When adding integers with different signs, you subtract the absolute value of the smaller number from the absolute value of the larger number and give the result the sign of the integer with the larger absolute value.
Here's a breakdown of the process:
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Find the Absolute Values: Determine the absolute value of each integer. The absolute value of a number is its distance from zero, ignoring its sign. For example, the absolute value of -5 is 5, and the absolute value of 3 is 3.
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Subtract: Subtract the smaller absolute value from the larger absolute value.
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Determine the Sign: The result takes the sign of the original integer that had the larger absolute value.
Examples:
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Example 1: -7 + 3
- Absolute values: |-7| = 7, |3| = 3
- Subtract: 7 - 3 = 4
- Sign: Since -7 has the larger absolute value, the answer is negative.
- Result: -7 + 3 = -4
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Example 2: 5 + (-2)
- Absolute values: |5| = 5, |-2| = 2
- Subtract: 5 - 2 = 3
- Sign: Since 5 has the larger absolute value, the answer is positive.
- Result: 5 + (-2) = 3
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Example 3: -4 + 9
- Absolute values: |-4| = 4, |9| = 9
- Subtract: 9 - 4 = 5
- Sign: Since 9 has the larger absolute value, the answer is positive.
- Result: -4 + 9 = 5
In summary, when the signs are different, focus on the absolute values to determine both the number and the sign of the final result. This avoids confusion and ensures accurate calculations.
