Question

True or false: for any 2 nonzero integers, the product and quotient have the same sign.

Answer 1

Yes, it is true.
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For example,

take two integers 12 and 4

12 × 4 = 48 : product is positive

12 ÷ 4 = 3: quotient is positive
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If you take -12 and 4

-12 × 4 = -48 : product is negative

-12 ÷ 4 = -3: quotient is negative