Solve (1/3+1/2)div1/5-1/18

$$( \frac { 1 } { 3 } + \frac { 1 } { 2 } ) \div \frac { 1 } { 5 } - \frac { 1 } { 18 }$$

Evaluate

$$\frac{37}{9}\approx 4.111111111$$

Solution Steps

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

$$\frac{\frac{2}{6}+\frac{3}{6}}{\frac{1}{5}}-\frac{1}{18}$$

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

$$\frac{\frac{2+3}{6}}{\frac{1}{5}}-\frac{1}{18}$$

Add 2 and 3 to get 5.

$$\frac{\frac{5}{6}}{\frac{1}{5}}-\frac{1}{18}$$

Divide \frac{5}{6} by \frac{1}{5} by multiplying \frac{5}{6} by the reciprocal of \frac{1}{5}.

$$\frac{5}{6}\times 5-\frac{1}{18}$$

Express \frac{5}{6}\times 5 as a single fraction.

$$\frac{5\times 5}{6}-\frac{1}{18}$$

Multiply 5 and 5 to get 25.

$$\frac{25}{6}-\frac{1}{18}$$

Least common multiple of 6 and 18 is 18. Convert \frac{25}{6} and \frac{1}{18} to fractions with denominator 18.

$$\frac{75}{18}-\frac{1}{18}$$

Since \frac{75}{18} and \frac{1}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{75-1}{18}$$

Subtract 1 from 75 to get 74.

$$\frac{74}{18}$$

Reduce the fraction \frac{74}{18} to lowest terms by extracting and canceling out 2.

$$\frac{37}{9}$$

Factor

$$\frac{37}{3 ^ {2}} = 4\frac{1}{9} = 4.111111111111111$$