Solve 49/frac{2{25}-5/16}

$$\frac{ 49 }{ \frac{ 2 }{ 25 } - \frac{ 5 }{ 16 } }$$

Evaluate

$$-\frac{19600}{93}\approx -210.752688172$$

Solution Steps

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

$$\frac{49}{\frac{32}{400}-\frac{125}{400}}$$

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

$$\frac{49}{\frac{32-125}{400}}$$

Subtract 125 from 32 to get -93.

$$\frac{49}{-\frac{93}{400}}$$

Divide 49 by -\frac{93}{400} by multiplying 49 by the reciprocal of -\frac{93}{400}.

$$49\left(-\frac{400}{93}\right)$$

Express 49\left(-\frac{400}{93}\right) as a single fraction.

$$\frac{49\left(-400\right)}{93}$$

Multiply 49 and -400 to get -19600.

$$\frac{-19600}{93}$$

Fraction \frac{-19600}{93} can be rewritten as -\frac{19600}{93} by extracting the negative sign.

$$-\frac{19600}{93}$$

Factor

$$-\frac{19600}{93} = -210\frac{70}{93} = -210.752688172043$$