Let's carefully analyze Michael's mistakes regarding the identity properties of addition and multiplication.
1. Identity Property of Addition:
Michael wrote [tex]\(8 + 1 = 8\)[/tex].
The identity property of addition states that any number plus zero is equal to the number itself. In other words:
[tex]\[
a + 0 = a
\][/tex]
So for this to hold true in the case of Michael's example:
[tex]\[
8 + 0 = 8
\][/tex]
Michael should have added 0 to 8, not 1.
2. Identity Property of Multiplication:
Michael wrote [tex]\(8 \cdot 0 = 0\)[/tex].
The identity property of multiplication states that any number multiplied by one is equal to the number itself. In other words:
[tex]\[
a \cdot 1 = a
\][/tex]
So for this to hold true in the case of Michael's example:
[tex]\[
8 \cdot 1 = 8
\][/tex]
Michael should have multiplied 1 by 8, not 0.
Given these corrections, Michael’s mistakes were:
1. He should have added [tex]\(0\)[/tex] to [tex]\(8\)[/tex] (for the identity property of addition).
2. He should have multiplied [tex]\(1\)[/tex] by [tex]\(8\)[/tex] (for the identity property of multiplication).
Thus, Michael's mistakes can be summarized correctly as follows:
- He should have added 0 to 8 and multiplied 1 by 8.
So the correct choice from the options given is:
- He should have added 0 to 8 and multiplied 1 by 8.
