Question

Question 1
Kim found 253×4
by using partial products. Her work is shown.

253×4 12 800 812

Part A
Explain Kim’s mistake in the box below.

(1 point)

Answer 1

Use partial products to find 253×4
. Show your work.

Answer 2

Kim's mistake in calculating \(253 \times 4\) using partial products lies in her partial products summation.

To correct her work, we can break down the multiplication into its parts:

1. **Decompose 253**:
- \(253 = 200 + 50 + 3\)

2. **Multiply each part by 4**:
- \(200 \times 4 = 800\)
- \(50 \times 4 = 200\)
- \(3 \times 4 = 12\)

3. **List the partial products**:
- \(800\), \(200\), and \(12\)

4. **Sum the partial products**:
- \(800 + 200 + 12 = 1012\)

In Kim's work, it seems she miscalculated or misrepresented the addition of these partial products, as indicated by the numbers she wrote \(12\,800\,812\). The correct total of the partial products should sum to \(1012\), not \(12,800, or \(812\). Therefore, her mistake lies in the miscalculation of the sum of the partial products.

Answer 3

To find \( 253 \times 4 \) using partial products, we can break down \( 253 \) into its place value components and then multiply each component by \( 4 \). Here's how to do it step-by-step:

1. **Decompose 253** into its place values:
- \( 253 = 200 + 50 + 3 \)

2. **Multiply each part by 4**:
- \( 200 \times 4 = 800 \)
- \( 50 \times 4 = 200 \)
- \( 3 \times 4 = 12 \)

3. **List the partial products**:
- \( 800 \)
- \( 200 \)
- \( 12 \)

4. **Sum the partial products**:
- \( 800 + 200 + 12 \)

Now, we perform the addition step-by-step:

- First, add \( 800 + 200 = 1000 \)
- Then, add \( 1000 + 12 = 1012 \)

Therefore, the final result of \( 253 \times 4 \) is:

\[
\boxed{1012}
\]