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This puzzle involves finding the missing digits in a partially completed multiplication problem. Here's how we can approach it step by step.

We are given:

\[
\begin{array}{c@{}c@{}c@{}c@{}c@{}c@{}c}
   & 2 & \_ & 4 \\
\times &   & 3 & 7 \\
\hline
   & 1 & , & 9 & 8 & \_ \\
+ & \_ & , & \_ & 2 & 0 \\
\hline
   & 1 & , & \_ & 5 & 8 \\
\end{array}
\]

### Approach:
1. **First Step: Break down the multiplication.**
   The problem seems to involve long multiplication. Let's first think about multiplying \( 24\_ \times 37 \) and then split into steps (multiplying by 7 and then by 30).

2. **Multiplication by 7:** We know that multiplying \(24\_\) by 7 gives a result that ends in \(1,980\_\).
3. **Multiplication by 30 (3 shifted by a place):** This leads to the partial sum \( \_, \_20 \), with some missing digits. 

4. **Final sum:** We know the final result is \( 1,\_58 \).

By carefully working through each multiplication and addition step, we will be able to deduce the missing digits.

Let me calculate the missing digits and explain.Let's break down the multiplication step by step:

We are multiplying:

\[
2\_4 \times 37
\]

This can be decomposed into:

\[
2\_4 \times 7 \quad \text{and} \quad 2\_4 \times 30
\]

### Step 1: Multiplication by 7
Let's handle the multiplication by 7 first:

\[
2\_4 \times 7 = 1,980\_
\]

The result from multiplying \(2\_4\) by 7 is \(1,980\_\). Since the number ends with a zero, this gives us a clue that the missing digit in \(2\_4\) should be a number that produces a product ending in zero when multiplied by 7.

Now, considering possibilities, the number \(2_4\) could be **284** because:

\[
284 \times 7 = 1,988
\]

This means that the missing digit in the product \(1,980\_\) is **8**.

### Step 2: Multiplication by 30
Now let's compute the second part, which is \(284 \times 30\):

\[
284 \times 30 = 8,520
\]

This matches the form of the partial sum:

\[
\_, \_20
\]

The missing digits here are **8, 5**.

### Step 3: Addition
Now, adding the two products:

\[
1,988 + 8,520 = 10,508
\]

This matches the final result:

\[
1, 0 5 8
\]

### Conclusion:
The missing digits are as follows:

- The missing digit in \(2\_4\) is **8** (so the number is 284).
- The missing digit in \(1,980\_\) is **8**.
- The missing digits in the second product are **8, 5**, making the number \(8,520\).

Let me know if you need more details! Here are 5 follow-up questions:

1. Why is the missing digit in \(2\_4\) 8?
2. What is the significance of the zero in \(1,980\_\)?
3. How do we handle multiplication with more complex numbers?
4. What strategy can be used to solve similar problems in future?
5. Could the missing digits have been anything else?

**Tip:** When solving digit puzzles like this, focus on clues such as the placement of zeros and known digit sums to guide you to the correct solution.

Find the missing digits in a multiplication and addition puzzle.

Solve a challenging puzzle that involves finding the missing digits in a multiplication and addition problem. Suitable for students in Grades 4-6, this puzzle tests skills in multiplication, addition, and understanding of place value.

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