Alright, let’s go through the correct step-by-step process to solve the multiplication problem [tex]\( 29 \times 31 \)[/tex] and identify where Lori made her mistake.
1. Write the numbers in columns for multiplication:
```
29
× 31
```
2. Multiply the ones digit of 31 by 29:
- First, multiply [tex]\(1\)[/tex] (the ones digit of 31) by [tex]\(29\)[/tex]:
[tex]\[
29 \times 1 = 29
\][/tex]
Thus, the first partial product (29 × 1) is 29.
- Write this result down:
```
29
```
3. Multiply the tens digit of 31 by 29:
- Now, multiply [tex]\(3\)[/tex] (the tens digit of 31) by [tex]\(29\)[/tex]:
[tex]\[
29 \times 3 = 87
\][/tex]
- Since we are actually multiplying 29 by 30 (due to the place value), we need to shift this result one place to the left (equivalent to multiplying by 10):
[tex]\[
870
\][/tex]
Here is where Lori made a mistake: she should place a 0 in the ones column before writing the result of [tex]\(29 \times 3\)[/tex].
- Write this result down:
```
+870
```
4. Add the partial products together:
- Align the partial products and add them together:
[tex]\[
\begin{array}{r}
29 \\
+ 870 \\
\hline
899 \\
\end{array}
\][/tex]
5. Final Result:
- After correctly adding the partial products, we get:
[tex]\[
29 \times 31 = 899
\][/tex]
Therefore, Lori made a mistake by not placing a 0 in the ones column before multiplying 3 by 9, which caused her to get an incorrect intermediate result. After correctly placing the 0 and performing the multiplication and addition steps, the correct answer is [tex]\( 899 \)[/tex].
