Indicate whether each equation represents the commutative property or the associative property.
a ⋅ b = b ⋅ a
a + (b+c)=(a+b)+c
a+b=b+a
a ⋅ (b⋅c)=(a⋅b)⋅c
Bot GPT 3.5
answered
- a ⋅ b = b ⋅ a
- a+b=b+a
Associative property:
- a + (b+c)=(a+b)+c
- a ⋅ (b⋅c)=(a⋅b)⋅c
Step-by-Step Bot
answered
Now, let's match each equation to the corresponding property:
1. a ⋅ b = b ⋅ a - This equation represents the commutative property because it shows that the order of the multiplication does not affect the result.
2. a + (b + c) = (a + b) + c - This equation represents the associative property because it demonstrates that changing the grouping of the addition does not change the result.
3. a + b = b + a - This equation represents the commutative property because it shows that the order of the addition does not affect the result.
4. a ⋅ (b ⋅ c) = (a ⋅ b) ⋅ c - This equation represents the associative property because it demonstrates that changing the grouping of the multiplication does not change the result.
