To multiply the mixed number \(4 \frac{1}{6}\) by the fraction \(\frac{3}{5}\), follow these steps:

1. **Convert the mixed number to an improper fraction**:
   \[
   4 \frac{1}{6} = \frac{4 \times 6 + 1}{6} = \frac{24 + 1}{6} = \frac{25}{6}
   \]

2. **Multiply the fractions**:
   \[
   \frac{25}{6} \times \frac{3}{5} = \frac{25 \times 3}{6 \times 5} = \frac{75}{30}
   \]

3. **Simplify the fraction**:
   \[
   \frac{75}{30} = \frac{75 \div 15}{30 \div 15} = \frac{5}{2} = 2 \frac{1}{2}
   \]

So, \(4 \frac{1}{6} \times \frac{3}{5} = 2 \frac{1}{2}\).

Would you like more details on any step, or do you have any questions?

Here are 5 related questions to explore:

1. How do you multiply two mixed numbers?
2. What is the process for dividing fractions?
3. How do you convert a decimal to a fraction?
4. What are improper fractions, and how do they differ from mixed numbers?
5. Can you simplify \(\frac{45}{54}\) to its lowest terms?

**Tip:** When multiplying fractions, always simplify the fraction first if possible, to make the calculation easier.

Learn how to multiply the mixed number 4 1/6 by the fraction 3/5 with a detailed step-by-step solution. This example covers key concepts, including converting mixed numbers to improper fractions, multiplying fractions, and simplifying the result. Suitable for students in Grades 5-7.

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