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To solve this, we need to find what operation should be placed between the 8 and the fraction \(\frac{2}{3}\) on the right-hand side to make the equation true.

The given equation is:
\[
8 \times \frac{3}{2} = 8 \, \_ \, \frac{2}{3}
\]

First, calculate the left side:
\[
8 \times \frac{3}{2} = \frac{8 \times 3}{2} = \frac{24}{2} = 12
\]

Now, we want the right-hand side to also equal 12:
\[
8 \, \_ \, \frac{2}{3} = 12
\]

Let's consider the operations:

1. **Addition**: 
   \[
   8 + \frac{2}{3} = 8 + 0.6667 \approx 8.67
   \]
   Not equal to 12.

2. **Subtraction**:
   \[
   8 - \frac{2}{3} = 8 - 0.6667 \approx 7.33
   \]
   Not equal to 12.

3. **Multiplication**:
   \[
   8 \times \frac{2}{3} = \frac{8 \times 2}{3} = \frac{16}{3} \approx 5.33
   \]
   Not equal to 12.

4. **Division**:
   \[
   8 \div \frac{2}{3} = 8 \times \frac{3}{2} = \frac{8 \times 3}{2} = 12
   \]
   This is equal to 12.

Therefore, the correct operation to make the equation true is **division** (÷).

Would you like more details or have any questions?

Here are 5 questions you could explore:
1. Why does dividing by a fraction result in multiplying by its reciprocal?
2. How can this principle be applied to solve more complex algebraic equations?
3. How do you handle equations with mixed operations involving fractions?
4. What other real-world problems could involve division by fractions?
5. Can this approach be used for equations with variables?

**Tip:** When dividing by a fraction, always multiply by its reciprocal to simplify the calculation!

What operation should fill in the blank to make the equation true? 8 × 3/2 = 8 __ 2/3

Learn how to determine the correct operation to make the equation 8 × 3/2 = 8 __ 2/3 true. This problem explores the multiplication and division of fractions and their reciprocal properties, suitable for students in Grades 5-7.

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