Positive groups of a negative value
3 × (−4) means three groups of −4. Combining them gives −4 + (−4) + (−4) = −12. A positive factor and a negative factor produce a negative product.
Multiply integers
Use groups and patterns to understand the multiplication sign rules.
Understand it
Make the idea make sense.
Extend a pattern through zero
Look at (−4) × 2 = −8, (−4) × 1 = −4, and (−4) × 0 = 0. As the second factor decreases by 1, the product increases by 4. Continuing gives (−4) × (−1) = 4 and (−4) × (−2) = 8.
Calculate the magnitude, then the sign
Multiply the absolute values. If the non-zero factors have the same sign, the product is positive. If they have different signs, the product is negative. Multiplication is commutative: changing the order of the factors does not change the product.
Treat zero as its own case
Any integer multiplied by zero gives zero. Zero is neither positive nor negative, so do not label a zero product as positive or negative.
Words worth knowing
- Factor
- A number being multiplied.
- Product
- The result of multiplication.
- Magnitude
- The size of a value, represented here by its absolute value.
Follow the pattern
What happens beyond zero?
Keep −4 as one factor. Change the other factor by one, then notice how the product changes.
−4 × 2 = −8
| Second factor | Expression | Product |
|---|---|---|
| 3 | (−4) × (3) | -12 |
| 2 | (−4) × (2) | -8 |
| 1 | (−4) × (1) | -4 |
| 0 | (−4) × (0) | 0 |
| -1 | (−4) × (-1) | 4 |
| -2 | (−4) × (-2) | 8 |
| -3 | (−4) × (-3) | 12 |
Khan Academy
Pause before the next calculation. Predict the sign and explain the model, then compare the reasoning.
See the thinking
One step at a time.
Predict each next step, then reveal the explanation.
(−6) × 4
- Multiply the absolute values: 6 × 4 = 24.
- The non-zero factors have different signs, so the product is negative.
- (−6) × 4 = −24.
(−7) × (−3)
- Multiply the absolute values: 7 × 3 = 21.
- The non-zero factors have the same sign, so the product is positive.
- (−7) × (−3) = 21.
5 × (−2) × (−3)
- Work from left to right: 5 × (−2) = −10.
- Then (−10) × (−3) = 30.
- The product is 30. Two negative factors give a positive product when the other factors are positive.
Try together
A little support. Your thinking.
Work through (−6) × (−4).
Nicely reasoned. Try a fresh question below, or revisit any step.
Your turn
Practice with purpose.
New questions, useful feedback and hints that build on your thinking.
Question 1 of 8Build confidence
Loading your practice…
Progress stays on this device.Hints help you learn. First-try answers and supported answers are recorded separately.
Connections
In the real world
All Class Notes →A team loses 4 points for each of 5 penalties. Its total signed change is 5 × (−4) = −20 points.