Answer:
When adding integers with different signs, the rule of subtracting is used.
- This rule is used because the positive value increases the sum and the negative value decreases the sum.
- When the signs are different, we take the absolute values of each number.
- The answer will have the sign of the number that had the larger absolute value.
Now, let's solve the given problems step-by-step:
1. -12 + 3:
- Since the signs are different (negative and positive), we subtract the absolute values of the numbers: |-12| - |3|.
- |-12| equals 12 and |3| equals 3.
- So, we have 12 - 3.
- The answer will get the sign of the number that had the larger absolute value, which is -12.
- Therefore, -12 + 3 equals -9.
2. 16 + (-13):
- The signs are different (positive and negative), so we subtract the absolute values: |16| - |(-13)|.
- |16| equals 16 and |(-13)| equals 13.
- Therefore, we have 16 - 13.
- The answer will get the sign of the number that had the larger absolute value, which is 16.
- Hence, 16 + (-13) equals 3.
3. The sum of 44 and -89:
- The signs are different (positive and negative), so we subtract the absolute values: |44| - |(-89)|.
- |44| equals 44 and |(-89)| equals 89.
- Therefore, we have 44 - 89.
- The answer will get the sign of the number that had the larger absolute value, which is -89.
- Thus, the sum of 44 and -89 is -45.
4. The total amount of yards gained or lost during the possession:
- We need to add up the yard values: +3, -2, and +5.
- The positive values represent yards gained, and the negative values represent yards lost.
- Adding +3, -2, and +5 gives us a total of 6 yards gained.
- Therefore, the total amount of yards gained or lost during this possession is 6 yards.