Solve {l}{5/8+7/8}{2/3-1/2}

$$\left. \begin{array} { l } { \frac { 5 } { 8 } + \frac { 7 } { 8 } } \\ { \frac { 2 } { 3 } - \frac { 1 } { 2 } } \end{array} \right.$$

Sort

$$\frac{1}{6},\frac{3}{2}$$

Solution Steps

Since \frac{5}{8} and \frac{7}{8} have the same denominator, add them by adding their numerators.

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

Add 5 and 7 to get 12.

$$sort(\frac{12}{8},\frac{2}{3}-\frac{1}{2})$$

Reduce the fraction \frac{12}{8} to lowest terms by extracting and canceling out 4.

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

Least common multiple of 3 and 2 is 6. Convert \frac{2}{3} and \frac{1}{2} to fractions with denominator 6.

$$sort(\frac{3}{2},\frac{4}{6}-\frac{3}{6})$$

Since \frac{4}{6} and \frac{3}{6} have the same denominator, subtract them by subtracting their numerators.

$$sort(\frac{3}{2},\frac{4-3}{6})$$

Subtract 3 from 4 to get 1.

$$sort(\frac{3}{2},\frac{1}{6})$$

Least common denominator of the numbers in the list \frac{3}{2},\frac{1}{6} is 6. Convert numbers in the list to fractions with denominator 6.

$$\frac{9}{6},\frac{1}{6}$$

To sort the list, start from a single element \frac{9}{6}.

$$\frac{9}{6}$$

Insert \frac{1}{6} to the appropriate location in the new list.

$$\frac{1}{6},\frac{9}{6}$$

Replace the obtained fractions with the initial values.

$$\frac{1}{6},\frac{3}{2}$$

Evaluate

$$\frac{3}{2},\ \frac{1}{6}$$