Solve 16/12/frac{2{25}-5/16}

$$\frac{ \frac{ 16 }{ 12 } }{ \frac{ 2 }{ 25 } - \frac{ 5 }{ 16 } }$$

Evaluate

$$-\frac{1600}{279}\approx -5.734767025$$

Solution Steps

Reduce the fraction \frac{16}{12} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{4}{3}}{\frac{2}{25}-\frac{5}{16}}$$

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

$$\frac{\frac{4}{3}}{\frac{32}{400}-\frac{125}{400}}$$

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

$$\frac{\frac{4}{3}}{\frac{32-125}{400}}$$

Subtract 125 from 32 to get -93.

$$\frac{\frac{4}{3}}{-\frac{93}{400}}$$

Divide \frac{4}{3} by -\frac{93}{400} by multiplying \frac{4}{3} by the reciprocal of -\frac{93}{400}.

$$\frac{4}{3}\left(-\frac{400}{93}\right)$$

Multiply \frac{4}{3} times -\frac{400}{93} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\left(-400\right)}{3\times 93}$$

Do the multiplications in the fraction \frac{4\left(-400\right)}{3\times 93}.

$$\frac{-1600}{279}$$

Fraction \frac{-1600}{279} can be rewritten as -\frac{1600}{279} by extracting the negative sign.

$$-\frac{1600}{279}$$

Factor

$$-\frac{1600}{279} = -5\frac{205}{279} = -5.734767025089606$$