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 free

Skills in this unit

Pick a skill to try three free questions on just that.

Standards covered:6.NS.C.56.NS.C.66.NS.C.7.c6.NS.C.77.NS.A.1.b7.NS.A.1.c7.NS.A.2.a7.NS.A.2.b6.EE.A.2.c7.NS.A.3

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)

  1. 1Step 1 — Multiply first (order of operations): 3 × (-2) = -6
  2. 2Step 2 — Now add: -8 + (-6). Same signs (both negative), so add and keep the negative sign.
  3. 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.

Master Integers & Operations — free

Interactive practice you solve by doing, an AI tutor when you're stuck, and mastery you can't fake. No credit card.

Start practicing free