Solve 1/9+1/15-1/6+1/30

$$\frac { 1 } { 9 } + \frac { 1 } { 15 } - \frac { 1 } { 6 } + \frac { 1 } { 30 }$$

Evaluate

$$\frac{2}{45}\approx 0.044444444$$

Solution Steps

Least common multiple of 9 and 15 is 45. Convert \frac{1}{9} and \frac{1}{15} to fractions with denominator 45.

$$\frac{5}{45}+\frac{3}{45}-\frac{1}{6}+\frac{1}{30}$$

Since \frac{5}{45} and \frac{3}{45} have the same denominator, add them by adding their numerators.

$$\frac{5+3}{45}-\frac{1}{6}+\frac{1}{30}$$

Add 5 and 3 to get 8.

$$\frac{8}{45}-\frac{1}{6}+\frac{1}{30}$$

Least common multiple of 45 and 6 is 90. Convert \frac{8}{45} and \frac{1}{6} to fractions with denominator 90.

$$\frac{16}{90}-\frac{15}{90}+\frac{1}{30}$$

Since \frac{16}{90} and \frac{15}{90} have the same denominator, subtract them by subtracting their numerators.

$$\frac{16-15}{90}+\frac{1}{30}$$

Subtract 15 from 16 to get 1.

$$\frac{1}{90}+\frac{1}{30}$$

Least common multiple of 90 and 30 is 90. Convert \frac{1}{90} and \frac{1}{30} to fractions with denominator 90.

$$\frac{1}{90}+\frac{3}{90}$$

Since \frac{1}{90} and \frac{3}{90} have the same denominator, add them by adding their numerators.

$$\frac{1+3}{90}$$

Add 1 and 3 to get 4.

$$\frac{4}{90}$$

Reduce the fraction \frac{4}{90} to lowest terms by extracting and canceling out 2.

$$\frac{2}{45}$$

Factor

$$\frac{2}{3 ^ {2} \cdot 5} = 0.044444444444444446$$