Solve 1/2*(1/5+1/2*1/8)-frac{1}{5}*(frac{1}{6}+frac{1}{2}*frac{1}{5})

$$\frac { 1 } { 2 } \times ( \frac { 1 } { 5 } + \frac { 1 } { 2 } \times \frac { 1 } { 8 } ) - \frac { 1 } { 5 } \times ( \frac { 1 } { 6 } + \frac { 1 } { 2 } \times \frac { 1 } { 5 } )$$

Evaluate

$$\frac{187}{2400}\approx 0.077916667$$

Solution Steps

Multiply \frac{1}{2} times \frac{1}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{2}\left(\frac{1}{5}+\frac{1\times 1}{2\times 8}\right)-\frac{1}{5}\left(\frac{1}{6}+\frac{1}{2}\times \frac{1}{5}\right)$$

Do the multiplications in the fraction \frac{1\times 1}{2\times 8}.

$$\frac{1}{2}\left(\frac{1}{5}+\frac{1}{16}\right)-\frac{1}{5}\left(\frac{1}{6}+\frac{1}{2}\times \frac{1}{5}\right)$$

Least common multiple of 5 and 16 is 80. Convert \frac{1}{5} and \frac{1}{16} to fractions with denominator 80.

$$\frac{1}{2}\left(\frac{16}{80}+\frac{5}{80}\right)-\frac{1}{5}\left(\frac{1}{6}+\frac{1}{2}\times \frac{1}{5}\right)$$

Since \frac{16}{80} and \frac{5}{80} have the same denominator, add them by adding their numerators.

$$\frac{1}{2}\times \frac{16+5}{80}-\frac{1}{5}\left(\frac{1}{6}+\frac{1}{2}\times \frac{1}{5}\right)$$

Add 16 and 5 to get 21.

$$\frac{1}{2}\times \frac{21}{80}-\frac{1}{5}\left(\frac{1}{6}+\frac{1}{2}\times \frac{1}{5}\right)$$

Multiply \frac{1}{2} times \frac{21}{80} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 21}{2\times 80}-\frac{1}{5}\left(\frac{1}{6}+\frac{1}{2}\times \frac{1}{5}\right)$$

Do the multiplications in the fraction \frac{1\times 21}{2\times 80}.

$$\frac{21}{160}-\frac{1}{5}\left(\frac{1}{6}+\frac{1}{2}\times \frac{1}{5}\right)$$

Multiply \frac{1}{2} times \frac{1}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{21}{160}-\frac{1}{5}\left(\frac{1}{6}+\frac{1\times 1}{2\times 5}\right)$$

Do the multiplications in the fraction \frac{1\times 1}{2\times 5}.

$$\frac{21}{160}-\frac{1}{5}\left(\frac{1}{6}+\frac{1}{10}\right)$$

Least common multiple of 6 and 10 is 30. Convert \frac{1}{6} and \frac{1}{10} to fractions with denominator 30.

$$\frac{21}{160}-\frac{1}{5}\left(\frac{5}{30}+\frac{3}{30}\right)$$

Since \frac{5}{30} and \frac{3}{30} have the same denominator, add them by adding their numerators.

$$\frac{21}{160}-\frac{1}{5}\times \frac{5+3}{30}$$

Add 5 and 3 to get 8.

$$\frac{21}{160}-\frac{1}{5}\times \frac{8}{30}$$

Reduce the fraction \frac{8}{30} to lowest terms by extracting and canceling out 2.

$$\frac{21}{160}-\frac{1}{5}\times \frac{4}{15}$$

Multiply \frac{1}{5} times \frac{4}{15} by multiplying numerator times numerator and denominator times denominator.

$$\frac{21}{160}-\frac{1\times 4}{5\times 15}$$

Do the multiplications in the fraction \frac{1\times 4}{5\times 15}.

$$\frac{21}{160}-\frac{4}{75}$$

Least common multiple of 160 and 75 is 2400. Convert \frac{21}{160} and \frac{4}{75} to fractions with denominator 2400.

$$\frac{315}{2400}-\frac{128}{2400}$$

Since \frac{315}{2400} and \frac{128}{2400} have the same denominator, subtract them by subtracting their numerators.

$$\frac{315-128}{2400}$$

Subtract 128 from 315 to get 187.

$$\frac{187}{2400}$$

Factor

$$\frac{11 \cdot 17}{2 ^ {5} \cdot 3 \cdot 5 ^ {2}} = 0.07791666666666666$$