Solve 9/frac{2{25}-5/16}

$$\frac{ 9 }{ \frac{ 2 }{ 25 } - \frac{ 5 }{ 16 } }$$

Evaluate

$$-\frac{1200}{31}\approx -38.709677419$$

Solution Steps

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

$$\frac{9}{\frac{32}{400}-\frac{125}{400}}$$

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

$$\frac{9}{\frac{32-125}{400}}$$

Subtract 125 from 32 to get -93.

$$\frac{9}{-\frac{93}{400}}$$

Divide 9 by -\frac{93}{400} by multiplying 9 by the reciprocal of -\frac{93}{400}.

$$9\left(-\frac{400}{93}\right)$$

Express 9\left(-\frac{400}{93}\right) as a single fraction.

$$\frac{9\left(-400\right)}{93}$$

Multiply 9 and -400 to get -3600.

$$\frac{-3600}{93}$$

Reduce the fraction \frac{-3600}{93} to lowest terms by extracting and canceling out 3.

$$-\frac{1200}{31}$$

Factor

$$-\frac{1200}{31} = -38\frac{22}{31} = -38.70967741935484$$