Question
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.
by using partial products. Her work is shown.
253×4 12 800 812
Part A
Explain Kim’s mistake in the box below.
Answers
GPT-4o mini
To explain Kim's mistake in her calculation using partial products for \(253 \times 4\), we first need to express \(253\) in terms of its place values:
\[
253 = 200 + 50 + 3
\]
When using partial products, the multiplication would be broken down as follows:
1. \(200 \times 4 = 800\)
2. \(50 \times 4 = 200\)
3. \(3 \times 4 = 12\)
Now, we would add the results of these products together:
\[
800 + 200 + 12 = 1012
\]
It appears that Kim wrote "12 800 812" in the box, which indicates a misunderstanding in how to combine the products or perhaps a misplacement of digits.
**Kim’s mistake:**
1. She may have improperly aligned or summed the products, resulting in an incorrect total.
2. The correct sum of the calculated partial products \(800 + 200 + 12\) should be \(1012\), not \(812\) or any variation like \(12 800\).
To conclude, Kim's error is in the addition step of the partial products, which leads to an incorrect final answer for \(253 \times 4\). The correct answer is \(1012\).
\[
253 = 200 + 50 + 3
\]
When using partial products, the multiplication would be broken down as follows:
1. \(200 \times 4 = 800\)
2. \(50 \times 4 = 200\)
3. \(3 \times 4 = 12\)
Now, we would add the results of these products together:
\[
800 + 200 + 12 = 1012
\]
It appears that Kim wrote "12 800 812" in the box, which indicates a misunderstanding in how to combine the products or perhaps a misplacement of digits.
**Kim’s mistake:**
1. She may have improperly aligned or summed the products, resulting in an incorrect total.
2. The correct sum of the calculated partial products \(800 + 200 + 12\) should be \(1012\), not \(812\) or any variation like \(12 800\).
To conclude, Kim's error is in the addition step of the partial products, which leads to an incorrect final answer for \(253 \times 4\). The correct answer is \(1012\).