Solve (6+33/15)*(15-73/4)-(2+11/15)*(13-73/4)

$$(6+ 3 \frac { 3 } { 15 } ) \times (15- 7 \frac { 3 } { 4 } )-(2+ 1 \frac { 1 } { 15 } ) \times (13- 7 \frac { 3 } { 4 } )$$

Evaluate

$$\frac{253}{5}=50.6$$

Solution Steps

Multiply 3 and 15 to get 45.

$$\left(6+\frac{45+3}{15}\right)\left(15-\frac{7\times 4+3}{4}\right)-\left(2+\frac{1\times 15+1}{15}\right)\left(13-\frac{7\times 4+3}{4}\right)$$

Add 45 and 3 to get 48.

$$\left(6+\frac{48}{15}\right)\left(15-\frac{7\times 4+3}{4}\right)-\left(2+\frac{1\times 15+1}{15}\right)\left(13-\frac{7\times 4+3}{4}\right)$$

Reduce the fraction \frac{48}{15} to lowest terms by extracting and canceling out 3.

$$\left(6+\frac{16}{5}\right)\left(15-\frac{7\times 4+3}{4}\right)-\left(2+\frac{1\times 15+1}{15}\right)\left(13-\frac{7\times 4+3}{4}\right)$$

Convert 6 to fraction \frac{30}{5}.

$$\left(\frac{30}{5}+\frac{16}{5}\right)\left(15-\frac{7\times 4+3}{4}\right)-\left(2+\frac{1\times 15+1}{15}\right)\left(13-\frac{7\times 4+3}{4}\right)$$

Since \frac{30}{5} and \frac{16}{5} have the same denominator, add them by adding their numerators.

$$\frac{30+16}{5}\left(15-\frac{7\times 4+3}{4}\right)-\left(2+\frac{1\times 15+1}{15}\right)\left(13-\frac{7\times 4+3}{4}\right)$$

Add 30 and 16 to get 46.

$$\frac{46}{5}\left(15-\frac{7\times 4+3}{4}\right)-\left(2+\frac{1\times 15+1}{15}\right)\left(13-\frac{7\times 4+3}{4}\right)$$

Multiply 7 and 4 to get 28.

$$\frac{46}{5}\left(15-\frac{28+3}{4}\right)-\left(2+\frac{1\times 15+1}{15}\right)\left(13-\frac{7\times 4+3}{4}\right)$$

Add 28 and 3 to get 31.

$$\frac{46}{5}\left(15-\frac{31}{4}\right)-\left(2+\frac{1\times 15+1}{15}\right)\left(13-\frac{7\times 4+3}{4}\right)$$

Convert 15 to fraction \frac{60}{4}.

$$\frac{46}{5}\left(\frac{60}{4}-\frac{31}{4}\right)-\left(2+\frac{1\times 15+1}{15}\right)\left(13-\frac{7\times 4+3}{4}\right)$$

Since \frac{60}{4} and \frac{31}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{46}{5}\times \frac{60-31}{4}-\left(2+\frac{1\times 15+1}{15}\right)\left(13-\frac{7\times 4+3}{4}\right)$$

Subtract 31 from 60 to get 29.

$$\frac{46}{5}\times \frac{29}{4}-\left(2+\frac{1\times 15+1}{15}\right)\left(13-\frac{7\times 4+3}{4}\right)$$

Multiply \frac{46}{5} times \frac{29}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{46\times 29}{5\times 4}-\left(2+\frac{1\times 15+1}{15}\right)\left(13-\frac{7\times 4+3}{4}\right)$$

Do the multiplications in the fraction \frac{46\times 29}{5\times 4}.

$$\frac{1334}{20}-\left(2+\frac{1\times 15+1}{15}\right)\left(13-\frac{7\times 4+3}{4}\right)$$

Reduce the fraction \frac{1334}{20} to lowest terms by extracting and canceling out 2.

$$\frac{667}{10}-\left(2+\frac{1\times 15+1}{15}\right)\left(13-\frac{7\times 4+3}{4}\right)$$

Multiply 1 and 15 to get 15.

$$\frac{667}{10}-\left(2+\frac{15+1}{15}\right)\left(13-\frac{7\times 4+3}{4}\right)$$

Add 15 and 1 to get 16.

$$\frac{667}{10}-\left(2+\frac{16}{15}\right)\left(13-\frac{7\times 4+3}{4}\right)$$

Convert 2 to fraction \frac{30}{15}.

$$\frac{667}{10}-\left(\frac{30}{15}+\frac{16}{15}\right)\left(13-\frac{7\times 4+3}{4}\right)$$

Since \frac{30}{15} and \frac{16}{15} have the same denominator, add them by adding their numerators.

$$\frac{667}{10}-\frac{30+16}{15}\left(13-\frac{7\times 4+3}{4}\right)$$

Add 30 and 16 to get 46.

$$\frac{667}{10}-\frac{46}{15}\left(13-\frac{7\times 4+3}{4}\right)$$

Multiply 7 and 4 to get 28.

$$\frac{667}{10}-\frac{46}{15}\left(13-\frac{28+3}{4}\right)$$

Add 28 and 3 to get 31.

$$\frac{667}{10}-\frac{46}{15}\left(13-\frac{31}{4}\right)$$

Convert 13 to fraction \frac{52}{4}.

$$\frac{667}{10}-\frac{46}{15}\left(\frac{52}{4}-\frac{31}{4}\right)$$

Since \frac{52}{4} and \frac{31}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{667}{10}-\frac{46}{15}\times \frac{52-31}{4}$$

Subtract 31 from 52 to get 21.

$$\frac{667}{10}-\frac{46}{15}\times \frac{21}{4}$$

Multiply \frac{46}{15} times \frac{21}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{667}{10}-\frac{46\times 21}{15\times 4}$$

Do the multiplications in the fraction \frac{46\times 21}{15\times 4}.

$$\frac{667}{10}-\frac{966}{60}$$

Reduce the fraction \frac{966}{60} to lowest terms by extracting and canceling out 6.

$$\frac{667}{10}-\frac{161}{10}$$

Since \frac{667}{10} and \frac{161}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{667-161}{10}$$

Subtract 161 from 667 to get 506.

$$\frac{506}{10}$$

Reduce the fraction \frac{506}{10} to lowest terms by extracting and canceling out 2.

$$\frac{253}{5}$$

Factor

$$\frac{11 \cdot 23}{5} = 50\frac{3}{5} = 50.6$$