Drag and drop.
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
The commutative property states that changing the order of the elements being added or multiplied does not change the result. The associative property states that changing the grouping of the elements being added or multiplied does not change the result.
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.
Communtative property:
- a ⋅ b = b ⋅ a
- a+b=b+a
Associative property:
- a + (b+c)=(a+b)+c
- a ⋅ (b⋅c)=(a⋅b)⋅c