The lesson
This lesson teaches Multiplying & Dividing Integers. Read each section in order, work through every example on paper, then use the practice problems and quick check at the bottom.
One rule for both operations
Multiplication and division follow the exact same sign rule, so you only have to remember one thing.
A ratio compares two quantities with the same units. Order matters: a ratio of cats to dogs is not the same as dogs to cats unless the problem says they are equivalent.
Write ratios in three ways: with a colon (3:4), as a phrase (3 to 4), or as a fraction (3/4) when it fits the context.
- 1Same signs (+ and +, or - and -) → the answer is positive.
- 2Different signs (+ and -) → the answer is negative.
Evaluate (-6) × (-4) and (-20) ÷ 5.
- 1(-6) × (-4): same signs → positive. 6 × 4 = 24, so the answer is 24.
- 2(-20) ÷ 5: different signs → negative. 20 ÷ 5 = 4, so the answer is -4.
Why this matters
Multiplying & Dividing Integers shows up constantly in same signs give a positive answer; different signs give a negative answer. It also connects to what you will see on homework, quizzes, and the next unit in this grade.
Teachers often move fast in class. This page is here so you can pause, re-read, and practice until the idea feels familiar, not just until you have memorized a rule for one day.
Common mistakes to avoid
Rushing to the answer without writing steps. Middle-school math rewards clear work, and you catch errors earlier when steps are visible.
Mixing up similar ideas from the same topic. If two terms feel alike, make a two-column note: what is the same, what is different, and one example of each.
Key ideas from this lesson
- One rule for both operations
- Same signs (+ and +, or - and -) → the answer is positive.
- Different signs (+ and -) → the answer is negative.
Video walkthrough
Integer Multiplication & Division
Why same signs make a positive and different signs make a negative.
Watch on YouTubePractice
For each problem: write your work in the box, type your answer, and check it. If you are stuck, reveal the solution one step at a time. Do not skip straight to the final answer.
Exercise 1
Try it yourselfEvaluate: (-5) × 6.
Step-by-step solution
- 1Different signs → negative.
- 25 × 6 = 30, so the answer is -30.
Exercise 2
Try it yourselfEvaluate: (-7) × (-2).
Step-by-step solution
- 1Same signs → positive.
- 27 × 2 = 14.
Exercise 3
Try it yourselfEvaluate: 48 ÷ (−6).
Step-by-step solution
- 1Different signs → negative.
- 248 ÷ 6 = 8, so the answer is -8.
Exercise 4
Try it yourselfEvaluate: (-4)³.
Step-by-step solution
- 1(-4)³ = (-4)(-4)(-4).
- 2Two negatives make +16; one more negative gives -64.
Exercise 5
Try it yourselfEvaluate: (-2)(-3)(-5).
Step-by-step solution
- 1Three negative factors (odd) → negative product.
- 22 × 3 × 5 = 30, so the answer is -30.
Quick check
Answer all questions. Retake the quiz until you feel confident before moving on.
Multiplying & Dividing Integers
Question 1 of 5
What is (-8) × 3?