Question

The rules for multiplying two integers can be extended to a product of 3 or more integers. Find the following products.

a)(3)(3)(-3)
b)(3)(-3)(-3)
c)(-3)(-3)(-3)
d)(3)(3)(3)(-3)
e)(3)(3)(-3)(-3)
f)(3)(-3)(-3)(-3)
Based on your results, complete the following statements:
(i)When a product of integers has an odd number of negative factors, then the sign of the product is ________ because...
(ii)When a product of integers has an even number of negative factors, then the sign of the product is ________ because...

Answer 1

When multiplying integers, the sign of the product is determined by the number of negative factors. If there are an odd number of negative factors, the product will be negative. If there are an even number of negative factors, the product will be positive.

Step-by-step explanation:

When multiplying integers, the rules state that:

1. When two positive numbers multiply, the answer has a positive sign.
2. When two negative numbers multiply, the answer has a positive sign.
3. When the two numbers multiplied have opposite signs, the answer has a negative sign.

Using these rules, we can find the products:

1. a) (3)(3)(-3) = -27
2. b) (3)(-3)(-3) = 27
3. c) (-3)(-3)(-3) = -27
4. d) (3)(3)(3)(-3) = -81
5. e) (3)(3)(-3)(-3) = 81
6. f) (3)(-3)(-3)(-3) = -81

(i) When a product of integers has an odd number of negative factors, then the sign of the product is negative because multiplying an odd number of negative numbers results in a negative sign.

(ii) When a product of integers has an even number of negative factors, then the sign of the product is positive because multiplying an even number of negative numbers results in a positive sign.