Evaluate: /(4) 11 * 3 / /(2) 3+/(1) 2

Expression: $$\frac { 4 } { 11 } \times 3 \div \frac { 2 } { 3 } + \frac { 1 } { 2 }$$

Express $\frac{4}{11}\times 3$ as a single fraction.

$$\frac{\frac{4\times 3}{11}}{\frac{2}{3}}+\frac{1}{2}$$

Multiply $4$ and $3$ to get $12$.

$$\frac{\frac{12}{11}}{\frac{2}{3}}+\frac{1}{2}$$

Divide $\frac{12}{11}$ by $\frac{2}{3}$ by multiplying $\frac{12}{11}$ by the reciprocal of $\frac{2}{3}$.

$$\frac{12}{11}\times \left(\frac{3}{2}\right)+\frac{1}{2}$$

Multiply $\frac{12}{11}$ times $\frac{3}{2}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{12\times 3}{11\times 2}+\frac{1}{2}$$

Do the multiplications in the fraction $\frac{12\times 3}{11\times 2}$.

$$\frac{36}{22}+\frac{1}{2}$$

Reduce the fraction $\frac{36}{22}$ to lowest terms by extracting and canceling out $2$.

$$\frac{18}{11}+\frac{1}{2}$$

Least common multiple of $11$ and $2$ is $22$. Convert $\frac{18}{11}$ and $\frac{1}{2}$ to fractions with denominator $22$.

$$\frac{36}{22}+\frac{11}{22}$$

Since $\frac{36}{22}$ and $\frac{11}{22}$ have the same denominator, add them by adding their numerators.

$$\frac{36+11}{22}$$

Add $36$ and $11$ to get $47$.

$$\frac{47}{22}$$