The lesson
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
Same signs give a positive answer; different signs give a negative answer.
These ideas show up on homework, quizzes, and the next unit in this grade. Getting comfortable here saves time later when the problems stack more steps together.
Common mistakes to avoid
Rushing to the answer without writing steps. Clear work helps you catch mistakes and shows your reasoning.
Re-reading the question too quickly. Underline what you are solving for before you start calculating.
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 walkthroughs
Integer Multiplication & Division
Why same signs make a positive and different signs make a negative.
Watch on YouTube
Why a Negative Times a Negative Makes Sense
Understand why same signs give a positive product.
Watch on YouTube
Multiplying and Dividing Negative Numbers
Apply integer rules to multiplication and division word problems.
Watch on YouTube
Negative Numbers
Compare and order positive and negative values on a number line.
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?