What happens to the sign of a product when you multiply two negative integers? What about when you multiply a positive and a negative integer?
Conjecture: The product of three negative integers equals a negative integer. Test: See solution.
Practice makes perfect
Let's attempt to find a pattern by calculating the product of three negative integers.
(- 4)(- 2)(- 3)&=- 24 [0.8em]
(- 5)(- 2)(- 4)&=- 40 [0.8em]
(- 7)(- 9)(- 10)&=- 630 [0.8em]
(- 8)(- 3)(- 6)&=- 144Examining the products, we see that all of them are negative. With this information we can make a conjecture.
Conjecture
The product of three negative integers equals
a negative integer.
Let's test this a few times with some other integers.
(- 11)(- 3)(- 2)&=- 66 [0.8em]
(- 8)(- 9)(- 3)&=- 216 [0.8em]
(- 5)(- 7)(- 15)&=- 525 [0.8em]
(- 3)(- 12)(- 13)&=- 468
It would appear that our conjecture is true.
