Solve 10/3(1/8-5/4-17/5-frac{8}{5})

$$\frac { 10 } { 3 } ( \frac { 1 } { 8 } - \frac { 5 } { 4 } - 1 \frac { 7 } { 5 } - \frac { 8 } { 5 } )$$

Evaluate

$$-\frac{205}{12}\approx -17.083333333$$

Solution Steps

Least common multiple of 8 and 4 is 8. Convert \frac{1}{8} and \frac{5}{4} to fractions with denominator 8.

$$\frac{10}{3}\left(\frac{1}{8}-\frac{10}{8}-\frac{1\times 5+7}{5}-\frac{8}{5}\right)$$

Since \frac{1}{8} and \frac{10}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{10}{3}\left(\frac{1-10}{8}-\frac{1\times 5+7}{5}-\frac{8}{5}\right)$$

Subtract 10 from 1 to get -9.

$$\frac{10}{3}\left(-\frac{9}{8}-\frac{1\times 5+7}{5}-\frac{8}{5}\right)$$

Multiply 1 and 5 to get 5.

$$\frac{10}{3}\left(-\frac{9}{8}-\frac{5+7}{5}-\frac{8}{5}\right)$$

Add 5 and 7 to get 12.

$$\frac{10}{3}\left(-\frac{9}{8}-\frac{12}{5}-\frac{8}{5}\right)$$

Least common multiple of 8 and 5 is 40. Convert -\frac{9}{8} and \frac{12}{5} to fractions with denominator 40.

$$\frac{10}{3}\left(-\frac{45}{40}-\frac{96}{40}-\frac{8}{5}\right)$$

Since -\frac{45}{40} and \frac{96}{40} have the same denominator, subtract them by subtracting their numerators.

$$\frac{10}{3}\left(\frac{-45-96}{40}-\frac{8}{5}\right)$$

Subtract 96 from -45 to get -141.

$$\frac{10}{3}\left(-\frac{141}{40}-\frac{8}{5}\right)$$

Least common multiple of 40 and 5 is 40. Convert -\frac{141}{40} and \frac{8}{5} to fractions with denominator 40.

$$\frac{10}{3}\left(-\frac{141}{40}-\frac{64}{40}\right)$$

Since -\frac{141}{40} and \frac{64}{40} have the same denominator, subtract them by subtracting their numerators.

$$\frac{10}{3}\times \frac{-141-64}{40}$$

Subtract 64 from -141 to get -205.

$$\frac{10}{3}\times \frac{-205}{40}$$

Reduce the fraction \frac{-205}{40} to lowest terms by extracting and canceling out 5.

$$\frac{10}{3}\left(-\frac{41}{8}\right)$$

Multiply \frac{10}{3} times -\frac{41}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{10\left(-41\right)}{3\times 8}$$

Do the multiplications in the fraction \frac{10\left(-41\right)}{3\times 8}.

$$\frac{-410}{24}$$

Reduce the fraction \frac{-410}{24} to lowest terms by extracting and canceling out 2.

$$-\frac{205}{12}$$

Factor

$$-\frac{205}{12} = -17\frac{1}{12} = -17.083333333333332$$