To multiply the mixed numbers \(1\frac{1}{4}\) and \(2\frac{3}{4}\), follow these steps:

1. **Convert the mixed numbers to improper fractions**:

   - \(1\frac{1}{4} = 1 + \frac{1}{4} = \frac{4}{4} + \frac{1}{4} = \frac{5}{4}\)
   - \(2\frac{3}{4} = 2 + \frac{3}{4} = \frac{8}{4} + \frac{3}{4} = \frac{11}{4}\)

2. **Multiply the improper fractions**:

   \[
   \frac{5}{4} \times \frac{11}{4} = \frac{5 \times 11}{4 \times 4} = \frac{55}{16}
   \]

3. **Convert the result back to a mixed number**:

   - Divide the numerator by the denominator: \(55 \div 16 = 3\) remainder \(7\).
   - The mixed number is \(3\frac{7}{16}\).

Therefore, the product of \(1\frac{1}{4}\) and \(2\frac{3}{4}\) is \(3\frac{7}{16}\).

If you have any more questions, want further details, or need a clarification, feel free to ask! Here are some related questions:

1. How do you convert between improper fractions and mixed numbers?
2. What is the process for multiplying fractions?
3. How do you add and subtract mixed numbers?
4. How do you convert a decimal to a fraction?
5. What are some tips for simplifying fractions?
6. How do you divide mixed numbers?
7. How can you compare two fractions?
8. What is the difference between a proper and an improper fraction?

**Tip**: Always simplify fractions to their lowest terms for easier calculations and comparison.

Learn how to multiply the mixed numbers 1¼ and 2¾ with a detailed step-by-step solution. This problem covers key concepts in fractions and multiplication of mixed numbers. Suitable for students in Grades 5-6.

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