Solve {l}{10/11*100-10/11}{5/(3)5/8*frac{3}{8}divfrac{5}{8}*frac{3}{8}}

$$\left. \begin{array} { l } { \frac { 10 } { 11 } \times 100 - \frac { 10 } { 11 } } \\ { \frac { 5 } { ( 3 ) } \frac { 5 } { 8 } \times \frac { 3 } { 8 } \div \frac { 5 } { 8 } \times \frac { 3 } { 8 } } \end{array} \right.$$

Sort

$$\frac{15}{64},90$$

Solution Steps

Express \frac{10}{11}\times 100 as a single fraction.

$$sort(\frac{10\times 100}{11}-\frac{10}{11},\frac{\frac{5}{3}\times \frac{5}{8}\times \frac{3}{8}}{\frac{5}{8}}\times \frac{3}{8})$$

Multiply 10 and 100 to get 1000.

$$sort(\frac{1000}{11}-\frac{10}{11},\frac{\frac{5}{3}\times \frac{5}{8}\times \frac{3}{8}}{\frac{5}{8}}\times \frac{3}{8})$$

Since \frac{1000}{11} and \frac{10}{11} have the same denominator, subtract them by subtracting their numerators.

$$sort(\frac{1000-10}{11},\frac{\frac{5}{3}\times \frac{5}{8}\times \frac{3}{8}}{\frac{5}{8}}\times \frac{3}{8})$$

Subtract 10 from 1000 to get 990.

$$sort(\frac{990}{11},\frac{\frac{5}{3}\times \frac{5}{8}\times \frac{3}{8}}{\frac{5}{8}}\times \frac{3}{8})$$

Divide 990 by 11 to get 90.

$$sort(90,\frac{\frac{5}{3}\times \frac{5}{8}\times \frac{3}{8}}{\frac{5}{8}}\times \frac{3}{8})$$

Cancel out \frac{5}{8} and \frac{5}{8}.

$$sort(90,\frac{5}{3}\times \frac{3}{8}\times \frac{3}{8})$$

Multiply \frac{5}{3} times \frac{3}{8} by multiplying numerator times numerator and denominator times denominator.

$$sort(90,\frac{5\times 3}{3\times 8}\times \frac{3}{8})$$

Cancel out 3 in both numerator and denominator.

$$sort(90,\frac{5}{8}\times \frac{3}{8})$$

Multiply \frac{5}{8} times \frac{3}{8} by multiplying numerator times numerator and denominator times denominator.

$$sort(90,\frac{5\times 3}{8\times 8})$$

Do the multiplications in the fraction \frac{5\times 3}{8\times 8}.

$$sort(90,\frac{15}{64})$$

Convert decimal numbers in the list 90,\frac{15}{64} to fractions.

$$90,\frac{15}{64}$$

To sort the list, start from a single element 90.

$$90$$

Insert \frac{15}{64} to the appropriate location in the new list.

$$\frac{15}{64},90$$

Evaluate

$$90,\ \frac{15}{64}$$