Solve -1/60*1/32+1/24*1/8-frac{5}{192}*frac{1}{2}

$$- \frac{ 1 }{ 60 } \times \frac{ 1 }{ 32 } + \frac{ 1 }{ 24 } \times \frac{ 1 }{ 8 } - \frac{ 5 }{ 192 } \times \frac{ 1 }{ 2 }$$

Evaluate

$$-\frac{1}{120}\approx -0.008333333$$

Solution Steps

Multiply -\frac{1}{60} times \frac{1}{32} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-1}{60\times 32}+\frac{1}{24}\times \frac{1}{8}-\frac{5}{192}\times \frac{1}{2}$$

Do the multiplications in the fraction \frac{-1}{60\times 32}.

$$\frac{-1}{1920}+\frac{1}{24}\times \frac{1}{8}-\frac{5}{192}\times \frac{1}{2}$$

Fraction \frac{-1}{1920} can be rewritten as -\frac{1}{1920} by extracting the negative sign.

$$-\frac{1}{1920}+\frac{1}{24}\times \frac{1}{8}-\frac{5}{192}\times \frac{1}{2}$$

Multiply \frac{1}{24} times \frac{1}{8} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{1}{1920}+\frac{1\times 1}{24\times 8}-\frac{5}{192}\times \frac{1}{2}$$

Do the multiplications in the fraction \frac{1\times 1}{24\times 8}.

$$-\frac{1}{1920}+\frac{1}{192}-\frac{5}{192}\times \frac{1}{2}$$

Least common multiple of 1920 and 192 is 1920. Convert -\frac{1}{1920} and \frac{1}{192} to fractions with denominator 1920.

$$-\frac{1}{1920}+\frac{10}{1920}-\frac{5}{192}\times \frac{1}{2}$$

Since -\frac{1}{1920} and \frac{10}{1920} have the same denominator, add them by adding their numerators.

$$\frac{-1+10}{1920}-\frac{5}{192}\times \frac{1}{2}$$

Add -1 and 10 to get 9.

$$\frac{9}{1920}-\frac{5}{192}\times \frac{1}{2}$$

Reduce the fraction \frac{9}{1920} to lowest terms by extracting and canceling out 3.

$$\frac{3}{640}-\frac{5}{192}\times \frac{1}{2}$$

Multiply \frac{5}{192} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3}{640}-\frac{5\times 1}{192\times 2}$$

Do the multiplications in the fraction \frac{5\times 1}{192\times 2}.

$$\frac{3}{640}-\frac{5}{384}$$

Least common multiple of 640 and 384 is 1920. Convert \frac{3}{640} and \frac{5}{384} to fractions with denominator 1920.

$$\frac{9}{1920}-\frac{25}{1920}$$

Since \frac{9}{1920} and \frac{25}{1920} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9-25}{1920}$$

Subtract 25 from 9 to get -16.

$$\frac{-16}{1920}$$

Reduce the fraction \frac{-16}{1920} to lowest terms by extracting and canceling out 16.

$$-\frac{1}{120}$$

Factor

$$-\frac{1}{120} = -0.008333333333333333$$