The Sign Rule:
- When multiplying integers with the same value (+ or -), or for example (-2) x (-2) = the product will always end up being positive
- When the value of the integers are different (+,-) or for example (+2) x (-3)= the product will always end up being negative.
1) When you have an even amount of (-) signs, the product will end up being positive.
(-4) x (-2) x (-1) = -8
+8 x (-1) = -8
2) When there is an odd number of (-) signs, the product is negative.
(-2) x (4) = -8 <----(++++) (++++)--->
remove 2 groups of 4 = -8 - - - - - - - -
Now, these are a few questions that I've solved using the sign rule : Math Links 8.2
17. Question: Without evaluating the products, identify the least product. Explain your reasoning.
(+99) x (+82)
(-99) x (-82)
(+99) x (-82)
To answer this question, I chose (+99) x (-82) because if you recognize the sign rule, you know that when you multiply two integers with different signs, you get a negative. In this case, I didn't have to calculate it because I just saw the signs and I already know it's going to be a negative.
9. Question: Determine each product.
a) (-6) x (-6) = +36
I know that because if you multiply 6 x 6, you get 36. Also, they have the same signs and that means they are positive.
b) (+9) x (+6) = +45
c) (-12) x (+2) = -24
I know this because if you multiply 12 x 2, you get 24. Also, they have different integers and based on the "sign law/rule", when there are two different signs they are going to end up being negative.
d) (+11) x 0 = 0