While there isn't a set of "three rules" specifically defined for subtracting integers, the process relies on understanding the following concepts and principles:
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Transform Subtraction into Addition: The fundamental rule is to rewrite subtraction as addition of the opposite. This means: a - b = a + (-b). Instead of subtracting, you add the negative of the number being subtracted (the subtrahend).
Example: 5 - 3 becomes 5 + (-3) = 2
Example: 2 - (-4) becomes 2 + 4 = 6 -
Apply Integer Addition Rules: Once you've transformed the subtraction into addition, you follow the rules for adding integers:
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Adding Integers with the Same Sign: If both integers have the same sign (both positive or both negative), add their absolute values and keep the same sign.
Example: (-3) + (-2) = -5 (Add 3 and 2, then keep the negative sign)
Example: 4 + 6 = 10 (Add 4 and 6, then keep the positive sign) -
Adding Integers with Different Signs: If the integers have different signs, find the difference between their absolute values and keep the sign of the integer with the larger absolute value.
Example: (-7) + 2 = -5 (The absolute values are 7 and 2. 7 - 2 = 5. Since 7 has a larger absolute value and is negative, the answer is -5)
Example: 5 + (-2) = 3 (The absolute values are 5 and 2. 5 - 2 = 3. Since 5 has a larger absolute value and is positive, the answer is 3)
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Understanding Zero and Additive Inverses:
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Subtracting Zero: Subtracting 0 from any integer results in the integer itself: a - 0 = a.
Example: 8 - 0 = 8
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Subtracting from Zero: Subtracting an integer a from zero results in the additive inverse (or opposite) of a: 0 - a = -a.
Example: 0 - 5 = -5
Example: 0 - (-3) = 3
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Essentially, mastering subtraction of integers comes down to understanding how to convert it into addition of integers and then applying the rules of addition, along with recognizing the properties of zero.
