Solve K=7/9-1/7+1/3+8/7-frac{1}{9}

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

Solve for K

$$K=2$$

Steps for Solving Linear Equation

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

$$K=\frac{49}{63}-\frac{9}{63}+\frac{1}{3}+\frac{8}{7}-\frac{1}{9}$$

Since \frac{49}{63} and \frac{9}{63} have the same denominator, subtract them by subtracting their numerators.

$$K=\frac{49-9}{63}+\frac{1}{3}+\frac{8}{7}-\frac{1}{9}$$

Subtract 9 from 49 to get 40.

$$K=\frac{40}{63}+\frac{1}{3}+\frac{8}{7}-\frac{1}{9}$$

Least common multiple of 63 and 3 is 63. Convert \frac{40}{63} and \frac{1}{3} to fractions with denominator 63.

$$K=\frac{40}{63}+\frac{21}{63}+\frac{8}{7}-\frac{1}{9}$$

Since \frac{40}{63} and \frac{21}{63} have the same denominator, add them by adding their numerators.

$$K=\frac{40+21}{63}+\frac{8}{7}-\frac{1}{9}$$

Add 40 and 21 to get 61.

$$K=\frac{61}{63}+\frac{8}{7}-\frac{1}{9}$$

Least common multiple of 63 and 7 is 63. Convert \frac{61}{63} and \frac{8}{7} to fractions with denominator 63.

$$K=\frac{61}{63}+\frac{72}{63}-\frac{1}{9}$$

Since \frac{61}{63} and \frac{72}{63} have the same denominator, add them by adding their numerators.

$$K=\frac{61+72}{63}-\frac{1}{9}$$

Add 61 and 72 to get 133.

$$K=\frac{133}{63}-\frac{1}{9}$$

Reduce the fraction \frac{133}{63} to lowest terms by extracting and canceling out 7.

$$K=\frac{19}{9}-\frac{1}{9}$$

Since \frac{19}{9} and \frac{1}{9} have the same denominator, subtract them by subtracting their numerators.

$$K=\frac{19-1}{9}$$

Subtract 1 from 19 to get 18.

$$K=\frac{18}{9}$$

Divide 18 by 9 to get 2.

$$K=2$$

Assign K

$$K≔2$$