Solve 8/9*(1/7-2/9)+13/21*frac{7}{-260}

$$\frac { 8 } { 9 } \times ( \frac { 1 } { 7 } - \frac { 2 } { 9 } ) + \frac { 13 } { 21 } \times \frac { 7 } { - 260 }$$

Evaluate

$$-\frac{989}{11340}\approx -0.087213404$$

Solution Steps

Least common multiple of 7 and 9 is 63. Convert \frac{1}{7} and \frac{2}{9} to fractions with denominator 63.

$$\frac{8}{9}\left(\frac{9}{63}-\frac{14}{63}\right)+\frac{13}{21}\times \frac{7}{-260}$$

Since \frac{9}{63} and \frac{14}{63} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8}{9}\times \frac{9-14}{63}+\frac{13}{21}\times \frac{7}{-260}$$

Subtract 14 from 9 to get -5.

$$\frac{8}{9}\left(-\frac{5}{63}\right)+\frac{13}{21}\times \frac{7}{-260}$$

Multiply \frac{8}{9} times -\frac{5}{63} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8\left(-5\right)}{9\times 63}+\frac{13}{21}\times \frac{7}{-260}$$

Do the multiplications in the fraction \frac{8\left(-5\right)}{9\times 63}.

$$\frac{-40}{567}+\frac{13}{21}\times \frac{7}{-260}$$

Fraction \frac{-40}{567} can be rewritten as -\frac{40}{567} by extracting the negative sign.

$$-\frac{40}{567}+\frac{13}{21}\times \frac{7}{-260}$$

Fraction \frac{7}{-260} can be rewritten as -\frac{7}{260} by extracting the negative sign.

$$-\frac{40}{567}+\frac{13}{21}\left(-\frac{7}{260}\right)$$

Multiply \frac{13}{21} times -\frac{7}{260} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{40}{567}+\frac{13\left(-7\right)}{21\times 260}$$

Do the multiplications in the fraction \frac{13\left(-7\right)}{21\times 260}.

$$-\frac{40}{567}+\frac{-91}{5460}$$

Reduce the fraction \frac{-91}{5460} to lowest terms by extracting and canceling out 91.

$$-\frac{40}{567}-\frac{1}{60}$$

Least common multiple of 567 and 60 is 11340. Convert -\frac{40}{567} and \frac{1}{60} to fractions with denominator 11340.

$$-\frac{800}{11340}-\frac{189}{11340}$$

Since -\frac{800}{11340} and \frac{189}{11340} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-800-189}{11340}$$

Subtract 189 from -800 to get -989.

$$-\frac{989}{11340}$$

Factor

$$-\frac{989}{11340} = -0.08721340388007055$$