To determine which of the given expressions can be rewritten using the associated properties, let's first clarify what the associative property entails. The associative property states that when adding or multiplying numbers, the way in which the numbers are grouped does not affect the sum or the product.
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For addition: The associative property states that \( (a + b) + c = a + (b + c) \).
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For multiplication: The associative property states that \( (a \cdot b) \cdot c = a \cdot (b \cdot c) \).
Let's evaluate each expression:
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(9.5) + 8 + 3
This can be rewritten using the associative property because we can group the numbers in different ways.- For example, \( (9.5 + 8) + 3 = 9.5 + (8 + 3) \).
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(5.8) + 3
This does not involve more than two numbers added together. The associative property cannot be applied with only two numbers as it doesn’t change the grouping. -
(9.5) . (8.3)
This expression is multiplication of two numbers, but like with addition of two numbers, it cannot be rewritten using the associative property without a third number. -
(5 + 8) . 3
This can also be rewritten using the associative property, especially since it consists of addition being multiplied by a number.- For example, \( (5 + 8) \cdot 3 = 3 \cdot (5 + 8) \) (though this is a reordering instead of grouping).
In conclusion, the expressions that can be rewritten using the associative properties are:
- (9.5) + 8 + 3
- (5 + 8) . 3
The expressions that cannot be rewritten using the associative property are:
- (5.8) + 3
- (9.5) . (8.3)
2 answers