Let's break this expression down step by step:

Expression:  
\[
\left[\frac{17}{9} + \left(\frac{-5}{36}\right)\right] + 4 \frac{1}{4}
\]

### Step 1: Simplify inside the brackets \(\left[\frac{17}{9} + \frac{-5}{36}\right]\)
- To add \(\frac{17}{9}\) and \(\frac{-5}{36}\), we need a common denominator. The least common denominator (LCD) of 9 and 36 is 36.

- Convert \(\frac{17}{9}\) to have a denominator of 36:
\[
\frac{17}{9} = \frac{17 \times 4}{9 \times 4} = \frac{68}{36}
\]

- Now add \(\frac{68}{36} + \frac{-5}{36} = \frac{68 - 5}{36} = \frac{63}{36} = \frac{7}{4}\)

### Step 2: Convert the mixed number \(4 \frac{1}{4}\) to an improper fraction
\[
4 \frac{1}{4} = \frac{4 \times 4 + 1}{4} = \frac{17}{4}
\]

### Step 3: Add the two fractions \(\frac{7}{4} + \frac{17}{4}\)
Since they have the same denominator:
\[
\frac{7}{4} + \frac{17}{4} = \frac{7 + 17}{4} = \frac{24}{4} = 6
\]

### Final Answer:
The value of the expression is \(6\).

Would you like a further breakdown, or have any questions?

Here are 5 related questions to practice:
1. Simplify \(\frac{23}{5} + \frac{-8}{10}\).
2. What is \(\left[\frac{13}{7} + \left(\frac{-2}{21}\right)\right] + 2\frac{2}{3}\)?
3. Convert \(3\frac{1}{5}\) to an improper fraction.
4. How do you find the least common denominator (LCD) for \(\frac{5}{6}\) and \(\frac{2}{9}\)?
5. Solve \(\frac{5}{12} + \frac{3}{4}\).

**Tip:** When adding or subtracting fractions, always find the least common denominator to simplify the process!

Explore how to simplify and add the fractions [17/9 + (-5/36)] + 4 1/4 with a step-by-step solution. This problem covers important mathematical concepts like finding the common denominator and converting mixed numbers to improper fractions. Suitable for students in Grades 6-8.

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