the new list.

$$\frac{1}{2},4$$

Evaluate

$$4,\ \frac{1}{2}$$