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The math problem you provided is a division of fractions:

\[ 4 \frac{1}{8} \div 2 \frac{1}{4} \]

First, we'll convert the mixed numbers to improper fractions.

1. Convert \(4 \frac{1}{8}\) to an improper fraction:
   \[
   4 \frac{1}{8} = \frac{4 \times 8 + 1}{8} = \frac{33}{8}
   \]

2. Convert \(2 \frac{1}{4}\) to an improper fraction:
   \[
   2 \frac{1}{4} = \frac{2 \times 4 + 1}{4} = \frac{9}{4}
   \]

Now, to divide the fractions, we multiply by the reciprocal of the divisor:
\[ 
\frac{33}{8} \div \frac{9}{4} = \frac{33}{8} \times \frac{4}{9} = \frac{33 \times 4}{8 \times 9} = \frac{132}{72}
\]

Next, we simplify \(\frac{132}{72}\):
   \[
   \text{GCD of 132 and 72 is 12}
   \]
   \[
   \frac{132 \div 12}{72 \div 12} = \frac{11}{6}
   \]

Thus, the simplest form of the answer is:
\[ \frac{11}{6} \text{ or } 1 \frac{5}{6} \]

Do you have any more questions or need further details on any part of this solution?

Here are some related questions you might consider:
1. How can we find the greatest common divisor (GCD) of two numbers?
2. What are other examples where we might use the multiplication of reciprocals?
3. Why do we convert mixed numbers to improper fractions for operations?
4. Can you solve similar problems involving addition or subtraction of mixed numbers?
5. How do you convert an improper fraction back to a mixed number?

**Tip:** When working with fractions, always reduce them to their simplest form to make your calculations easier and your results clearer.

Learn how to divide mixed fractions with the problem 4 1/8 ÷ 2 1/4. This step-by-step solution covers the conversion of mixed numbers to improper fractions, using reciprocal multiplication, and simplifying the answer. Ideal for Grades 5-7.

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