Question
Which of the following expressions could you rewrite using the Associative Property?
(5+8)⋅3
(9⋅5)+8+3
(5⋅8)+3
(9⋅5)⋅(8⋅3)
(5+8)⋅3
(9⋅5)+8+3
(5⋅8)+3
(9⋅5)⋅(8⋅3)
Answers
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Answered by
GPT-4o mini
The Associative Property refers to how we group numbers in addition or multiplication. It states that the way in which numbers are grouped does not affect the sum or the product.
The Associative Property applies to:
1. Addition: \( (a + b) + c = a + (b + c) \)
2. Multiplication: \( (a \cdot b) \cdot c = a \cdot (b \cdot c) \)
Now, let's evaluate the given expressions:
1. **(5 + 8) ⋅ 3**
- This is a multiplication expression that includes addition, but it cannot be rewritten using the Associative Property since the multiplication is not grouped.
2. **(9 ⋅ 5) + 8 + 3**
- This expression is addition with a multiplication grouped. However, it is possible to regroup the addition (not multiplication) but does not directly apply the Associative Property.
3. **(5 ⋅ 8) + 3**
- Similar to the previous expression, it involves multiplication and addition. The addition part can be regrouped, but it doesn't involve using the Associative Property for multiplication.
4. **(9 ⋅ 5) ⋅ (8 ⋅ 3)**
- Here, we have a multiplication of two products. We can apply the Associative Property because it is multiplication. For example, we can rewrite it as \( 9 ⋅ (5 ⋅ (8 ⋅ 3)) \) or \( (9 ⋅ 5 ⋅ 8) ⋅ 3 \).
Therefore, the expression that can be rewritten using the Associative Property is:
**(9 ⋅ 5) ⋅ (8 ⋅ 3)**
The Associative Property applies to:
1. Addition: \( (a + b) + c = a + (b + c) \)
2. Multiplication: \( (a \cdot b) \cdot c = a \cdot (b \cdot c) \)
Now, let's evaluate the given expressions:
1. **(5 + 8) ⋅ 3**
- This is a multiplication expression that includes addition, but it cannot be rewritten using the Associative Property since the multiplication is not grouped.
2. **(9 ⋅ 5) + 8 + 3**
- This expression is addition with a multiplication grouped. However, it is possible to regroup the addition (not multiplication) but does not directly apply the Associative Property.
3. **(5 ⋅ 8) + 3**
- Similar to the previous expression, it involves multiplication and addition. The addition part can be regrouped, but it doesn't involve using the Associative Property for multiplication.
4. **(9 ⋅ 5) ⋅ (8 ⋅ 3)**
- Here, we have a multiplication of two products. We can apply the Associative Property because it is multiplication. For example, we can rewrite it as \( 9 ⋅ (5 ⋅ (8 ⋅ 3)) \) or \( (9 ⋅ 5 ⋅ 8) ⋅ 3 \).
Therefore, the expression that can be rewritten using the Associative Property is:
**(9 ⋅ 5) ⋅ (8 ⋅ 3)**
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