Solve 4/3-4/9-2/27+40

$$\frac { 4 } { 3 } - \frac { 4 } { 9 } - \frac { 2 } { 27 } + 40$$

Evaluate

$$\frac{1102}{27}\approx 40.814814815$$

Solution Steps

Least common multiple of 3 and 9 is 9. Convert \frac{4}{3} and \frac{4}{9} to fractions with denominator 9.

$$\frac{12}{9}-\frac{4}{9}-\frac{2}{27}+40$$

Since \frac{12}{9} and \frac{4}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{12-4}{9}-\frac{2}{27}+40$$

Subtract 4 from 12 to get 8.

$$\frac{8}{9}-\frac{2}{27}+40$$

Least common multiple of 9 and 27 is 27. Convert \frac{8}{9} and \frac{2}{27} to fractions with denominator 27.

$$\frac{24}{27}-\frac{2}{27}+40$$

Since \frac{24}{27} and \frac{2}{27} have the same denominator, subtract them by subtracting their numerators.

$$\frac{24-2}{27}+40$$

Subtract 2 from 24 to get 22.

$$\frac{22}{27}+40$$

Convert 40 to fraction \frac{1080}{27}.

$$\frac{22}{27}+\frac{1080}{27}$$

Since \frac{22}{27} and \frac{1080}{27} have the same denominator, add them by adding their numerators.

$$\frac{22+1080}{27}$$

Add 22 and 1080 to get 1102.

$$\frac{1102}{27}$$

Factor

$$\frac{2 \cdot 19 \cdot 29}{3 ^ {3}} = 40\frac{22}{27} = 40.81481481481482$$