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.
What you'll learn
- Use sign rules for products and quotients
- Multiply and divide integers fluently
- Apply integer operations in context
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.
- The factors have the same sign.
- A negative times a negative is positive.
- 6 x 4 = 24, so -6 x -4 = 24.
Answer: 24
Practice problems
1. Compute -3 x 8.
Show solution
- Warm-up: First identify exactly what the question is asking: Compute -3 x 8.
- For signed numbers, track both distance from zero and direction so the sign of the answer makes sense.
- The signs are different, so the product is negative.
- 3 x 8 = 24, so the answer is -24.
- 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
- Warm-up: First identify exactly what the question is asking: Compute -7 x -5.
- For signed numbers, track both distance from zero and direction so the sign of the answer makes sense.
- The signs are the same, so the product is positive.
- 7 x 5 = 35.
- 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
- Warm-up: First identify exactly what the question is asking: Compute 36 divided by -4.
- For signed numbers, track both distance from zero and direction so the sign of the answer makes sense.
- The signs are different, so the quotient is negative.
- 36 divided by 4 is 9.
- 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
- Core Practice: First identify exactly what the question is asking: Compute -42 divided by -6.
- For signed numbers, track both distance from zero and direction so the sign of the answer makes sense.
- The signs are the same, so the quotient is positive.
- 42 divided by 6 is 7.
- 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
- Core Practice: First identify exactly what the question is asking: Which expression has a positive value?
- Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
- A negative times a negative is positive.
- -4 x -6 = 24.
- 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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