Multiply. Write rour answer as a mixed number in simplest form. $$ 3 \frac{1}{3} \times 2 \frac{1}{7} $$

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To multiply the mixed numbers $$ 3 \frac{1}{3} $$ and $$ 2 \frac{1}{7} $$ and express the answer as a mixed number in its simplest form, follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions

First, convert each mixed number to an improper fraction.

1. **For $$ 3 \frac{1}{3} $$:**
   $$
   3 \frac{1}{3} = \frac{3 \times 3 + 1}{3} = \frac{9 + 1}{3} = \frac{10}{3}
   $$

2. **For $$ 2 \frac{1}{7} $$:**
   $$
   2 \frac{1}{7} = \frac{2 \times 7 + 1}{7} = \frac{14 + 1}{7} = \frac{15}{7}
   $$

### Step 2: Multiply the Improper Fractions

Multiply the two improper fractions:

$$
\frac{10}{3} \times \frac{15}{7} = \frac{10 \times 15}{3 \times 7} = \frac{150}{21}
$$

### Step 3: Simplify the Fraction

Simplify $$ \frac{150}{21} $$:

1. **Find the Greatest Common Divisor (GCD) of 150 and 21:**
   - The GCD of 150 and 21 is 3.

2. **Divide Numerator and Denominator by the GCD:**
   $$
   \frac{150 \div 3}{21 \div 3} = \frac{50}{7}
   $$

### Step 4: Convert Back to a Mixed Number

Convert $$ \frac{50}{7} $$ back to a mixed number:

1. **Divide 50 by 7:**
   - $$ 50 \div 7 = 7 $$ with a remainder of 1.

2. **Express as Mixed Number:**
   $$
   \frac{50}{7} = 7 \frac{1}{7}
   $$

### Final Answer

$$
3 \frac{1}{3} \times 2 \frac{1}{7} = 7 \frac{1}{7}
$$
$$ 7 \frac{1}{7} $$

Multiply. Write rour answer as a mixed number in simplest form.

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