Math 7 · Unit 3, Lesson 4: Multiplying Signed Numbers · Tile 2 of 4
Negative Times Negative
Taking away debts makes you richer
The strange one
Here is the strange one: a negative times a negative is positive. Watch the pattern. Each time the first number goes down by 1, the answer goes up by 3. Keep going past zero, and the answers keep going up.
Your little brother owes you 3 dollars a week, and you cancel 2 weeks of it. Taking away 2 debts of 3 dollars, (−2) × (−3), makes you 6 dollars better off. That matches Lesson 2: subtracting a debt is the same as gaining money.
The sign rules
| Factors | Product |
|---|---|
| positive × positive | positive |
| negative × negative | positive |
| positive × negative | negative |
| negative × positive | negative |
In words: same signs, positive answer. Different signs, negative answer.
The product of two numbers with the same sign is positive. The product of two numbers with different signs is negative.
Same signs, positive. Different signs, negative. Two negatives cancel each other out.
Elle and Finn talk it over
So two negatives make a positive. If I'm grumpy and you're grumpy, we're happy?
Only if we multiply. If we add, we're just twice as grumpy.
Got it. Never add grumpy people.
That's real math. −2 × (−3) = 6, but −2 + −3 = −5. Check which one you're doing before you pick a sign.
NC standard: NC.7.NS.2.