1: How could you rewrite the expression (-3+5)+8+(-1) using the Associative Property of Addition?
A- -3-8+(5+1)
B- (-3+(-1))+(5+8)
C- -3(5+8)+(-1)
D- 5+8+3+1
2: Which property is represented by 5+(-8)=-8+5?
A- Identity
B- Associative
C- Commutative
D- Distributive
1: The Associative Property of Addition states that the grouping of numbers does not affect the sum. To rewrite the expression (-3+5)+8+(-1) using this property, we need to regroup the numbers.
(-3+5)+8+(-1):
We can group the first two numbers (-3 and 5) and the last two numbers (8 and -1):
((-3+5)+8)+(-1)
Now, we can simplify the expression within each set of parentheses:
((-3+5)+8)+(-1) = (2+8)+(-1)
Finally, we simplify further to get the rewritten expression:
(2+8)+(-1) = 10+(-1)
So, the expression (-3+5)+8+(-1) can be rewritten as 10+(-1), or simply 10-1.
Answer: D- 10-1
2: The property represented by 5+(-8)=-8+5 is the Commutative Property of Addition.
The Commutative Property of Addition states that the order of addition does not affect the sum. In other words, you can add two numbers in any order and still get the same result.
In this case, 5+(-8) and -8+5 have the same sum. Therefore, the property being represented here is the Commutative Property of Addition.
Answer: C- Commutative
#1 None of the above
The Associative Property property says that
(a+b)+c = a+(b+c)
That is, you can move the parentheses around, but you don't change the ordering of the numbers.
A and B might be candidates, but they also switch things around, which is using the Commutative Property.
#2. So, as noted above, choice C is the correct one here.