Sign of a Long Product
Even negatives give +, odd negatives give −.
Count the negative factors.
Even (2, 4, 6, …): the product is positive.
Odd (1, 3, 5, …): the product is negative.
Any zero: the product is 0.
Multiply three or more integers in any order, and predict the sign of a long product by counting the negative numbers.
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Even negatives give +, odd negatives give −.
Why (a × b) × c = a × (b × c) for integers.
Find two ways:
Same product.
One product, three groupings, one answer.
Problem. Multiply in different orders. Is the product always the same? (Textbook p. 40)
Work out products of three integers.
(Textbook p. 42, Q1b)
An even number of negatives gives +, an odd number gives −.
The book prints the last line as . That is a printing slip. The book's own sentence below it says five s give a negative product, and is correct.
(−2) × (−1) × (−5) × (−3): sign first, then size.
Problem. Find . (Textbook p. 42, Q1c)
Predict the sign before you multiply.