Alright Lori, let's carefully solve this multiplication problem step by step.
We need to calculate [tex]\(29 \times 31\)[/tex].
### Step-by-Step Multiplication:
1. Break down each number by place value:
- [tex]\(29\)[/tex] can be seen as [tex]\(20 + 9\)[/tex]
- [tex]\(31\)[/tex] can be seen as [tex]\(30 + 1\)[/tex]
2. Multiply each part separately:
- First, multiply [tex]\(9\)[/tex] by [tex]\(1\)[/tex]:
[tex]\[
9 \times 1 = 9
\][/tex]
- Then, multiply [tex]\(9\)[/tex] by [tex]\(3\)[/tex] (which represents 30 because it’s in the tens place):
[tex]\[
9 \times 3 = 27
\][/tex]
Here, we have to remember to regroup the 2 (which means you carry over the 2 tens).
3. Now, consider the [tex]\(20\)[/tex] (2 in the tens place):
- Multiply [tex]\(2\)[/tex] by [tex]\(1\)[/tex]:
[tex]\[
2 \times 1 = 2
\][/tex]
- Then, multiply [tex]\(2\)[/tex] by [tex]\(3\)[/tex] (again, representing 30):
[tex]\[
2 \times 3 = 6
\][/tex]
After regrouping the 2 from the previous multiplication (9*3), this becomes:
[tex]\[
6 + 2 = 8
\][/tex]
4. Add the results together with correct placement:
- Our partial results are: 9, 27, 2, and 8.
5. Summarize the steps with correct place value:
We compute:
[tex]\[
29 \times 31 = (9 + 270 + 20 + 60) = 899
\][/tex]
Thus, Lori's mistake was not properly regrouping the 2 and providing the correct sum. The correct answer is 899, not 699.
