Solve (1/3+3/4-5/9)div1/6

$$( \frac{ 1 }{ 3 } + \frac{ 3 }{ 4 } - \frac{ 5 }{ 9 } ) \div \frac{ 1 }{ 6 }$$

Evaluate

$$\frac{19}{6}\approx 3.166666667$$

Solution Steps

Least common multiple of 3 and 4 is 12. Convert \frac{1}{3} and \frac{3}{4} to fractions with denominator 12.

$$\frac{\frac{4}{12}+\frac{9}{12}-\frac{5}{9}}{\frac{1}{6}}$$

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

$$\frac{\frac{4+9}{12}-\frac{5}{9}}{\frac{1}{6}}$$

Add 4 and 9 to get 13.

$$\frac{\frac{13}{12}-\frac{5}{9}}{\frac{1}{6}}$$

Least common multiple of 12 and 9 is 36. Convert \frac{13}{12} and \frac{5}{9} to fractions with denominator 36.

$$\frac{\frac{39}{36}-\frac{20}{36}}{\frac{1}{6}}$$

Since \frac{39}{36} and \frac{20}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{39-20}{36}}{\frac{1}{6}}$$

Subtract 20 from 39 to get 19.

$$\frac{\frac{19}{36}}{\frac{1}{6}}$$

Divide \frac{19}{36} by \frac{1}{6} by multiplying \frac{19}{36} by the reciprocal of \frac{1}{6}.

$$\frac{19}{36}\times 6$$

Express \frac{19}{36}\times 6 as a single fraction.

$$\frac{19\times 6}{36}$$

Multiply 19 and 6 to get 114.

$$\frac{114}{36}$$

Reduce the fraction \frac{114}{36} to lowest terms by extracting and canceling out 6.

$$\frac{19}{6}$$

Factor

$$\frac{19}{2 \cdot 3} = 3\frac{1}{6} = 3.1666666666666665$$