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Answer:
a. Zachary is correct
b. (-1)(-3) = 3 (Scott & Tina are wrong); (5)(-2) = -10 (Aaron is wrong); (1)(3) = 3
Step-by-step explanation:
a. An even number of minus signs in a product will mean the product is positive; an odd number will mean the product is negative. Zachary's observation is consistent with this rule. Zachary is correct.
We can show the others are incorrect using a counter-example.
(-1)(-3) = 3 . . . . shows Scott, Aaron, and Tina are incorrect
Tina's rule is not consistent with the commutative property of multiplication.
Aaron's rule applies to addition, but not to multiplication.
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b. The example used above is one example. Here are two more.
(-1)(-3) = 3 . . . . . shows Zachary correct; Scott, Aaron, Tina incorrect
(5)(-2) = -10 . . . . Aaron's own example shows him incorrect
(1)(3) = 3 . . . . . . agrees with all students' observations
