Solve (3/5-1/8)*(11/1-3/2-frac{2}{1})

$$( \frac { 3 } { 5 } - \frac { 1 } { 8 } ) \cdot ( \frac { 11 } { 1 } - \frac { 3 } { 2 } - \frac { 2 } { 1 } )$$

Evaluate

$$\frac{57}{16}=3.5625$$

Solution Steps

Least common multiple of 5 and 8 is 40. Convert \frac{3}{5} and \frac{1}{8} to fractions with denominator 40.

$$\left(\frac{24}{40}-\frac{5}{40}\right)\left(\frac{11}{1}-\frac{3}{2}-\frac{2}{1}\right)$$

Since \frac{24}{40} and \frac{5}{40} have the same denominator, subtract them by subtracting their numerators.

$$\frac{24-5}{40}\left(\frac{11}{1}-\frac{3}{2}-\frac{2}{1}\right)$$

Subtract 5 from 24 to get 19.

$$\frac{19}{40}\left(\frac{11}{1}-\frac{3}{2}-\frac{2}{1}\right)$$

Anything divided by one gives itself.

$$\frac{19}{40}\left(11-\frac{3}{2}-\frac{2}{1}\right)$$

Convert 11 to fraction \frac{22}{2}.

$$\frac{19}{40}\left(\frac{22}{2}-\frac{3}{2}-\frac{2}{1}\right)$$

Since \frac{22}{2} and \frac{3}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{19}{40}\left(\frac{22-3}{2}-\frac{2}{1}\right)$$

Subtract 3 from 22 to get 19.

$$\frac{19}{40}\left(\frac{19}{2}-\frac{2}{1}\right)$$

Anything divided by one gives itself.

$$\frac{19}{40}\left(\frac{19}{2}-2\right)$$

Convert 2 to fraction \frac{4}{2}.

$$\frac{19}{40}\left(\frac{19}{2}-\frac{4}{2}\right)$$

Since \frac{19}{2} and \frac{4}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{19}{40}\times \frac{19-4}{2}$$

Subtract 4 from 19 to get 15.

$$\frac{19}{40}\times \frac{15}{2}$$

Multiply \frac{19}{40} times \frac{15}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{19\times 15}{40\times 2}$$

Do the multiplications in the fraction \frac{19\times 15}{40\times 2}.

$$\frac{285}{80}$$

Reduce the fraction \frac{285}{80} to lowest terms by extracting and canceling out 5.

$$\frac{57}{16}$$

Factor

$$\frac{3 \cdot 19}{2 ^ {4}} = 3\frac{9}{16} = 3.5625$$