Drag and drop.
Indicate whether each equation represents the commutative property or the associative property.
5+6=6+5
3 ⋅ 5 = 5 ⋅ 3
3⋅(4⋅2)=(3⋅4)⋅2
2 +(3+4)=(2+3)+4
5+6=6+5 - Commutative Property
3⋅5 = 5⋅3 - Commutative Property
3⋅(4⋅2)=(3⋅4)⋅2 - Associative Property
2 +(3+4)=(2+3)+4 - Associative Property
To determine whether each equation represents the commutative property or the associative property, we'll need to understand what each property means.
1. Commutative Property: This property states that the order of the numbers being added or multiplied does not affect the result.
2. Associative Property: This property states that the grouping of numbers being added or multiplied does not affect the result.
Now let's analyze each equation:
1. 5 + 6 = 6 + 5
This equation represents the commutative property because the order of the numbers being added can be changed without affecting the result.
2. 3 ⋅ 5 = 5 ⋅ 3
This equation also represents the commutative property because the order of the numbers being multiplied can be changed without affecting the result.
3. 3 ⋅ (4 ⋅ 2) = (3 ⋅ 4) ⋅ 2
This equation represents the associative property because the grouping of numbers being multiplied can be changed without affecting the result.
4. 2 + (3 + 4) = (2 + 3) + 4
This equation also represents the associative property because the grouping of numbers being added can be changed without affecting the result.
In summary:
- Equations 1 and 2 represent the commutative property.
- Equations 3 and 4 represent the associative property.