Solve 8/5/frac{2{25}-5/16}16div-3=

$$\frac{ \frac{ 8 }{ 5 } }{ \frac{ 2 }{ 25 } - \frac{ 5 }{ 16 } } 16 \div -3=$$

Evaluate

$$\frac{10240}{279}\approx 36.702508961$$

Solution Steps

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

$$\frac{\frac{\frac{8}{5}}{\frac{32}{400}-\frac{125}{400}}\times 16}{-3}$$

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

$$\frac{\frac{\frac{8}{5}}{\frac{32-125}{400}}\times 16}{-3}$$

Subtract 125 from 32 to get -93.

$$\frac{\frac{\frac{8}{5}}{-\frac{93}{400}}\times 16}{-3}$$

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

$$\frac{\frac{8}{5}\left(-\frac{400}{93}\right)\times 16}{-3}$$

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

$$\frac{\frac{8\left(-400\right)}{5\times 93}\times 16}{-3}$$

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

$$\frac{\frac{-3200}{465}\times 16}{-3}$$

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

$$\frac{-\frac{640}{93}\times 16}{-3}$$

Express -\frac{640}{93}\times 16 as a single fraction.

$$\frac{\frac{-640\times 16}{93}}{-3}$$

Multiply -640 and 16 to get -10240.

$$\frac{\frac{-10240}{93}}{-3}$$

Fraction \frac{-10240}{93} can be rewritten as -\frac{10240}{93} by extracting the negative sign.

$$\frac{-\frac{10240}{93}}{-3}$$

Express \frac{-\frac{10240}{93}}{-3} as a single fraction.

$$\frac{-10240}{93\left(-3\right)}$$

Multiply 93 and -3 to get -279.

$$\frac{-10240}{-279}$$

Fraction \frac{-10240}{-279} can be simplified to \frac{10240}{279} by removing the negative sign from both the numerator and the denominator.

$$\frac{10240}{279}$$

Factor

$$\frac{2 ^ {11} \cdot 5}{3 ^ {2} \cdot 31} = 36\frac{196}{279} = 36.702508960573475$$