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
