Solve 1/5+-5/9+2/3

$$\frac { 1 } { 5 } + \frac { - 5 } { 9 } + \frac { 2 } { 3 }$$

Evaluate

$$\frac{14}{45}\approx 0.311111111$$

Solution Steps

Fraction \frac{-5}{9} can be rewritten as -\frac{5}{9} by extracting the negative sign.

$$\frac{1}{5}-\frac{5}{9}+\frac{2}{3}$$

Least common multiple of 5 and 9 is 45. Convert \frac{1}{5} and \frac{5}{9} to fractions with denominator 45.

$$\frac{9}{45}-\frac{25}{45}+\frac{2}{3}$$

Since \frac{9}{45} and \frac{25}{45} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9-25}{45}+\frac{2}{3}$$

Subtract 25 from 9 to get -16.

$$-\frac{16}{45}+\frac{2}{3}$$

Least common multiple of 45 and 3 is 45. Convert -\frac{16}{45} and \frac{2}{3} to fractions with denominator 45.

$$-\frac{16}{45}+\frac{30}{45}$$

Since -\frac{16}{45} and \frac{30}{45} have the same denominator, add them by adding their numerators.

$$\frac{-16+30}{45}$$

Add -16 and 30 to get 14.

$$\frac{14}{45}$$

Factor

$$\frac{2 \cdot 7}{3 ^ {2} \cdot 5} = 0.3111111111111111$$