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Multiplying and Dividing Integers

A free Pre-Algebra lesson from the “Number Foundations” unit, with a worked example and practice problems including step-by-step solutions.

Integer multiplication and division use sign patterns. A positive times a positive is positive, a negative times a negative is positive, and a positive times a negative is negative. Division follows the same sign rules. In Number Foundations, the goal is not just to get an answer but to recognize the structure of the problem, choose a reliable strategy, and explain why the result is reasonable. The practice set now includes targeted skill work, transfer questions, and mixed review so students build fluency and retention.

What you'll learn

Why it matters: Repeated debits, average daily temperature changes, and stock-price moves across multiple days use signed multiplication and division. Sign rules turn 'a loss of five dollars repeated four times' into a single negative twenty.

Worked example

Problem. Compute -6 x -4.

  1. The factors have the same sign.
  2. A negative times a negative is positive.
  3. 6 x 4 = 24, so -6 x -4 = 24.
  4. Connect the calculation back to Multiplying and Dividing Integers so the method, not just the arithmetic, is clear.

Answer: 24

Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (typed response and multiple choice). Counts include repeated prompts and variants.

Practice problems

1. Compute -3 x 8.

Show solution
  1. The signs are different, so the product is negative.
  2. 3 x 8 = 24, so the answer is -24.

Answer: -24

2. Compute -7 x -5.

Show solution
  1. The signs are the same, so the product is positive.
  2. 7 x 5 = 35.

Answer: 35

3. Compute 36 divided by -4.

Show solution
  1. The signs are different, so the quotient is negative.
  2. 36 divided by 4 is 9.

Answer: -9

4. Compute -42 divided by -6.

Show solution
  1. The signs are the same, so the quotient is positive.
  2. 42 divided by 6 is 7.

Answer: 7

5. Which expression has a positive value?

Choices: -5 x 3 · 8 divided by -2 · -4 x -6 · 7 x -1

Show solution
  1. A negative times a negative is positive.
  2. -4 x -6 = 24.

Answer: -4 x -6

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