Of course, I can help you understand this step-by-step.
Lori attempted to solve the multiplication problem [tex]\( 29 \times 31 \)[/tex] and got [tex]\( 699 \)[/tex] as the result, which is incorrect. Let's solve this correctly step-by-step to identify her mistakes.
1. Step 1: Multiply the unit digit of the second number (31) by the first number (29):
Multiply [tex]\( 29 \)[/tex] by [tex]\( 1 \)[/tex] (the units place of [tex]\( 31 \)[/tex]):
[tex]\[
29 \times 1 = 29
\][/tex]
Write this product down.
2. Step 2: Multiply the tens digit of the second number (31) by the first number (29):
Multiply [tex]\( 29 \)[/tex] by [tex]\( 30 \)[/tex] (which is the tens place value of [tex]\( 31 \)[/tex], represented as [tex]\( 3 \)[/tex] but multiplied by [tex]\( 10 \)[/tex]):
[tex]\[
29 \times 30
\][/tex]
To do this, break it down further:
[tex]\[
29 \times 3 = 87
\][/tex]
Since we are actually multiplying by thirty, we need to add a zero at the end:
[tex]\[
29 \times 30 = 870
\][/tex]
3. Step 3: Add the results from both steps:
Now add the two partial products obtained from the above steps:
[tex]\[
29 \, (\text{from } 29 \times 1) \\\\
+ 870 \, (\text{from } 29 \times 30)
\][/tex]
[tex]\[
899
\][/tex]
Hence, the correct result of multiplying [tex]\( 29 \times 31 \)[/tex] is [tex]\( 899 \)[/tex]. Lori's error was not placing the zero correctly when multiplying [tex]\( 29 \)[/tex] by [tex]\( 30 \)[/tex], and thus her total came out incorrect as [tex]\( 699 \)[/tex] instead of the correct [tex]\( 899 \)[/tex].
To summarize:
- First row: [tex]\( 29 \times 1 = 29 \)[/tex]
- Second row: [tex]\( 29 \times 30 = 870 \)[/tex] (Remember to add a zero at the end after multiplying by the tens digit [tex]\( 3 \)[/tex])
- Final result: [tex]\( 29 + 870 = 899 \)[/tex]
