Grade 6–7 · Free math lesson
Integers & Operations
After this lesson, you will be able to add, subtract, multiply, and divide positive and negative whole numbers with confidence.
Practice Integers & Operations freeSkills in this unit
Pick a skill to try three free questions on just that.
- Integers on the number line and opposites
- Absolute value
- Comparing and ordering integers
- Adding integers
- Subtracting integers
- Multiplying and dividing integers
- Order of operations with integers
- Integer word problems
What Are Integers?
Integers are whole numbers that can be positive, negative, or zero. Think of a thermometer — numbers go up (positive) and down (negative) from zero.
Example: ...-3, -2, -1, 0, 1, 2, 3... All of these are integers. -5 is an integer. 2.5 is NOT.
Remember: If you can count it on fingers OR owe it to a friend, it's an integer!
Adding & Subtracting Integers
Adding a negative number is the same as subtracting. Picture walking left (negative) or right (positive) on a number line.
Example: 5 + (-3) = 5 - 3 = 2. Start at 5, walk 3 steps left, land on 2.
Remember: Same signs? ADD and keep the sign. Different signs? SUBTRACT and keep the bigger number's sign.
Multiplying & Dividing Integers
When you multiply or divide two integers, the signs tell you if the answer is positive or negative. Same signs give a positive result, different signs give a negative result.
Example: -3 × 4 = -12 (different signs → negative). -3 × -4 = 12 (same signs → positive).
Remember: Count the negatives: ODD number of negatives = negative answer. EVEN number = positive answer.
Worked example
Solve: -8 + 3 × (-2)
- 1Step 1 — Multiply first (order of operations): 3 × (-2) = -6
- 2Step 2 — Now add: -8 + (-6). Same signs (both negative), so add and keep the negative sign.
- 3Step 3 — -8 + (-6) = -14
Answer: -14
The #1 mistake to avoid
Students forget to multiply BEFORE adding. Always handle × and ÷ before + and −. Use the phrase 'Please Excuse My Dear Aunt Sally' (PEMDAS) to remember the order.
Key takeaways
- Integers include all whole numbers: negative, zero, and positive.
- Adding a negative = subtracting. Use a number line to picture your moves.
- For multiply/divide: same signs → positive, different signs → negative.
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