Solve F=3/11+14/21+-2/3

$$F = \frac { 3 } { 11 } + \frac { 14 } { 21 } + \frac { - 2 } { 3 }$$

Solve for F

$$F=\frac{3}{11}\approx 0.272727273$$

Steps for Solving Linear Equation

Reduce the fraction \frac{14}{21} to lowest terms by extracting and canceling out 7.

$$F=\frac{3}{11}+\frac{2}{3}+\frac{-2}{3}$$

Least common multiple of 11 and 3 is 33. Convert \frac{3}{11} and \frac{2}{3} to fractions with denominator 33.

$$F=\frac{9}{33}+\frac{22}{33}+\frac{-2}{3}$$

Since \frac{9}{33} and \frac{22}{33} have the same denominator, add them by adding their numerators.

$$F=\frac{9+22}{33}+\frac{-2}{3}$$

Add 9 and 22 to get 31.

$$F=\frac{31}{33}+\frac{-2}{3}$$

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

$$F=\frac{31}{33}-\frac{2}{3}$$

Least common multiple of 33 and 3 is 33. Convert \frac{31}{33} and \frac{2}{3} to fractions with denominator 33.

$$F=\frac{31}{33}-\frac{22}{33}$$

Since \frac{31}{33} and \frac{22}{33} have the same denominator, subtract them by subtracting their numerators.

$$F=\frac{31-22}{33}$$

Subtract 22 from 31 to get 9.

$$F=\frac{9}{33}$$

Reduce the fraction \frac{9}{33} to lowest terms by extracting and canceling out 3.

$$F=\frac{3}{11}$$

Assign F

$$F≔\frac{3}{11}$$