Solve 21/8-38/7/frac{2{7}+1/7-frac{3}{8}}-frac{8}{9}

$$\frac{ 2 \frac{ 1 }{ 8 } -3 \frac{ 8 }{ 7 } }{ \frac{ 2 }{ 7 } + \frac{ 1 }{ 7 } - \frac{ 3 }{ 8 } } - \frac{ 8 }{ 9 }$$

Evaluate

$$-\frac{347}{9}\approx -38.555555556$$

Solution Steps

Multiply 2 and 8 to get 16.

$$\frac{\frac{16+1}{8}-\frac{3\times 7+8}{7}}{\frac{2}{7}+\frac{1}{7}-\frac{3}{8}}-\frac{8}{9}$$

Add 16 and 1 to get 17.

$$\frac{\frac{17}{8}-\frac{3\times 7+8}{7}}{\frac{2}{7}+\frac{1}{7}-\frac{3}{8}}-\frac{8}{9}$$

Multiply 3 and 7 to get 21.

$$\frac{\frac{17}{8}-\frac{21+8}{7}}{\frac{2}{7}+\frac{1}{7}-\frac{3}{8}}-\frac{8}{9}$$

Add 21 and 8 to get 29.

$$\frac{\frac{17}{8}-\frac{29}{7}}{\frac{2}{7}+\frac{1}{7}-\frac{3}{8}}-\frac{8}{9}$$

Least common multiple of 8 and 7 is 56. Convert \frac{17}{8} and \frac{29}{7} to fractions with denominator 56.

$$\frac{\frac{119}{56}-\frac{232}{56}}{\frac{2}{7}+\frac{1}{7}-\frac{3}{8}}-\frac{8}{9}$$

Since \frac{119}{56} and \frac{232}{56} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{119-232}{56}}{\frac{2}{7}+\frac{1}{7}-\frac{3}{8}}-\frac{8}{9}$$

Subtract 232 from 119 to get -113.

$$\frac{-\frac{113}{56}}{\frac{2}{7}+\frac{1}{7}-\frac{3}{8}}-\frac{8}{9}$$

Since \frac{2}{7} and \frac{1}{7} have the same denominator, add them by adding their numerators.

$$\frac{-\frac{113}{56}}{\frac{2+1}{7}-\frac{3}{8}}-\frac{8}{9}$$

Add 2 and 1 to get 3.

$$\frac{-\frac{113}{56}}{\frac{3}{7}-\frac{3}{8}}-\frac{8}{9}$$

Least common multiple of 7 and 8 is 56. Convert \frac{3}{7} and \frac{3}{8} to fractions with denominator 56.

$$\frac{-\frac{113}{56}}{\frac{24}{56}-\frac{21}{56}}-\frac{8}{9}$$

Since \frac{24}{56} and \frac{21}{56} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{113}{56}}{\frac{24-21}{56}}-\frac{8}{9}$$

Subtract 21 from 24 to get 3.

$$\frac{-\frac{113}{56}}{\frac{3}{56}}-\frac{8}{9}$$

Divide -\frac{113}{56} by \frac{3}{56} by multiplying -\frac{113}{56} by the reciprocal of \frac{3}{56}.

$$-\frac{113}{56}\times \frac{56}{3}-\frac{8}{9}$$

Multiply -\frac{113}{56} times \frac{56}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-113\times 56}{56\times 3}-\frac{8}{9}$$

Cancel out 56 in both numerator and denominator.

$$\frac{-113}{3}-\frac{8}{9}$$

Fraction \frac{-113}{3} can be rewritten as -\frac{113}{3} by extracting the negative sign.

$$-\frac{113}{3}-\frac{8}{9}$$

Least common multiple of 3 and 9 is 9. Convert -\frac{113}{3} and \frac{8}{9} to fractions with denominator 9.

$$-\frac{339}{9}-\frac{8}{9}$$

Since -\frac{339}{9} and \frac{8}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-339-8}{9}$$

Subtract 8 from -339 to get -347.

$$-\frac{347}{9}$$

Factor

$$-\frac{347}{9} = -38\frac{5}{9} = -38.55555555555556$$