Solve -10/3(1/8-5/4+7/3-frac{8}{5})

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

Evaluate

$$\frac{47}{36}\approx 1.305555556$$

Solution Steps

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

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

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

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

Subtract 10 from 1 to get -9.

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

Least common multiple of 8 and 3 is 24. Convert -\frac{9}{8} and \frac{7}{3} to fractions with denominator 24.

$$-\frac{10}{3}\left(-\frac{27}{24}+\frac{56}{24}-\frac{8}{5}\right)$$

Since -\frac{27}{24} and \frac{56}{24} have the same denominator, add them by adding their numerators.

$$-\frac{10}{3}\left(\frac{-27+56}{24}-\frac{8}{5}\right)$$

Add -27 and 56 to get 29.

$$-\frac{10}{3}\left(\frac{29}{24}-\frac{8}{5}\right)$$

Least common multiple of 24 and 5 is 120. Convert \frac{29}{24} and \frac{8}{5} to fractions with denominator 120.

$$-\frac{10}{3}\left(\frac{145}{120}-\frac{192}{120}\right)$$

Since \frac{145}{120} and \frac{192}{120} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{10}{3}\times \frac{145-192}{120}$$

Subtract 192 from 145 to get -47.

$$-\frac{10}{3}\left(-\frac{47}{120}\right)$$

Multiply -\frac{10}{3} times -\frac{47}{120} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-10\left(-47\right)}{3\times 120}$$

Do the multiplications in the fraction \frac{-10\left(-47\right)}{3\times 120}.

$$\frac{470}{360}$$

Reduce the fraction \frac{470}{360} to lowest terms by extracting and canceling out 10.

$$\frac{47}{36}$$

Factor

$$\frac{47}{2 ^ {2} \cdot 3 ^ {2}} = 1\frac{11}{36} = 1.3055555555555556$$