Solve (+5/8)*(-8/3)+1/6/4-frac{5{2}}

$$\frac { ( + \frac { 5 } { 8 } ) \cdot ( \frac { - 8 } { 3 } ) + \frac { 1 } { 6 } } { 4 - \frac { 5 } { 2 } }$$

Evaluate

$$-1$$

Solution Steps

Fraction \frac{-8}{3} can be rewritten as -\frac{8}{3} by extracting the negative sign.

$$\frac{\frac{5}{8}\left(-\frac{8}{3}\right)+\frac{1}{6}}{4-\frac{5}{2}}$$

Multiply \frac{5}{8} times -\frac{8}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{5\left(-8\right)}{8\times 3}+\frac{1}{6}}{4-\frac{5}{2}}$$

Do the multiplications in the fraction \frac{5\left(-8\right)}{8\times 3}.

$$\frac{\frac{-40}{24}+\frac{1}{6}}{4-\frac{5}{2}}$$

Reduce the fraction \frac{-40}{24} to lowest terms by extracting and canceling out 8.

$$\frac{-\frac{5}{3}+\frac{1}{6}}{4-\frac{5}{2}}$$

Least common multiple of 3 and 6 is 6. Convert -\frac{5}{3} and \frac{1}{6} to fractions with denominator 6.

$$\frac{-\frac{10}{6}+\frac{1}{6}}{4-\frac{5}{2}}$$

Since -\frac{10}{6} and \frac{1}{6} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-10+1}{6}}{4-\frac{5}{2}}$$

Add -10 and 1 to get -9.

$$\frac{\frac{-9}{6}}{4-\frac{5}{2}}$$

Reduce the fraction \frac{-9}{6} to lowest terms by extracting and canceling out 3.

$$\frac{-\frac{3}{2}}{4-\frac{5}{2}}$$

Convert 4 to fraction \frac{8}{2}.

$$\frac{-\frac{3}{2}}{\frac{8}{2}-\frac{5}{2}}$$

Since \frac{8}{2} and \frac{5}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{3}{2}}{\frac{8-5}{2}}$$

Subtract 5 from 8 to get 3.

$$\frac{-\frac{3}{2}}{\frac{3}{2}}$$

Divide -\frac{3}{2} by \frac{3}{2} to get -1.

$$-1$$

Factor

$$-1$$