We need to evaluate the expression $\frac{3}{4} + \frac{1}{4} \times \frac{2}{3}$.

1. Problem Description

We need to evaluate the expression $\frac{3}{4} + \frac{1}{4} \times \frac{2}{3}$.

2. Solution Steps

Following the order of operations, we first multiply the fractions $\frac{1}{4}$ and $\frac{2}{3}$.

Multiplication of fractions:

$\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$

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

We can simplify $\frac{2}{12}$ to $\frac{1}{6}$ by dividing both the numerator and the denominator by

2.

Now we have $\frac{3}{4} + \frac{1}{6}$.

To add the fractions, we need a common denominator. The least common multiple of 4 and 6 is

1

2. We convert $\frac{3}{4}$ to a fraction with a denominator of 12:

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

We convert $\frac{1}{6}$ to a fraction with a denominator of 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

$\frac{11}{12}$