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

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

Evaluate

$$-\frac{6421}{7440}\approx -0.863037634$$

Solution Steps

Divide 16 by 16 to get 1.

$$\frac{\frac{8}{5}}{\frac{2}{25}-\frac{5}{16}}\times \frac{2}{25}\times 1-\frac{5}{16}\times \frac{25}{25}$$

Divide 25 by 25 to get 1.

$$\frac{\frac{8}{5}}{\frac{2}{25}-\frac{5}{16}}\times \frac{2}{25}\times 1-\frac{5}{16}\times 1$$

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

$$\frac{\frac{8}{5}}{\frac{32}{400}-\frac{125}{400}}\times \frac{2}{25}\times 1-\frac{5}{16}\times 1$$

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

$$\frac{\frac{8}{5}}{\frac{32-125}{400}}\times \frac{2}{25}\times 1-\frac{5}{16}\times 1$$

Subtract 125 from 32 to get -93.

$$\frac{\frac{8}{5}}{-\frac{93}{400}}\times \frac{2}{25}\times 1-\frac{5}{16}\times 1$$

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

$$\frac{8}{5}\left(-\frac{400}{93}\right)\times \frac{2}{25}\times 1-\frac{5}{16}\times 1$$

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

$$\frac{8\left(-400\right)}{5\times 93}\times \frac{2}{25}\times 1-\frac{5}{16}\times 1$$

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

$$\frac{-3200}{465}\times \frac{2}{25}\times 1-\frac{5}{16}\times 1$$

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

$$-\frac{640}{93}\times \frac{2}{25}-\frac{5}{16}\times 1$$

Multiply -\frac{640}{93} times \frac{2}{25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-640\times 2}{93\times 25}\times 1-\frac{5}{16}\times 1$$

Do the multiplications in the fraction \frac{-640\times 2}{93\times 25}.

$$\frac{-1280}{2325}\times 1-\frac{5}{16}\times 1$$

Reduce the fraction \frac{-1280}{2325} to lowest terms by extracting and canceling out 5.

$$-\frac{256}{465}-\frac{5}{16}\times 1$$

Multiply \frac{5}{16} and 1 to get \frac{5}{16}.

$$-\frac{256}{465}-\frac{5}{16}$$

Least common multiple of 465 and 16 is 7440. Convert -\frac{256}{465} and \frac{5}{16} to fractions with denominator 7440.

$$-\frac{4096}{7440}-\frac{2325}{7440}$$

Since -\frac{4096}{7440} and \frac{2325}{7440} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-4096-2325}{7440}$$

Subtract 2325 from -4096 to get -6421.

$$-\frac{6421}{7440}$$

Factor

$$-\frac{6421}{7440} = -0.8630376344086022$$