The problem requires us to evaluate the expression $\frac{1}{3} + \frac{1}{4} - 4\frac{5}{12}$.

1. Problem Description

The problem requires us to evaluate the expression $\frac{1}{3} + \frac{1}{4} - 4\frac{5}{12}$.

2. Solution Steps

First, let's convert the mixed number $4\frac{5}{12}$ to an improper fraction:

$4\frac{5}{12} = \frac{4 \times 12 + 5}{12} = \frac{48 + 5}{12} = \frac{53}{12}$.

So the expression becomes:

$\frac{1}{3} + \frac{1}{4} - \frac{53}{12}$.

To add and subtract these fractions, we need a common denominator. The least common multiple of 3, 4, and 12 is

1

2. So, we rewrite the fractions with the common denominator 12:

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

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

Now the expression is:

$\frac{4}{12} + \frac{3}{12} - \frac{53}{12}$.

Combine the fractions:

$\frac{4 + 3 - 53}{12} = \frac{7 - 53}{12} = \frac{-46}{12}$.

We can simplify the fraction by dividing both numerator and denominator by their greatest common divisor, which is 2:

$\frac{-46}{12} = \frac{-46 \div 2}{12 \div 2} = \frac{-23}{6}$.

We can also express the improper fraction as a mixed number:

$\frac{-23}{6} = -3\frac{5}{6}$.

3. Final Answer

The final answer is $- \frac{23}{6}$ or $-3\frac{5}{6}$.