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:
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(9⋅5)⋅(8⋅3) - This expression involves multiplication, but it is not simply regrouping numbers; it appears to combine two groups of products.
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(5+8)⋅3 - This expression incorporates addition and multiplication, but it's also not just a rearrangement or regrouping of a single operation.
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(9⋅5)+8+3 - This expression combines multiplication and addition without regrouping like terms, so it does not apply.
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(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.
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