Which of the following expressions could you rewrite using the Associative Property?

(1 point) Responses
(9⋅5)⋅(8⋅3)
(5+8)⋅3
(9⋅5)+8+3
(5⋅8)+3

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
2 months ago

The Associative Property states that the way in which numbers are grouped in addition or multiplication does not change the result. In mathematical terms, this can be expressed as:

- For addition: \( (a + b) + c = a + (b + c) \)
- For multiplication: \( (a \cdot b) \cdot c = a \cdot (b \cdot c) \)

Let's evaluate the given expressions:

1. **(9⋅5)⋅(8⋅3)** - This expression involves multiplication, but it is not simply regrouping numbers; it appears to combine two groups of products.

2. **(5+8)⋅3** - This expression incorporates addition and multiplication, but it's also not just a rearrangement or regrouping of a single operation.

3. **(9⋅5)+8+3** - This expression combines multiplication and addition without regrouping like terms, so it does not apply.

4. **(5⋅8)+3** - Similar to the previous expression, this one does not exhibit any regrouping of numbers using associative property.

None of the expressions provided above fits the Associative Property.

**Conclusion**: None of the expressions listed can be rewritten specifically using the Associative Property as phrased.