Integer Addition
Name _________________ P ___
Add:
−𝟓 + (−𝟑) =
Same signs
add absolute values
Answer will be negative.
5
+3
−𝟓 + (−𝟑) = −𝟖
8
1) Add:
𝟏𝟐 + (−𝟖) =
Add:
−𝟐𝟏 + 𝟏𝟓 =
Different signs
subtract absolute values
Answer will be negative.
21
- 15
−𝟐𝟏 + 𝟏𝟓 = −𝟔
6
2) Add:
−𝟓 + 𝟐𝟔 =
using |Absolute Values |
3) Add:
𝟏𝟎 + 𝟏𝟐 =
4) Add:
−𝟐𝟓 + (−𝟑𝟏) =
5) Add:
𝟏𝟏 + (−𝟏𝟕) =
6) Add:
−𝟑𝟔 + 𝟏𝟑 =
7) Add:
−𝟏𝟎𝟓 + (−𝟐𝟔) =
8) Add:
−𝟕𝟎 + 𝟐𝟏 =
9) Add:
𝟒𝟏 + (−𝟑𝟐) =
10) Add:
𝟐𝟎 + 𝟏𝟎𝟒 =
Adding Integers using Absolute Values
Remember what absolute value is:



Absolute value measures the distance between a number and zero.
Absolute value symbols look like vertical bars around a number, like |5|.
Absolute values always have positive measurements. |-6| = 6, |-2| = 2, |9| = 9
Integer Addition Rules
SAME SIGN
 If both integers are positive, they are both on the right side of zero on the number line.
 The sum will be even further to the right. (No zero pairs, all positives!)
 More distance from zero means absolute values add, and the result is positive.
5 + 7 → 𝑠𝑎𝑚𝑒 𝑠𝑖𝑔𝑛𝑠, 𝑎𝑏𝑠𝑜𝑙𝑢𝑡𝑒 𝑣𝑎𝑙𝑢𝑒𝑠 𝑎𝑑𝑑 →
5 + 7 = 12 →
𝑎𝑛𝑠𝑤𝑒𝑟 𝑖𝑠 𝑜𝑛 𝑡ℎ𝑒 𝑟𝑖𝑔ℎ𝑡 𝑠𝑖𝑑𝑒
𝟓 + 𝟕 = 𝟏𝟐



If both integers are negative, they are both on the left side of zero on the number line.
The sum will be even further to the left. (No zero pairs, all negatives!)
More distance from zero means absolute values add, and the result is negative.
−4 + (−2) → 𝑠𝑎𝑚𝑒 𝑠𝑖𝑔𝑛𝑠, 𝑎𝑏𝑠𝑜𝑙𝑢𝑡𝑒 𝑣𝑎𝑙𝑢𝑒𝑠 𝑎𝑑𝑑 →
4+2 = 6→
𝑎𝑛𝑠𝑤𝑒𝑟 𝑖𝑠 𝑜𝑛 𝑡ℎ𝑒 𝑙𝑒𝑓𝑡 𝑠𝑖𝑑𝑒
−𝟒 + (−𝟐) = −𝟔
DIFFERENT SIGNS
 If the integers have different signs, then some zero pairs exist and will cancel.
 The sum will be closer to zero, so the absolute values subtract. (Distance is undone by canceling zero pairs!)
 The answer is made out of “leftovers” that keep the same sign as the stronger integer.
7 + (−11) → 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡 𝑠𝑖𝑔𝑛𝑠, 𝑎𝑏𝑠𝑜𝑙𝑢𝑡𝑒 𝑣𝑎𝑙𝑢𝑒𝑠 𝑠𝑢𝑏𝑡𝑟𝑎𝑐𝑡 →
11 − 7 = 4 →
𝑙𝑒𝑓𝑡𝑜𝑣𝑒𝑟𝑠 𝑤𝑖𝑙𝑙 𝑏𝑒 𝑛𝑒𝑔𝑎𝑡𝑖𝑣𝑒 →
𝟕 + (−𝟏𝟏) = −𝟒
With practice, you can apply these ideas in mental math.
For now you must always show your work. That means draw a model or show the rules!
Example: - 87 + 26 =
Work:
-87 + 26 =
different signs (fighting!)
|-87| = 87 |26| = 26
subtract absolute values,
87
negative wins!
- 26
61
So
- 87 + 26 = - 61