What are Integers?
Integers are whole numbers that can be positive, negative, or zero.
Examples: …, -3, -2, -1, 0, 1, 2, 3, …
The Number Line
-5 -4 -3 -2 -1 0 1 2 3 4 5 Negative ←----------------------------------------→ Positive
Adding Integers
Rule 1: Same Signs
When adding numbers with the same sign, add their absolute values and keep the sign.
Examples:
- 7 + 5 = 12
- (-7) + (-5) = -12
Rule 2: Different Signs
When adding numbers with different signs, subtract and use the sign of the larger number.
Examples:
- 9 + (-5) = 4
- (-12) + 7 = -5
Subtracting Integers: KEEP-CHANGE-CHANGE
To subtract, change subtraction to addition and flip the sign of the second number.
Examples:
- 8 – 5 = 8 + (-5) = 3
- 8 – (-5) = 8 + 5 = 13
- -8 – 5 = -8 + (-5) = -13
Multiplying and Dividing Integers
Sign Rules
| Operation | Same Signs | Different Signs |
|---|---|---|
| Multiplication | Positive result | Negative result |
| Division | Positive result | Negative result |
Examples:
- 5 × 3 = 15
- (-5) × (-3) = 15
- (-5) × 3 = -15
- 20 ÷ 4 = 5
- (-20) ÷ (-4) = 5
- (-20) ÷ 4 = -5
Practice Problems (100 Total)
Addition (Problems 1-25)
- 7 + 13 = 20
- (-9) + (-6) = -15
- 16 + (-9) = 7
- (-19) + 12 = -7
- (-11) + 11 = 0
Click to see all 25 addition problems
- 25 + 18 = 43
- (-14) + (-21) = -35
- 22 + (-15) = 7
- (-28) + 15 = -13
- 17 + (-17) = 0
- 34 + 29 = 63
- (-45) + (-23) = -68
- 50 + (-32) = 18
- (-61) + 40 = -21
- 8 + 15 + 7 = 30
- (-5) + (-10) + (-8) = -23
- 12 + (-20) + 8 = 0
- (-14) + 9 + (-3) = -8
- 100 + (-75) = 25
- (-88) + 88 = 0
- 6 + 9 + 12 = 27
- (-7) + (-7) + (-7) = -21
- 25 + (-10) + (-5) = 10
- (-30) + 15 + 20 = 5
- 41 + (-18) + 9 = 32
Subtraction (Problems 26-50)
- 15 – 8 = 7
- 10 – 25 = -15
- (-12) – 7 = -19
- (-9) – (-4) = -5
- 14 – (-6) = 20
[Problems 31-50 available in full content…]
Multiplication (Problems 51-75)
- 7 × 6 = 42
- (-5) × 4 = -20
- 6 × (-9) = -54
- (-7) × (-6) = 42
- (-10) × 10 = -100
[Problems 56-75 available in full content…]
Division (Problems 76-100)
- 36 ÷ 6 = 6
- (-40) ÷ 5 = -8
- 56 ÷ (-8) = -7
- (-54) ÷ (-6) = 9
- (-120) ÷ 10 = -12
[Problems 81-100 available in full content…]
Real-World Applications
Temperature
If the temperature is 5°C and drops by 12°C, what’s the new temperature?
Solution: 5 – 12 = -7°C
Bank Account
You have $50. You withdraw $30, then withdraw $35. What’s your balance?
Solution: 50 – 30 – 35 = -$15 (overdrawn!)
Flashcard
Common Mistakes to Avoid
- ❌ Thinking -3 > -1
- ✅ Correct: -1 > -3
- ❌ (-5) × (-3) = -15
- ✅ Correct: (-5) × (-3) = 15
- ❌ 8 – (-5) = 3
- ✅ Correct: 8 – (-5) = 13
Mastery Checklist
By the end of this week, you should be able to:
- ✅ Add integers with same and different signs
- ✅ Subtract integers using Keep-Change-Change
- ✅ Multiply integers using sign rules
- ✅ Divide integers using sign rules
- ✅ Solve multi-step integer problems
- ✅ Apply integers to real-world situations
Next Week Preview
Next week we’ll explore Fractions and Decimals – learning operations with parts of whole numbers!
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