Solve 33div(1+1/2+1/3)

$$33 \div ( 1 + \frac { 1 } { 2 } + \frac { 1 } { 3 } )$$

Evaluate

$$18$$

Solution Steps

Convert 1 to fraction \frac{2}{2}.

$$\frac{33}{\frac{2}{2}+\frac{1}{2}+\frac{1}{3}}$$

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

$$\frac{33}{\frac{2+1}{2}+\frac{1}{3}}$$

Add 2 and 1 to get 3.

$$\frac{33}{\frac{3}{2}+\frac{1}{3}}$$

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

$$\frac{33}{\frac{9}{6}+\frac{2}{6}}$$

Since \frac{9}{6} and \frac{2}{6} have the same denominator, add them by adding their numerators.

$$\frac{33}{\frac{9+2}{6}}$$

Add 9 and 2 to get 11.

$$\frac{33}{\frac{11}{6}}$$

Divide 33 by \frac{11}{6} by multiplying 33 by the reciprocal of \frac{11}{6}.

$$33\times \frac{6}{11}$$

Express 33\times \frac{6}{11} as a single fraction.

$$\frac{33\times 6}{11}$$

Multiply 33 and 6 to get 198.

$$\frac{198}{11}$$

Divide 198 by 11 to get 18.

$$18$$

Factor

$$2\times 3^{2}$$