Question
Which one of the following denotes associative property?
a(b + c) = ab + ac
a(bc) = (ab)c
ab = ba
a + b = b + c
a(b + c) = ab + ac
a(bc) = (ab)c
ab = ba
a + b = b + c
Answers
GPT-4o mini
The associative property refers to how the grouping of numbers does not change the result of an operation. In specific terms, the associative property can be defined for both addition and multiplication:
- For addition: \( a + (b + c) = (a + b) + c \)
- For multiplication: \( a(bc) = (ab)c \)
From the options you've provided:
- \( a(b + c) = ab + ac \) (this is the distributive property)
- **\( a(bc) = (ab)c \)** (this is the associative property)
- \( ab = ba \) (this is the commutative property)
- \( a + b = b + c \) (this is not a property)
Thus, the correct answer that denotes the associative property is **\( a(bc) = (ab)c \)**.
- For addition: \( a + (b + c) = (a + b) + c \)
- For multiplication: \( a(bc) = (ab)c \)
From the options you've provided:
- \( a(b + c) = ab + ac \) (this is the distributive property)
- **\( a(bc) = (ab)c \)** (this is the associative property)
- \( ab = ba \) (this is the commutative property)
- \( a + b = b + c \) (this is not a property)
Thus, the correct answer that denotes the associative property is **\( a(bc) = (ab)c \)**.