The problem is to evaluate the expression $\frac{3}{4} + \frac{1}{4} \times \frac{2}{3}$.

1. Problem Description

The problem is to evaluate the expression $\frac{3}{4} + \frac{1}{4} \times \frac{2}{3}$.

2. Solution Steps

To solve this problem, we need to follow the order of operations (PEMDAS/BODMAS), which states that multiplication should be performed before addition.

First, we multiply the two fractions $\frac{1}{4}$ and $\frac{2}{3}$:

$\frac{1}{4} \times \frac{2}{3} = \frac{1 \times 2}{4 \times 3} = \frac{2}{12}$

We can simplify the fraction $\frac{2}{12}$ by dividing both the numerator and the denominator by their greatest common divisor, which is 2:

$\frac{2}{12} = \frac{2 \div 2}{12 \div 2} = \frac{1}{6}$

Now we add the result to the first fraction:

$\frac{3}{4} + \frac{1}{6}$

To add these fractions, we need to find a common denominator. The least common multiple (LCM) of 4 and 6 is

1

2. We convert both fractions to have a denominator of 12:

$\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}$

$\frac{1}{6} = \frac{1 \times 2}{6 \times 2} = \frac{2}{12}$

Now we can add the fractions:

$\frac{9}{12} + \frac{2}{12} = \frac{9 + 2}{12} = \frac{11}{12}$

3. Final Answer

$\frac{11}{12}$