To add \((-3)\) and \((-17)\) using properties of operations, we can follow these steps:
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Associative Property of Addition: This property states that the way in which numbers are grouped does not change their sum. However, in this case, we're only adding two numbers.
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Commutative Property of Addition: This property states that the order in which two numbers are added does not change their sum. Again, for two numbers, this doesn't change anything.
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Adding the Numbers: We can simply add the two negative numbers together: \[ (-3) + (-17) = -3 - 17 \] When adding two negative numbers, we can think of it as taking away from a number line.
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Now, adding the absolute values: \[ 3 + 17 = 20 \] Since we’re working with negative values: \[ -3 + (-17) = -20 \]
Thus, the final result is: \[ (-3) + (-17) = -20 \]