To subtract signed numbers, you change the subtraction problem into an addition problem by adding the opposite (additive inverse) of the number being subtracted. In other words, change the sign of the second number and then add.
Here's a breakdown:
The Rule: a - b = a + (-b)
Explanation:
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Identify the two numbers involved in the subtraction: 'a' (the number being subtracted from) and 'b' (the number being subtracted).
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Find the opposite (additive inverse) of 'b': The opposite of a positive number is negative, and the opposite of a negative number is positive. For example, the opposite of 5 is -5, and the opposite of -3 is 3.
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Change the subtraction to addition: Instead of subtracting 'b' from 'a', you now add the opposite of 'b' to 'a'.
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Apply the rules for adding signed numbers:
- Same signs: Add the absolute values of the numbers and keep the sign.
- Different signs: Subtract the smaller absolute value from the larger absolute value. Keep the sign of the number with the larger absolute value.
Examples:
- 5 - 3:
- Change to addition: 5 + (-3)
- Add: 5 + (-3) = 2 (Different signs, subtract 3 from 5 and keep the positive sign because 5 has the larger absolute value)
- (-2) - 4:
- Change to addition: (-2) + (-4)
- Add: (-2) + (-4) = -6 (Same signs, add 2 and 4 and keep the negative sign)
- 7 - (-1):
- Change to addition: 7 + (+1) (or 7 + 1)
- Add: 7 + 1 = 8 (Same signs, add 7 and 1 and keep the positive sign)
- (-6) - (-2):
- Change to addition: (-6) + (+2) (or (-6) + 2)
- Add: (-6) + 2 = -4 (Different signs, subtract 2 from 6 and keep the negative sign because 6 has the larger absolute value)
In summary, when subtracting signed numbers, you're essentially adding the additive inverse. Understanding this conversion simplifies the process and reduces the likelihood of errors.
