Question

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

Answer 1

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.