Solve 8/5/frac{2{25}-5/16}-frac{25/6}{frac{75}{49}+frac{15}{89}}

$$\frac{ \frac{ 8 }{ 5 } }{ \frac{ 2 }{ 25 } - \frac{ 5 }{ 16 } } - \frac{ \frac{ 25 }{ 6 } }{ \frac{ 75 }{ 49 } + \frac{ 15 }{ 89 } }$$

Evaluate

$$-\frac{2572915}{275652}\approx -9.333924659$$

Solution Steps

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

$$\frac{\frac{8}{5}}{\frac{32}{400}-\frac{125}{400}}-\frac{\frac{25}{6}}{\frac{75}{49}+\frac{15}{89}}$$

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

$$\frac{\frac{8}{5}}{\frac{32-125}{400}}-\frac{\frac{25}{6}}{\frac{75}{49}+\frac{15}{89}}$$

Subtract 125 from 32 to get -93.

$$\frac{\frac{8}{5}}{-\frac{93}{400}}-\frac{\frac{25}{6}}{\frac{75}{49}+\frac{15}{89}}$$

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

$$\frac{8}{5}\left(-\frac{400}{93}\right)-\frac{\frac{25}{6}}{\frac{75}{49}+\frac{15}{89}}$$

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

$$\frac{8\left(-400\right)}{5\times 93}-\frac{\frac{25}{6}}{\frac{75}{49}+\frac{15}{89}}$$

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

$$\frac{-3200}{465}-\frac{\frac{25}{6}}{\frac{75}{49}+\frac{15}{89}}$$

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

$$-\frac{640}{93}-\frac{\frac{25}{6}}{\frac{75}{49}+\frac{15}{89}}$$

Least common multiple of 49 and 89 is 4361. Convert \frac{75}{49} and \frac{15}{89} to fractions with denominator 4361.

$$-\frac{640}{93}-\frac{\frac{25}{6}}{\frac{6675}{4361}+\frac{735}{4361}}$$

Since \frac{6675}{4361} and \frac{735}{4361} have the same denominator, add them by adding their numerators.

$$-\frac{640}{93}-\frac{\frac{25}{6}}{\frac{6675+735}{4361}}$$

Add 6675 and 735 to get 7410.

$$-\frac{640}{93}-\frac{\frac{25}{6}}{\frac{7410}{4361}}$$

Divide \frac{25}{6} by \frac{7410}{4361} by multiplying \frac{25}{6} by the reciprocal of \frac{7410}{4361}.

$$-\frac{640}{93}-\frac{25}{6}\times \frac{4361}{7410}$$

Multiply \frac{25}{6} times \frac{4361}{7410} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{640}{93}-\frac{25\times 4361}{6\times 7410}$$

Do the multiplications in the fraction \frac{25\times 4361}{6\times 7410}.

$$-\frac{640}{93}-\frac{109025}{44460}$$

Reduce the fraction \frac{109025}{44460} to lowest terms by extracting and canceling out 5.

$$-\frac{640}{93}-\frac{21805}{8892}$$

Least common multiple of 93 and 8892 is 275652. Convert -\frac{640}{93} and \frac{21805}{8892} to fractions with denominator 275652.

$$-\frac{1896960}{275652}-\frac{675955}{275652}$$

Since -\frac{1896960}{275652} and \frac{675955}{275652} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-1896960-675955}{275652}$$

Subtract 675955 from -1896960 to get -2572915.

$$-\frac{2572915}{275652}$$

Factor

$$-\frac{2572915}{275652} = -9\frac{92047}{275652} = -9.333924658627545$$