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

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

Evaluate

$$-\frac{16000}{93}\approx -172.043010753$$

Solution Steps

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

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

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

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

Subtract 125 from 32 to get -93.

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

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

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

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

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

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

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

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

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

Express -\frac{640}{93}\times 25 as a single fraction.

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

Multiply -640 and 25 to get -16000.

$$\frac{-16000}{93}$$

Fraction \frac{-16000}{93} can be rewritten as -\frac{16000}{93} by extracting the negative sign.

$$-\frac{16000}{93}$$

Factor

$$-\frac{16000}{93} = -172\frac{4}{93} = -172.04301075268816$$