Solve 7/9,quad31/5*(13/4-3/4*frac{1}{3})

$$\frac { 7 } { 9 } , \quad 3 \frac { 1 } { 5 } \cdot ( 1 \frac { 3 } { 4 } - \frac { 3 } { 4 } \cdot \frac { 1 } { 3 } )$$

Sort

$$\frac{7}{9},\frac{24}{5}$$

Solution Steps

Multiply 3 and 5 to get 15.

$$sort(\frac{7}{9},\frac{15+1}{5}\left(\frac{1\times 4+3}{4}-\frac{3}{4}\times \frac{1}{3}\right))$$

Add 15 and 1 to get 16.

$$sort(\frac{7}{9},\frac{16}{5}\left(\frac{1\times 4+3}{4}-\frac{3}{4}\times \frac{1}{3}\right))$$

Multiply 1 and 4 to get 4.

$$sort(\frac{7}{9},\frac{16}{5}\left(\frac{4+3}{4}-\frac{3}{4}\times \frac{1}{3}\right))$$

Add 4 and 3 to get 7.

$$sort(\frac{7}{9},\frac{16}{5}\left(\frac{7}{4}-\frac{3}{4}\times \frac{1}{3}\right))$$

Multiply \frac{3}{4} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$sort(\frac{7}{9},\frac{16}{5}\left(\frac{7}{4}-\frac{3\times 1}{4\times 3}\right))$$

Cancel out 3 in both numerator and denominator.

$$sort(\frac{7}{9},\frac{16}{5}\left(\frac{7}{4}-\frac{1}{4}\right))$$

Since \frac{7}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

$$sort(\frac{7}{9},\frac{16}{5}\times \frac{7-1}{4})$$

Subtract 1 from 7 to get 6.

$$sort(\frac{7}{9},\frac{16}{5}\times \frac{6}{4})$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$sort(\frac{7}{9},\frac{16}{5}\times \frac{3}{2})$$

Multiply \frac{16}{5} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$sort(\frac{7}{9},\frac{16\times 3}{5\times 2})$$

Do the multiplications in the fraction \frac{16\times 3}{5\times 2}.

$$sort(\frac{7}{9},\frac{48}{10})$$

Reduce the fraction \frac{48}{10} to lowest terms by extracting and canceling out 2.

$$sort(\frac{7}{9},\frac{24}{5})$$

Least common denominator of the numbers in the list \frac{7}{9},\frac{24}{5} is 45. Convert numbers in the list to fractions with denominator 45.

$$\frac{35}{45},\frac{216}{45}$$

Evaluate

$$\frac{7}{9},\frac{24}{5}$$