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 when you are adding or multiplying numbers, the way in which the numbers are grouped does not change the result. In mathematical terms, it can be expressed as:

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

Given your options, the expressions that could be rewritten using the Associative Property are:

1. **(9⋅5)⋅(8⋅3)** - This expression involves multiplication and has different groupings that could be rearranged; however, it can be interpreted as two separate products and doesn't involve three numbers.

2. **(5+8)⋅3** - This expression involves both addition and multiplication and can be rearranged, but it is primarily multiplication.

3. **(9⋅5)+8+3** - This expression involves addition, and you could change how the addition is grouped, for example: \( ((9⋅5)+8)+3 = (9⋅5)+(8+3) \).

4. **(5⋅8)+3** - This expression focuses specifically on a grouping that can be rearranged using addition, as it could be rewritten as \( (5⋅8+3) \) or other variations, but not primarily move around functions.

The best candidate is **(9⋅5)+8+3**, as it explicitly has the associative property in addition, where grouping can be changed.