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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

Practice problems

1. Compute -3 x 8.

Show solution
  1. Warm-up: First identify exactly what the question is asking: Compute -3 x 8.
  2. For signed numbers, track both distance from zero and direction so the sign of the answer makes sense.
  3. The signs are different, so the product is negative.
  4. 3 x 8 = 24, so the answer is -24.
  5. Check the result by substituting or estimating: the response should match -24 and make sense in the original problem.

Answer: -24

2. Compute -7 x -5.

Show solution
  1. Warm-up: First identify exactly what the question is asking: Compute -7 x -5.
  2. For signed numbers, track both distance from zero and direction so the sign of the answer makes sense.
  3. The signs are the same, so the product is positive.
  4. 7 x 5 = 35.
  5. Check the result by substituting or estimating: the response should match 35 and make sense in the original problem.

Answer: 35

3. Compute 36 divided by -4.

Show solution
  1. Warm-up: First identify exactly what the question is asking: Compute 36 divided by -4.
  2. For signed numbers, track both distance from zero and direction so the sign of the answer makes sense.
  3. The signs are different, so the quotient is negative.
  4. 36 divided by 4 is 9.
  5. Check the result by substituting or estimating: the response should match -9 and make sense in the original problem.

Answer: -9

4. Compute -42 divided by -6.

Show solution
  1. Core Practice: First identify exactly what the question is asking: Compute -42 divided by -6.
  2. For signed numbers, track both distance from zero and direction so the sign of the answer makes sense.
  3. The signs are the same, so the quotient is positive.
  4. 42 divided by 6 is 7.
  5. Check the result by substituting or estimating: the response should match 7 and make sense in the original problem.

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. Core Practice: First identify exactly what the question is asking: Which expression has a positive value?
  2. Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
  3. A negative times a negative is positive.
  4. -4 x -6 = 24.
  5. Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.

Answer: -4 x -6

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