Solve {r}{1/5*6/7}{5/8*7/2}{frac{8}{9}*frac{7}{2}}

$$\left. \begin{array} { r } { \frac { 1 } { 5 } \times \frac { 6 } { 7 } } \\ { \frac { 5 } { 8 } \times \frac { 7 } { 2 } } \\ { \frac { 8 } { 9 } \times \frac { 7 } { 2 } } \end{array} \right.$$

Sort

$$\frac{6}{35},\ \frac{35}{16},\ \frac{28}{9}$$

Solution Steps

Multiply \frac{1}{5} times \frac{6}{7} by multiplying numerator times numerator and denominator times denominator.

$$sort(\frac{1\times 6}{5\times 7},\frac{5}{8}\times \frac{7}{2},\frac{8}{9}\times \frac{7}{2})$$

Do the multiplications in the fraction \frac{1\times 6}{5\times 7}.

$$sort(\frac{6}{35},\frac{5}{8}\times \frac{7}{2},\frac{8}{9}\times \frac{7}{2})$$

Multiply \frac{5}{8} times \frac{7}{2} by multiplying numerator times numerator and denominator times denominator.

$$sort(\frac{6}{35},\frac{5\times 7}{8\times 2},\frac{8}{9}\times \frac{7}{2})$$

Do the multiplications in the fraction \frac{5\times 7}{8\times 2}.

$$sort(\frac{6}{35},\frac{35}{16},\frac{8}{9}\times \frac{7}{2})$$

Multiply \frac{8}{9} times \frac{7}{2} by multiplying numerator times numerator and denominator times denominator.

$$sort(\frac{6}{35},\frac{35}{16},\frac{8\times 7}{9\times 2})$$

Do the multiplications in the fraction \frac{8\times 7}{9\times 2}.

$$sort(\frac{6}{35},\frac{35}{16},\frac{56}{18})$$

Reduce the fraction \frac{56}{18} to lowest terms by extracting and canceling out 2.

$$sort(\frac{6}{35},\frac{35}{16},\frac{28}{9})$$

Least common denominator of the numbers in the list \frac{6}{35},\frac{35}{16},\frac{28}{9} is 5040. Convert numbers in the list to fractions with denominator 5040.

$$\frac{864}{5040},\frac{11025}{5040},\frac{15680}{5040}$$

Evaluate

$$\frac{6}{35},\ \frac{35}{16},\ \frac{28}{9}$$