Learn integer operations
Integer operations use positive numbers, negative numbers, and zero. Sign rules determine the direction or sign of each result.
You will choose the correct sign rule for adding, subtracting, multiplying, and dividing integers.
The idea in plain English
Integers are positive whole numbers, negative whole numbers, and zero.
Addition uses direction and size. Multiplication and division use a simpler same-sign or different-sign rule.
How to recognise this kind of question
- At least one number has a negative sign.
- The operation may be +, −, ×, or ÷.
- Parentheses may separate a subtraction sign from a negative number.
Quick decision: First identify the operation. Addition rules and multiplication rules are not interchangeable.
The method
- Identify the operation and the signs of both integers.
- Apply the correct sign rule before calculating.
- Estimate the result's sign and size as a quick check.
Worked examples
−8 + 13
- The signs differ, so subtract the smaller absolute value from the larger.
- 13 − 8 = 5, and 13 has the larger absolute value.
Answer: 5
−6 × −4
- The signs are the same, so the answer is positive.
- Multiply 6 × 4.
Answer: 24
Your turn—with help
7 − (−5)
Need a hint?
Subtracting a negative becomes adding a positive.
Show the answer and steps
- Rewrite as 7 + 5.
- Add: 7 + 5 = 12.
Answer: 12
Watch out for this mistake
Incorrect: −8 + 3 = 11
Why it fails: The same-sign multiplication rule was used for addition.
Do this instead: For different-sign addition, subtract 8 − 3 and keep the sign of −8: −5.
Quick check
Try these without looking. Then open each answer to check your thinking.
−9 + 4
Need a hint?
Different signs: subtract the smaller size from the larger.
Show the answer and steps
- 9 − 4 = 5.
- The larger absolute value came from −9, so the answer is negative.
Answer: −5
−3 − 8
Need a hint?
Move 8 more units left.
Show the answer and steps
- Rewrite as −3 + (−8).
- Add the sizes and keep the negative sign.
Answer: −11
−20 ÷ 5
Need a hint?
Different signs give a negative result.
Show the answer and steps
- 20 ÷ 5 = 4.
- Apply the negative sign.
Answer: −4
Common mistakes
- Treating every pair of negative signs the same way.
- Using multiplication sign rules for addition.
- Forgetting that subtracting a negative becomes addition.
Practice tips
- Use a number line for addition and subtraction checks.
- Practice one operation at a time before using mixed sets.