Page 64 - ArithBook5thEd ~ BCC

The sign of a product of several factors is

• positive if the number of negative factors is even,
• negative if the number of negative factors is odd.

This is true because every pair of negative factors has a positive product. If there is an even number
of negative factors, they can be “paired off” (in any convenient order), producing a product of positive
numbers which is, of course, positive. But if the number of negative factors is odd, there is always one
“unpaired” negative factor, which makes the total product negative.

Example 65.
(−1)(2)(−3)(−4) = −24 (an odd number (three) of negative factors makes a negative product),

(−1)(−2)(−3)(−4) = 24 (an even number (four) of negative factors makes a positive product).

2.5.1 Exercises

Find the products.

1. 8 × (−6)

2. −9 × 7

3. (−6) × (−9)

4. (−1) × 5

5. (914)(−1)
6. (0)(−888)

7. (−1) × (−1)

8. (−1) × (−1) × (−1)

9. 65 × (−31)

10. (−503) × (−6)

11. (−162)(1000)

12. 1(−1)
13. (−3)(−50)(−2)

14. (−3)(5)(−7)(1)

15. (3)(−10)(2)(−5)

16. (−6)(−5)(−4)(−3)(0)

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