Solve 8/5/frac{2{25}-5/16}22/25

$$\frac{ \frac{ 8 }{ 5 } }{ \frac{ 2 }{ 25 } - \frac{ 5 }{ 16 } } \frac{ 22 }{ 25 }$$

Evaluate

$$-\frac{2816}{465}\approx -6.055913978$$

Solution Steps

Least common multiple of 25 and 16 is 400. Convert \frac{2}{25} and \frac{5}{16} to fractions with denominator 400.

$$\frac{\frac{8}{5}}{\frac{32}{400}-\frac{125}{400}}\times \frac{22}{25}$$

Since \frac{32}{400} and \frac{125}{400} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{8}{5}}{\frac{32-125}{400}}\times \frac{22}{25}$$

Subtract 125 from 32 to get -93.

$$\frac{\frac{8}{5}}{-\frac{93}{400}}\times \frac{22}{25}$$

Divide \frac{8}{5} by -\frac{93}{400} by multiplying \frac{8}{5} by the reciprocal of -\frac{93}{400}.

$$\frac{8}{5}\left(-\frac{400}{93}\right)\times \frac{22}{25}$$

Multiply \frac{8}{5} times -\frac{400}{93} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8\left(-400\right)}{5\times 93}\times \frac{22}{25}$$

Do the multiplications in the fraction \frac{8\left(-400\right)}{5\times 93}.

$$\frac{-3200}{465}\times \frac{22}{25}$$

Reduce the fraction \frac{-3200}{465} to lowest terms by extracting and canceling out 5.

$$-\frac{640}{93}\times \frac{22}{25}$$

Multiply -\frac{640}{93} times \frac{22}{25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-640\times 22}{93\times 25}$$

Do the multiplications in the fraction \frac{-640\times 22}{93\times 25}.

$$\frac{-14080}{2325}$$

Reduce the fraction \frac{-14080}{2325} to lowest terms by extracting and canceling out 5.

$$-\frac{2816}{465}$$

Factor

$$-\frac{2816}{465} = -6\frac{26}{465} = -6.055913978494623$$