Math 7 · Unit 3, Lesson 4: Multiplying Signed Numbers · Tile 1 of 4
Debts Over and Over
A negative times a positive
Three groups of a debt
You already know 3 × 4 means three groups of 4. So 3 × (−4) means three groups of −4. That's owing 4 dollars, three times. Add it up: −4 + −4 + −4 = −12.
Order does not matter when you multiply, so −4 × 3 is also −12.
The words
| Elle (math-speak) | Finn (plain English) |
|---|---|
| Factor | A number being multiplied. In 3 × (−4), the factors are 3 and −4. |
| Product | The answer you get when you multiply. Product comes from produce, what the multiplying makes. |
One negative factor
ElleMath-speak
The product of a positive number and a negative number is negative.
FinnPlain English
Owing money over and over just means you owe more. One negative factor, and the answer is negative.
3 × (−4)−4 + −4 + −4 Three groups−12
5(−3)five groups of −3−15
12 × (−1)−12 Times −1 gives the opposite
That is why −12 is the opposite of 12: it is 12 times −1.
NC standard: NC.7.NS.2.
Where to go next
Let me try a few6 problems on debts over and over.
Next: Tile 2, Negative Times NegativeTaking away debts makes you richer
All tilesAll 4 parts of this lesson.
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