Solve (1/2-1/3)div5/18+1/3+frac{1}{6}

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

Evaluate

$$\frac{11}{10}=1.1$$

Solution Steps

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

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

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

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

Subtract 2 from 3 to get 1.

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

Divide \frac{1}{6} by \frac{5}{18} by multiplying \frac{1}{6} by the reciprocal of \frac{5}{18}.

$$\frac{1}{6}\times \frac{18}{5}+\frac{1}{3}+\frac{1}{6}$$

Multiply \frac{1}{6} times \frac{18}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 18}{6\times 5}+\frac{1}{3}+\frac{1}{6}$$

Do the multiplications in the fraction \frac{1\times 18}{6\times 5}.

$$\frac{18}{30}+\frac{1}{3}+\frac{1}{6}$$

Reduce the fraction \frac{18}{30} to lowest terms by extracting and canceling out 6.

$$\frac{3}{5}+\frac{1}{3}+\frac{1}{6}$$

Least common multiple of 5 and 3 is 15. Convert \frac{3}{5} and \frac{1}{3} to fractions with denominator 15.

$$\frac{9}{15}+\frac{5}{15}+\frac{1}{6}$$

Since \frac{9}{15} and \frac{5}{15} have the same denominator, add them by adding their numerators.

$$\frac{9+5}{15}+\frac{1}{6}$$

Add 9 and 5 to get 14.

$$\frac{14}{15}+\frac{1}{6}$$

Least common multiple of 15 and 6 is 30. Convert \frac{14}{15} and \frac{1}{6} to fractions with denominator 30.

$$\frac{28}{30}+\frac{5}{30}$$

Since \frac{28}{30} and \frac{5}{30} have the same denominator, add them by adding their numerators.

$$\frac{28+5}{30}$$

Add 28 and 5 to get 33.

$$\frac{33}{30}$$

Reduce the fraction \frac{33}{30} to lowest terms by extracting and canceling out 3.

$$\frac{11}{10}$$

Factor

$$\frac{11}{2 \cdot 5} = 1\frac{1}{10} = 1.1$$