https://file.aiquickdraw.com/mathbot/file/17261931882659rzgbv2o.jpg

Let's analyze and solve the math problems from the image. Here's what we can see:

1. **Question a: Fill in the missing number**

   - Given:
     \[
     12 \times 30 = (12 \times \text{[ ]}) \times 10 = 432
     \]
   - To solve for the missing number, let \( x \) be the missing number.
   - The equation can be simplified to:
     \[
     12 \times 30 = 360
     \]
   - Now, we have:
     \[
     (12 \times x) \times 10 = 432
     \]
   - Simplifying:
     \[
     12x \times 10 = 432 \implies 12x = \frac{432}{10} = 43.2
     \]
   - Solving for \( x \):
     \[
     x = \frac{43.2}{12} = 3.6
     \]

2. **Question b: Find the product**

   - Given:
     \[
     49 \times 90 = (49 \times 3) \times \text{[ ]} \times 100 = 12600
     \]
   - First, compute \( 49 \times 90 \):
     \[
     49 \times 90 = 4410
     \]
   - Then:
     \[
     (49 \times 3) \times y \times 100 = 12600
     \]
     where \( y \) is the missing number.

   - We know \( 49 \times 3 = 147 \), so:
     \[
     147 \times y \times 100 = 12600 \implies 147y = \frac{12600}{100} = 126
     \]
   - Solving for \( y \):
     \[
     y = \frac{126}{147} = \frac{6}{7} \approx 0.857
     \]

So, the missing numbers are:
- For part (a): 3.6
- For part (b): Approximately 0.857

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

Here are five related questions:
1. How do you calculate the product of two numbers?
2. What is the process for solving equations with missing numbers?
3. Can you explain the properties of multiplication and division?
4. What are some tips for simplifying complex equations?
5. How can rounding affect calculations?

**Tip:** Always double-check your calculations by reversing the operations!

Fill in the missing number and find the product based on the equations in the image.

Learn how to solve for missing numbers in multiplication and division problems. We walk through two example problems involving the equations 12 × 30 and 49 × 90, exploring step-by-step solutions to find the missing values. Suitable for students in Grades 5-6.

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