Solve -2/58/3/frac{2{9}}+frac{39/5-frac{7}{8}}{frac{-3}{8}frac{27}{18}}

$$\frac{ - \frac{ 2 }{ 5 } \frac{ 8 }{ 3 } }{ \frac{ 2 }{ 9 } } + \frac{ \frac{ 39 }{ 5 } - \frac{ 7 }{ 8 } }{ \frac{ -3 }{ 8 } \frac{ 27 }{ 18 } }$$

Evaluate

$$-\frac{154}{9}\approx -17.111111111$$

Solution Steps

Multiply -\frac{2}{5} times \frac{8}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{-2\times 8}{5\times 3}}{\frac{2}{9}}+\frac{\frac{39}{5}-\frac{7}{8}}{\frac{-3}{8}\times \frac{27}{18}}$$

Do the multiplications in the fraction \frac{-2\times 8}{5\times 3}.

$$\frac{\frac{-16}{15}}{\frac{2}{9}}+\frac{\frac{39}{5}-\frac{7}{8}}{\frac{-3}{8}\times \frac{27}{18}}$$

Fraction \frac{-16}{15} can be rewritten as -\frac{16}{15} by extracting the negative sign.

$$\frac{-\frac{16}{15}}{\frac{2}{9}}+\frac{\frac{39}{5}-\frac{7}{8}}{\frac{-3}{8}\times \frac{27}{18}}$$

Divide -\frac{16}{15} by \frac{2}{9} by multiplying -\frac{16}{15} by the reciprocal of \frac{2}{9}.

$$-\frac{16}{15}\times \frac{9}{2}+\frac{\frac{39}{5}-\frac{7}{8}}{\frac{-3}{8}\times \frac{27}{18}}$$

Multiply -\frac{16}{15} times \frac{9}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-16\times 9}{15\times 2}+\frac{\frac{39}{5}-\frac{7}{8}}{\frac{-3}{8}\times \frac{27}{18}}$$

Do the multiplications in the fraction \frac{-16\times 9}{15\times 2}.

$$\frac{-144}{30}+\frac{\frac{39}{5}-\frac{7}{8}}{\frac{-3}{8}\times \frac{27}{18}}$$

Reduce the fraction \frac{-144}{30} to lowest terms by extracting and canceling out 6.

$$-\frac{24}{5}+\frac{\frac{39}{5}-\frac{7}{8}}{\frac{-3}{8}\times \frac{27}{18}}$$

Least common multiple of 5 and 8 is 40. Convert \frac{39}{5} and \frac{7}{8} to fractions with denominator 40.

$$-\frac{24}{5}+\frac{\frac{312}{40}-\frac{35}{40}}{\frac{-3}{8}\times \frac{27}{18}}$$

Since \frac{312}{40} and \frac{35}{40} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{24}{5}+\frac{\frac{312-35}{40}}{\frac{-3}{8}\times \frac{27}{18}}$$

Subtract 35 from 312 to get 277.

$$-\frac{24}{5}+\frac{\frac{277}{40}}{\frac{-3}{8}\times \frac{27}{18}}$$

Fraction \frac{-3}{8} can be rewritten as -\frac{3}{8} by extracting the negative sign.

$$-\frac{24}{5}+\frac{\frac{277}{40}}{-\frac{3}{8}\times \frac{27}{18}}$$

Reduce the fraction \frac{27}{18} to lowest terms by extracting and canceling out 9.

$$-\frac{24}{5}+\frac{\frac{277}{40}}{-\frac{3}{8}\times \frac{3}{2}}$$

Multiply -\frac{3}{8} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{24}{5}+\frac{\frac{277}{40}}{\frac{-3\times 3}{8\times 2}}$$

Do the multiplications in the fraction \frac{-3\times 3}{8\times 2}.

$$-\frac{24}{5}+\frac{\frac{277}{40}}{\frac{-9}{16}}$$

Fraction \frac{-9}{16} can be rewritten as -\frac{9}{16} by extracting the negative sign.

$$-\frac{24}{5}+\frac{\frac{277}{40}}{-\frac{9}{16}}$$

Divide \frac{277}{40} by -\frac{9}{16} by multiplying \frac{277}{40} by the reciprocal of -\frac{9}{16}.

$$-\frac{24}{5}+\frac{277}{40}\left(-\frac{16}{9}\right)$$

Multiply \frac{277}{40} times -\frac{16}{9} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{24}{5}+\frac{277\left(-16\right)}{40\times 9}$$

Do the multiplications in the fraction \frac{277\left(-16\right)}{40\times 9}.

$$-\frac{24}{5}+\frac{-4432}{360}$$

Reduce the fraction \frac{-4432}{360} to lowest terms by extracting and canceling out 8.

$$-\frac{24}{5}-\frac{554}{45}$$

Least common multiple of 5 and 45 is 45. Convert -\frac{24}{5} and \frac{554}{45} to fractions with denominator 45.

$$-\frac{216}{45}-\frac{554}{45}$$

Since -\frac{216}{45} and \frac{554}{45} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-216-554}{45}$$

Subtract 554 from -216 to get -770.

$$\frac{-770}{45}$$

Reduce the fraction \frac{-770}{45} to lowest terms by extracting and canceling out 5.

$$-\frac{154}{9}$$

Factor

$$-\frac{154}{9} = -17\frac{1}{9} = -17.11111111111111$$