Integer Operations Worksheet- Practice Problems
What Is an Integer Operations Worksheet?
An integer operations worksheet is a practice tool packed with problems involving positive and negative whole numbers. These worksheets cover the four basic operations: addition, subtraction, multiplication, and division of integers.
Teachers use them. Parents use them. Students who want to actually get better at math use them. The point is simple: repetition builds mastery.
You won't find fancy graphics or motivational quotes on a good worksheet. You'll find problems. That's it. The work does the teaching.
Integer Operations Rules You Need to Memorize
Before you touch a worksheet, you need these rules locked in your head. No exceptions.
Addition Rules
- Same signs: Add the numbers, keep the sign. (+5) + (+3) = +8. (-5) + (-3) = -8.
- Different signs: Subtract the smaller absolute value from the larger, keep the sign of the number with the larger absolute value. (+7) + (-4) = +3. (-7) + (+4) = -3.
Subtraction Rule
Change subtraction to addition and flip the sign of the second number. Keep-Change-Change. (+6) - (-3) becomes (+6) + (+3) = +9.
Multiplication and Division Rules
- Same signs: Answer is positive. (-4) × (-3) = +12. (+12) ÷ (+3) = +4.
- Different signs: Answer is negative. (-4) × (+3) = -12. (+12) ÷ (-3) = -4.
Practice Problems: Addition and Subtraction
Work through these. No calculator until you've tried.
Addition Problems
- (-7) + (-12) = ?
- (+15) + (-8) = ?
- (-23) + (+17) = ?
- (+9) + (+14) = ?
- (-6) + (+6) = ?
Subtraction Problems
- (+8) - (+5) = ?
- (+8) - (-5) = ?
- (-11) - (+4) = ?
- (-11) - (-4) = ?
- (+3) - (+10) = ?
Answers
Addition: -19, +7, -6, +23, 0
Subtraction: +3, +13, -15, -7, -7
Practice Problems: Multiplication and Division
These trip up more students. Take your time.
Multiplication Problems
- (-6) × (-4) = ?
- (+7) × (-3) = ?
- (-5) × (+8) = ?
- (-2) × (-2) × (-3) = ?
- (+4) × (+9) = ?
Division Problems
- (-36) ÷ (+6) = ?
- (+24) ÷ (-4) = ?
- (-48) ÷ (-8) = ?
- (+45) ÷ (+9) = ?
- (-18) ÷ (+3) = ?
Answers
Multiplication: +24, -21, -40, -12, +36
Division: -6, -6, +6, +5, -6
Integer Operations Comparison Table
| Operation | Same Signs | Different Signs | Example |
|---|---|---|---|
| Addition | Add, keep sign | Subtract, keep larger sign | (-5) + (-3) = -8 |
| Subtraction | Convert to addition | Convert to addition | (+7) - (-2) = +9 |
| Multiplication | Positive | Negative | (-4) × (+3) = -12 |
| Division | Positive | Negative | (-20) ÷ (+5) = -4 |
Mixed Operations Practice
These require you to apply multiple rules. Read carefully.
- (-4) + (-6) × (+2) = ?
- (+12) ÷ (-3) - (-5) = ?
- (-8) × (+3) + (-4) = ?
- (+20) + (-4) × (-2) = ?
- (-15) ÷ (+3) + (-7) × (-1) = ?
Answers: -16, +9, -28, +28, +2
Common Mistakes to Avoid
- Forgetting the sign rule: Students see two negatives and automatically make the answer positive. This only works for multiplication and division. Not addition.
- Messing up subtraction: Skipping the "keep-change-change" step. Don't try to do it in your head until you've practiced the method.
- Ignoring order of operations: Multiply and divide before adding and subtracting. Always.
- Rushing through negative numbers: They behave differently than positives. Slow down.
How to Use These Worksheets Effectively
- Set a timer. Start with 10 minutes for 20 problems. Track your speed and accuracy.
- Show your work. Write out each step. Don't do mental math on easy problems until they're actually easy.
- Check your answers immediately. Wrong habits practiced 50 times are harder to fix than wrong habits practiced 5 times.
- Focus on weak areas. If multiplication of negatives is your problem, do 30 of those. Not 30 mixed problems.
- Repeat weekly. Come back to the same worksheet tomorrow. If you get it right the second time, you actually learned it.
Where to Find Integer Operations Worksheets
Free resources exist. You don't need to pay for basic practice sheets.
- Khan Academy — Free, adaptive practice with instant feedback
- Kuta Software — Generate unlimited problems, free trials available
- Math-Drills.com — Massive collection of worksheets by topic and difficulty
- Quizizz/Quizlet — Gamified integer practice with leaderboards
When to Move On
Stop practicing addition and subtraction when you can score 90% or higher on 20 problems in under 10 minutes. For multiplication and division, the same standard applies.
If you're still making errors, you're not ready to move on. Integer operations show up in fractions, equations, and algebra. Weak foundations here will cost you later.