Answer :
Lori made a mistake in her multiplication, and we will address what she did wrong and correct it step-by-step:
### Step-by-Step Correction for [tex]\( 29 \times 31 \)[/tex]:
1. Multiplication of the ones' place of the multiplier:
- The multiplier is 31, so we first multiply the 1 in the ones' place (rightmost digit) by each digit of the multiplicand (29).
[tex]\[ 29 \times 1 = 29 \][/tex]
We write this down as the first partial product:
[tex]\[ \quad \ \ 29 \][/tex]
2. Multiplication of the tens' place of the multiplier:
- Next, we multiply the 3 in the tens' place by each digit of the multiplicand (29). Before we do this, we must place a 0 in the ones' place to indicate we are multiplying by the tens place (effectively 30).
[tex]\[ \begin{array}{r} \quad \ 29 \\ + \underline{(29 \times 30)} \end{array} \][/tex]
- Now, performing the multiplication:
- [tex]\(9 \times 3 = 27\)[/tex], write down 7 and carry over 2.
- [tex]\(2 \times 3 = 6\)[/tex], add the carried over 2: [tex]\(6 + 2 = 8\)[/tex].
Therefore, the second partial product is:
[tex]\[ 87 \quad \text{(Place the 0 in the ones' column and then write 87)} \][/tex]
3. Arrange and Add the Partial Products:
Now, add the two partial products together:
[tex]\[ \begin{array}{r} \ \ 29 \\ + 870 \\ \hline \ \ 899 \end{array} \][/tex]
So, the correct result should be [tex]\(899\)[/tex] for the multiplication [tex]\(29 \times 31\)[/tex].
### Step-by-Step Correction for [tex]\( 29 \times 31 \)[/tex]:
1. Multiplication of the ones' place of the multiplier:
- The multiplier is 31, so we first multiply the 1 in the ones' place (rightmost digit) by each digit of the multiplicand (29).
[tex]\[ 29 \times 1 = 29 \][/tex]
We write this down as the first partial product:
[tex]\[ \quad \ \ 29 \][/tex]
2. Multiplication of the tens' place of the multiplier:
- Next, we multiply the 3 in the tens' place by each digit of the multiplicand (29). Before we do this, we must place a 0 in the ones' place to indicate we are multiplying by the tens place (effectively 30).
[tex]\[ \begin{array}{r} \quad \ 29 \\ + \underline{(29 \times 30)} \end{array} \][/tex]
- Now, performing the multiplication:
- [tex]\(9 \times 3 = 27\)[/tex], write down 7 and carry over 2.
- [tex]\(2 \times 3 = 6\)[/tex], add the carried over 2: [tex]\(6 + 2 = 8\)[/tex].
Therefore, the second partial product is:
[tex]\[ 87 \quad \text{(Place the 0 in the ones' column and then write 87)} \][/tex]
3. Arrange and Add the Partial Products:
Now, add the two partial products together:
[tex]\[ \begin{array}{r} \ \ 29 \\ + 870 \\ \hline \ \ 899 \end{array} \][/tex]
So, the correct result should be [tex]\(899\)[/tex] for the multiplication [tex]\(29 \times 31\)[/tex].
