Solve 800/50/frac{2{25}-5/16}

$$\frac{ \frac{ 800 }{ 50 } }{ \frac{ 2 }{ 25 } - \frac{ 5 }{ 16 } }$$

Evaluate

$$-\frac{6400}{93}\approx -68.817204301$$

Solution Steps

Divide 800 by 50 to get 16.

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

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

$$\frac{16}{\frac{32}{400}-\frac{125}{400}}$$

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

$$\frac{16}{\frac{32-125}{400}}$$

Subtract 125 from 32 to get -93.

$$\frac{16}{-\frac{93}{400}}$$

Divide 16 by -\frac{93}{400} by multiplying 16 by the reciprocal of -\frac{93}{400}.

$$16\left(-\frac{400}{93}\right)$$

Express 16\left(-\frac{400}{93}\right) as a single fraction.

$$\frac{16\left(-400\right)}{93}$$

Multiply 16 and -400 to get -6400.

$$\frac{-6400}{93}$$

Fraction \frac{-6400}{93} can be rewritten as -\frac{6400}{93} by extracting the negative sign.

$$-\frac{6400}{93}$$

Factor

$$-\frac{6400}{93} = -68\frac{76}{93} = -68.81720430107526$$