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The expression you provided is:

\[
5 \frac{2}{8} - 1 \frac{2}{7}
\]

To solve this, follow these steps:

### Step 1: Convert mixed numbers into improper fractions.
- For \( 5 \frac{2}{8} \), convert it as follows:
  \[
  5 \frac{2}{8} = \frac{(5 \times 8) + 2}{8} = \frac{40 + 2}{8} = \frac{42}{8}
  \]
  Simplify \( \frac{42}{8} \):
  \[
  \frac{42}{8} = \frac{21}{4}
  \]

- For \( 1 \frac{2}{7} \), convert it as follows:
  \[
  1 \frac{2}{7} = \frac{(1 \times 7) + 2}{7} = \frac{7 + 2}{7} = \frac{9}{7}
  \]

### Step 2: Perform the subtraction.

The expression now becomes:
\[
\frac{21}{4} - \frac{9}{7}
\]

### Step 3: Find the common denominator.
- The least common denominator (LCD) of 4 and 7 is 28.
- Rewrite both fractions with the LCD of 28:
  \[
  \frac{21}{4} = \frac{21 \times 7}{4 \times 7} = \frac{147}{28}
  \]
  \[
  \frac{9}{7} = \frac{9 \times 4}{7 \times 4} = \frac{36}{28}
  \]

### Step 4: Subtract the fractions.
\[
\frac{147}{28} - \frac{36}{28} = \frac{147 - 36}{28} = \frac{111}{28}
\]

### Step 5: Simplify the result (if possible).
\[
\frac{111}{28}
\]
This fraction cannot be simplified further.

### Final Answer:
\[
\boxed{\frac{111}{28}}
\]

Let me know if you need further details, or if you'd like more explanations!

Here are 5 related questions to expand this concept:
1. How do you convert an improper fraction back to a mixed number?
2. What are some ways to find the least common denominator quickly?
3. How do you add or subtract fractions with unlike denominators?
4. How would you handle mixed numbers when multiplying or dividing?
5. Can this result be expressed as a decimal?

**Tip:** Always simplify mixed numbers to improper fractions before performing operations for ease of calculation!

Learn how to subtract mixed numbers by converting them to improper fractions and finding the least common denominator. This example solves 5 2/8 - 1 2/7 step by step, ideal for students in Grades 5-7.

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