Integer Operations
Master adding, subtracting, multiplying, and dividing positive and negative numbers.
Understanding Integer Operations
What Are Integers?
Integers are whole numbers that can be positive, negative, or zero.
Examples: ..., -3, -2, -1, 0, 1, 2, 3, ...
Working with negative numbers follows specific rules. Once you learn these rules, integer operations become straightforward!
Adding Integers
+ Same Signs
5 + 3 = 8 (both positive)
-5 + (-3) = -8 (both negative)
+- Different Signs
5 + (-3) = 2 (5 is larger, positive)
-5 + 3 = -2 (5 is larger, negative)
Visualize: -4 + 7 on a Number Line
-4 + 7 = 3
Subtracting Integers
The Subtraction Rule
Subtracting is the same as adding the opposite!
Convert to Addition
5 - 8 = 5 + (-8) = -3
-3 - 4 = -3 + (-4) = -7
-2 - (-6) = -2 + 6 = 4
Double Negatives
7 - (-3) = 7 + 3 = 10
-5 - (-2) = -5 + 2 = -3
Multiplying and Dividing Integers
Multiplication and division follow the same sign rules:
Sign Rules for Multiplication and Division
| Signs | Result | Example (Multiply) | Example (Divide) |
|---|---|---|---|
| + and + | Positive | 6 x 3 = 18 | 18 / 3 = 6 |
| - and - | Positive | (-6) x (-3) = 18 | (-18) / (-3) = 6 |
| + and - | Negative | 6 x (-3) = -18 | 18 / (-3) = -6 |
| - and + | Negative | (-6) x 3 = -18 | (-18) / 3 = -6 |
Easy Way to Remember
"Same signs = Positive, Different signs = Negative"
This works for both multiplication AND division!
Quick Summary
- Adding same signs: Add and keep the sign
- Adding different signs: Subtract and use sign of larger absolute value
- Subtracting: Add the opposite (keep-change-change)
- Multiplying/Dividing: Same signs = positive, different signs = negative
Worked Examples
Let's work through examples of each operation.
Example 1: Adding Integers
Both numbers are negative (same signs).
8 + 5 = 13, and we keep the negative sign.
Example 2: Adding with Different Signs
Different signs (one negative, one positive).
|-12| = 12, |7| = 7
12 - 7 = 5
12 > 7, and -12 is negative, so the answer is negative.
Example 3: Subtracting Integers
4 - 9 = 4 + (-9)
9 - 4 = 5, and 9 > 4, so use the negative sign.
Example 4: Subtracting a Negative
-3 - (-8) = -3 + 8
8 - 3 = 5, and 8 > 3, so positive.
Example 5: Multiplying Integers
Both negative = same signs = positive result.
7 x 4 = 28
Example 6: Dividing Integers
Negative and positive = different signs = negative result.
36 / 4 = 9
Practice Problems
Try these integer operation problems!
Problem 1: Addition
-6 + (-9) = ?
Problem 2: Subtraction
7 - 12 = ?
Problem 3: Subtracting a Negative
-4 - (-10) = ?
Problem 4: Multiplication
(-8) x 5 = ?
Problem 5: Division
(-48) / (-6) = ?
Check Your Understanding: Integer Operations Challenge
Test your skills with this 6-question challenge!
Integer Operations Challenge
Challenge Complete!
Next Steps
Key Takeaways:
- Same signs when adding: add and keep the sign
- Different signs when adding: subtract and use sign of larger absolute value
- Subtraction: convert to adding the opposite
- Multiply/Divide: same signs = positive, different signs = negative
- Practice with real-world contexts like temperature and money
- Double-check your work by estimating if the answer should be positive or negative
- Move on to learn about writing and evaluating expressions!