Adding and Subtracting Integers
Grade 7 · Math · Study Guide
Learn the rules for adding and subtracting positive and negative whole numbers using number lines and clear strategies.
Integers are all whole numbers and their opposites: ..., -3, -2, -1, 0, 1, 2, 3, ... The number line is your best friend when working with integers. Positive numbers sit to the right of zero, and negative numbers sit to the left. The further left you go, the smaller the number gets, so -100 is much less than -1.
When adding integers with the same sign, add the absolute values and keep that sign. For example, -4 + (-3) = -7. Both numbers are negative, so you add 4 and 3 to get 7, then keep the negative sign. When adding integers with different signs, subtract the smaller absolute value from the larger and keep the sign of the number with the bigger absolute value. So -8 + 5 = -3 because 8 is larger and the negative wins.
Subtracting integers has a handy shortcut: subtracting a number is the same as adding its opposite. The rule is: keep the first number, change subtraction to addition, and change the sign of the second number. This is sometimes called KCC — Keep, Change, Change. So 7 - (-3) becomes 7 + 3 = 10, and -5 - 4 becomes -5 + (-4) = -9.
Negative numbers appear everywhere in real life: temperature below zero, debt, sea level, and even football yardage when a team loses yards. When the temperature drops from 3°F to -8°F, it fell 11 degrees — that is an integer subtraction problem.
Absolute value, written |n|, means the distance from zero on the number line, always a positive number or zero. |-7| = 7 and |7| = 7 because both are 7 steps from zero. Knowing absolute value helps you apply the addition and subtraction rules correctly every time.
| Signs | Rule | Example |
|---|---|---|
| Both positive | Add; answer is positive | 4 + 6 = 10 |
| Both negative | Add absolute values; answer is negative | (-4) + (-6) = -10 |
| Different signs | Subtract absolute values; keep sign of larger absolute value | (-9) + 4 = -5 |
| Original Problem | After KCC | Answer |
|---|---|---|
| 7 - 3 | 7 + (-3) | 4 |
| 7 - (-3) | 7 + 3 | 10 |
| -5 - 4 | -5 + (-4) | -9 |
| -5 - (-4) | -5 + 4 | -1 |
Key terms
- Integer
- Any whole number, its opposite, or zero: ..., -2, -1, 0, 1, 2, ...
- Absolute value
- A number's distance from zero on the number line; always positive or zero
- Opposite
- Two numbers that are the same distance from zero but on different sides, like 5 and -5
- KCC rule
- Keep, Change, Change — a shortcut to rewrite subtraction as adding the opposite
- Additive inverse
- The opposite of a number; any number plus its additive inverse equals zero
Practice questions
What is -8 + (-5)?
- -3
- 3
- -13
- 13
Show answer
Answer: -13
Subtracting an integer is the same as adding its opposite.
Show answer
Answer: True
The absolute value of -14 is ___.
Show answer
Answer: 14
Using KCC, which expression is equivalent to -3 - (-9)?
- -3 - 9
- -3 + 9
- 3 - 9
- -3 × 9
Show answer
Answer: -3 + 9
The sum of two negative integers is always negative.
Show answer
Answer: True
Fun facts
- The coldest temperature ever recorded on Earth was -128.6°F in Antarctica — that is an integer so extreme you need to add 129 just to reach 1°F above zero!
- Stock traders use positive and negative integers every day: a stock that gains $4 and then loses $7 ends up -$3 from where it started.
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