Solve 2/6+1/9*x/3-1/2

$$\frac { 2 } { 6 } + \frac { 1 } { 9 } \cdot \frac { x } { 3 } - \frac { 1 } { 2 }$$

Evaluate

$$\frac{x}{27}-\frac{1}{6}$$

Solution Steps

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

$$\frac{1}{3}+\frac{1}{9}\times \frac{x}{3}-\frac{1}{2}$$

Multiply \frac{1}{9} times \frac{x}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{3}+\frac{x}{9\times 3}-\frac{1}{2}$$

Least common multiple of 3 and 2 is 6. Convert \frac{1}{3} and \frac{1}{2} to fractions with denominator 6.

$$\frac{2}{6}+\frac{x}{9\times 3}-\frac{3}{6}$$

Since \frac{2}{6} and \frac{3}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2-3}{6}+\frac{x}{9\times 3}$$

Subtract 3 from 2 to get -1.

$$-\frac{1}{6}+\frac{x}{9\times 3}$$

Multiply 9 and 3 to get 27.

$$-\frac{1}{6}+\frac{x}{27}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 6 and 27 is 54. Multiply -\frac{1}{6} times \frac{9}{9}. Multiply \frac{x}{27} times \frac{2}{2}.

$$-\frac{9}{54}+\frac{2x}{54}$$

Since -\frac{9}{54} and \frac{2x}{54} have the same denominator, add them by adding their numerators.

$$\frac{-9+2x}{54}$$

Factor

$$\frac{2x-9}{54}$$

Solution Steps

Factor out \frac{1}{54}.

$$\frac{-9+2x}{54}$$

Consider 18+2x-27. Multiply and combine like terms.

$$2x-9$$

Rewrite the complete factored expression.

$$\frac{2x-9}{54}$$