Solve 12/frac{1{2}+1/3}

$$\frac{ 12 }{ \frac{ 1 }{ 2 } + \frac{ 1 }{ 3 } }$$

Evaluate

$$\frac{72}{5}=14.4$$

Solution Steps

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

$$\frac{12}{\frac{3}{6}+\frac{2}{6}}$$

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

$$\frac{12}{\frac{3+2}{6}}$$

Add 3 and 2 to get 5.

$$\frac{12}{\frac{5}{6}}$$

Divide 12 by \frac{5}{6} by multiplying 12 by the reciprocal of \frac{5}{6}.

$$12\times \frac{6}{5}$$

Express 12\times \frac{6}{5} as a single fraction.

$$\frac{12\times 6}{5}$$

Multiply 12 and 6 to get 72.

$$\frac{72}{5}$$

Factor

$$\frac{2 ^ {3} \cdot 3 ^ {2}}{5} = 14\frac{2}{5} = 14.4$$