Solve 8/5/frac{2{15}-5/16}

$$\frac { \frac { 8 } { 5 } } { \frac { 2 } { 15 } - \frac { 5 } { 16 } }$$

Evaluate

$$-\frac{384}{43}\approx -8.930232558$$

Solution Steps

Least common multiple of 15 and 16 is 240. Convert \frac{2}{15} and \frac{5}{16} to fractions with denominator 240.

$$\frac{\frac{8}{5}}{\frac{32}{240}-\frac{75}{240}}$$

Since \frac{32}{240} and \frac{75}{240} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{8}{5}}{\frac{32-75}{240}}$$

Subtract 75 from 32 to get -43.

$$\frac{\frac{8}{5}}{-\frac{43}{240}}$$

Divide \frac{8}{5} by -\frac{43}{240} by multiplying \frac{8}{5} by the reciprocal of -\frac{43}{240}.

$$\frac{8}{5}\left(-\frac{240}{43}\right)$$

Multiply \frac{8}{5} times -\frac{240}{43} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8\left(-240\right)}{5\times 43}$$

Do the multiplications in the fraction \frac{8\left(-240\right)}{5\times 43}.

$$\frac{-1920}{215}$$

Reduce the fraction \frac{-1920}{215} to lowest terms by extracting and canceling out 5.

$$-\frac{384}{43}$$

Factor

$$-\frac{384}{43} = -8\frac{40}{43} = -8.930232558139535$$