Solve {l}{33/5div12/7}{5/9div10/11}

$$\left. \begin{array} { l } { 3 \frac { 3 } { 5 } \div 1 \frac { 2 } { 7 } } \\ { \frac { 5 } { 9 } \div \frac { 10 } { 11 } } \end{array} \right.$$

Sort

$$\frac{11}{18},\frac{14}{5}$$

Solution Steps

Divide \frac{3\times 5+3}{5} by \frac{1\times 7+2}{7} by multiplying \frac{3\times 5+3}{5} by the reciprocal of \frac{1\times 7+2}{7}.

$$sort(\frac{\left(3\times 5+3\right)\times 7}{5\left(1\times 7+2\right)},\frac{\frac{5}{9}}{\frac{10}{11}})$$

Multiply 3 and 5 to get 15.

$$sort(\frac{\left(15+3\right)\times 7}{5\left(1\times 7+2\right)},\frac{\frac{5}{9}}{\frac{10}{11}})$$

Add 15 and 3 to get 18.

$$sort(\frac{18\times 7}{5\left(1\times 7+2\right)},\frac{\frac{5}{9}}{\frac{10}{11}})$$

Multiply 18 and 7 to get 126.

$$sort(\frac{126}{5\left(1\times 7+2\right)},\frac{\frac{5}{9}}{\frac{10}{11}})$$

Multiply 1 and 7 to get 7.

$$sort(\frac{126}{5\left(7+2\right)},\frac{\frac{5}{9}}{\frac{10}{11}})$$

Add 7 and 2 to get 9.

$$sort(\frac{126}{5\times 9},\frac{\frac{5}{9}}{\frac{10}{11}})$$

Multiply 5 and 9 to get 45.

$$sort(\frac{126}{45},\frac{\frac{5}{9}}{\frac{10}{11}})$$

Reduce the fraction \frac{126}{45} to lowest terms by extracting and canceling out 9.

$$sort(\frac{14}{5},\frac{\frac{5}{9}}{\frac{10}{11}})$$

Divide \frac{5}{9} by \frac{10}{11} by multiplying \frac{5}{9} by the reciprocal of \frac{10}{11}.

$$sort(\frac{14}{5},\frac{5}{9}\times \frac{11}{10})$$

Multiply \frac{5}{9} times \frac{11}{10} by multiplying numerator times numerator and denominator times denominator.

$$sort(\frac{14}{5},\frac{5\times 11}{9\times 10})$$

Do the multiplications in the fraction \frac{5\times 11}{9\times 10}.

$$sort(\frac{14}{5},\frac{55}{90})$$

Reduce the fraction \frac{55}{90} to lowest terms by extracting and canceling out 5.

$$sort(\frac{14}{5},\frac{11}{18})$$

Least common denominator of the numbers in the list \frac{14}{5},\frac{11}{18} is 90. Convert numbers in the list to fractions with denominator 90.

$$\frac{252}{90},\frac{55}{90}$$

To sort the list, start from a single element \frac{252}{90}.

$$\frac{252}{90}$$

Insert \frac{55}{90} to the appropriate location in the new list.

$$\frac{55}{90},\frac{252}{90}$$

Replace the obtained fractions with the initial values.

$$\frac{11}{18},\frac{14}{5}$$

Evaluate

$$\frac{14}{5},\ \frac{11}{18}$$