Solve (1/3+1/6+5/18)div1/36

$$( \frac{ 1 }{ 3 } + \frac{ 1 }{ 6 } + \frac{ 5 }{ 18 } ) \div \frac{ 1 }{ 36 }$$

Evaluate

$$28$$

Solution Steps

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

$$\frac{\frac{2}{6}+\frac{1}{6}+\frac{5}{18}}{\frac{1}{36}}$$

Since \frac{2}{6} and \frac{1}{6} have the same denominator, add them by adding their numerators.

$$\frac{\frac{2+1}{6}+\frac{5}{18}}{\frac{1}{36}}$$

Add 2 and 1 to get 3.

$$\frac{\frac{3}{6}+\frac{5}{18}}{\frac{1}{36}}$$

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{1}{2}+\frac{5}{18}}{\frac{1}{36}}$$

Least common multiple of 2 and 18 is 18. Convert \frac{1}{2} and \frac{5}{18} to fractions with denominator 18.

$$\frac{\frac{9}{18}+\frac{5}{18}}{\frac{1}{36}}$$

Since \frac{9}{18} and \frac{5}{18} have the same denominator, add them by adding their numerators.

$$\frac{\frac{9+5}{18}}{\frac{1}{36}}$$

Add 9 and 5 to get 14.

$$\frac{\frac{14}{18}}{\frac{1}{36}}$$

Reduce the fraction \frac{14}{18} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{7}{9}}{\frac{1}{36}}$$

Divide \frac{7}{9} by \frac{1}{36} by multiplying \frac{7}{9} by the reciprocal of \frac{1}{36}.

$$\frac{7}{9}\times 36$$

Express \frac{7}{9}\times 36 as a single fraction.

$$\frac{7\times 36}{9}$$

Multiply 7 and 36 to get 252.

$$\frac{252}{9}$$

Divide 252 by 9 to get 28.

$$28$$

Factor

$$2^{2}\times 7$$