Solve (-31/6)*(+18/36+1/5-10/57+frac{5}{1})

$$( - 3 \frac { 1 } { 6 } ) \cdot ( + \frac { 18 } { 36 } + \frac { 1 } { 5 } - \frac { 10 } { 57 } + \frac { 5 } { 1 } )$$

Evaluate

$$-\frac{3149}{180}\approx -17.494444444$$

Solution Steps

Multiply 3 and 6 to get 18.

$$\left(-\frac{18+1}{6}\right)\left(\frac{18}{36}+\frac{1}{5}-\frac{10}{57}+\frac{5}{1}\right)$$

Add 18 and 1 to get 19.

$$-\frac{19}{6}\left(\frac{18}{36}+\frac{1}{5}-\frac{10}{57}+\frac{5}{1}\right)$$

Reduce the fraction \frac{18}{36} to lowest terms by extracting and canceling out 18.

$$-\frac{19}{6}\left(\frac{1}{2}+\frac{1}{5}-\frac{10}{57}+\frac{5}{1}\right)$$

Least common multiple of 2 and 5 is 10. Convert \frac{1}{2} and \frac{1}{5} to fractions with denominator 10.

$$-\frac{19}{6}\left(\frac{5}{10}+\frac{2}{10}-\frac{10}{57}+\frac{5}{1}\right)$$

Since \frac{5}{10} and \frac{2}{10} have the same denominator, add them by adding their numerators.

$$-\frac{19}{6}\left(\frac{5+2}{10}-\frac{10}{57}+\frac{5}{1}\right)$$

Add 5 and 2 to get 7.

$$-\frac{19}{6}\left(\frac{7}{10}-\frac{10}{57}+\frac{5}{1}\right)$$

Least common multiple of 10 and 57 is 570. Convert \frac{7}{10} and \frac{10}{57} to fractions with denominator 570.

$$-\frac{19}{6}\left(\frac{399}{570}-\frac{100}{570}+\frac{5}{1}\right)$$

Since \frac{399}{570} and \frac{100}{570} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{19}{6}\left(\frac{399-100}{570}+\frac{5}{1}\right)$$

Subtract 100 from 399 to get 299.

$$-\frac{19}{6}\left(\frac{299}{570}+\frac{5}{1}\right)$$

Anything divided by one gives itself.

$$-\frac{19}{6}\left(\frac{299}{570}+5\right)$$

Convert 5 to fraction \frac{2850}{570}.

$$-\frac{19}{6}\left(\frac{299}{570}+\frac{2850}{570}\right)$$

Since \frac{299}{570} and \frac{2850}{570} have the same denominator, add them by adding their numerators.

$$-\frac{19}{6}\times \frac{299+2850}{570}$$

Add 299 and 2850 to get 3149.

$$-\frac{19}{6}\times \frac{3149}{570}$$

Multiply -\frac{19}{6} times \frac{3149}{570} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-19\times 3149}{6\times 570}$$

Do the multiplications in the fraction \frac{-19\times 3149}{6\times 570}.

$$\frac{-59831}{3420}$$

Reduce the fraction \frac{-59831}{3420} to lowest terms by extracting and canceling out 19.

$$-\frac{3149}{180}$$

Factor

$$-\frac{3149}{180} = -17\frac{89}{180} = -17.494444444444444$$