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To solve this multiplication problem involving mixed numbers and fractions, let's break it down step by step.

### The problem is:

\[
3 \frac{1}{2} \times \frac{9}{10}
\]

### Step 1: Convert the mixed number to an improper fraction

First, convert \( 3 \frac{1}{2} \) to an improper fraction.

\[
3 \frac{1}{2} = \frac{(3 \times 2) + 1}{2} = \frac{7}{2}
\]

So the expression becomes:

\[
\frac{7}{2} \times \frac{9}{10}
\]

### Step 2: Multiply the fractions

Now, multiply the numerators and denominators:

\[
\frac{7}{2} \times \frac{9}{10} = \frac{7 \times 9}{2 \times 10} = \frac{63}{20}
\]

### Step 3: Convert the result to a mixed number

Now, convert the improper fraction \( \frac{63}{20} \) to a mixed number. Divide 63 by 20:

\[
63 \div 20 = 3 \text{ remainder } 3
\]

So, \( \frac{63}{20} = 3 \frac{3}{20} \).

### Final Answer:

The answer in mixed number form is:

\[
3 \frac{3}{20}
\]

Would you like further explanation or details on any part of this process?

Here are 5 related questions you might find useful:
1. How do you simplify fractions after multiplying them?
2. How do you convert improper fractions to mixed numbers?
3. What are the steps for multiplying mixed numbers directly?
4. How do you handle division of mixed numbers?
5. How can you multiply three or more fractions together?

**Tip:** When multiplying fractions, always check if you can simplify the fractions before multiplying to make the calculations easier.

What is 3 1/2 × 9/10 in simplest form as a mixed number?

Learn how to solve the multiplication of mixed numbers and fractions with this example: 3 1/2 × 9/10. Includes converting mixed numbers to improper fractions, multiplying, simplifying, and expressing the result as a mixed number. Ideal for students in Grades 5-7.

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