To solve the problem \(32 \frac{1}{8} - 17 \frac{3}{4}\), follow these steps:

1. **Convert mixed numbers to improper fractions**:
   \[
   32 \frac{1}{8} = \frac{256 + 1}{8} = \frac{257}{8}
   \]
   \[
   17 \frac{3}{4} = \frac{68 + 3}{4} = \frac{71}{4}
   \]

2. **Find a common denominator**:  
   The least common denominator between 8 and 4 is 8.
   \[
   \frac{71}{4} = \frac{71 \times 2}{4 \times 2} = \frac{142}{8}
   \]

3. **Subtract the fractions**:
   \[
   \frac{257}{8} - \frac{142}{8} = \frac{257 - 142}{8} = \frac{115}{8}
   \]

4. **Convert the improper fraction back to a mixed number**:
   \[
   \frac{115}{8} = 14 \frac{3}{8}
   \]

So, \(32 \frac{1}{8} - 17 \frac{3}{4} = 14 \frac{3}{8}\).

Would you like further details or have any questions?

Here are some related questions to consider:
1. How do you add mixed numbers?
2. How do you subtract fractions with different denominators?
3. How do you multiply mixed numbers?
4. What are the steps to convert improper fractions to mixed numbers?
5. How do you solve word problems involving mixed numbers?

**Tip**: Always find a common denominator when adding or subtracting fractions.

Learn how to subtract mixed numbers with different denominators in this step-by-step guide. We break down the subtraction of 32 1/8 from 17 3/4 by converting to improper fractions, finding a common denominator, and converting back to a mixed number. Suitable for Grades 5-7.

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