MULTIPLYING INTEGERS
MULTIPLYING INTEGERS
2 Possible Situations
The Signs are the Same
|Same |
|(() x (() = + |
|(+) x (+) = + |
| |
|Different |
|(() x (+) = ( |
|(+) x (() = ( |
When the factors (2 numbers that you multiply) have the same sign, the product (consider of multiplication) is positive.
Example #1:
(+5) x (+6) = +30
or
(5) (6) = 30
Example #2:
((12) x ((4) = +48
or
(12 x (4 = +48
(Figure out that it is positive, then multiply 12 x 4)
The Signs are Different
*When the factors (2 numbers that you multiply) have different signs, the product (consider of multiplication) is negative.
Example #1: Example #2:
((6) x (+8) = (48 (+9) x ((11) = (99
or or
(6 + 8= (48 +9 x (11= (99
(Figure out that it is negative, then multiply 6 x 8)
_____________________
Let’s look at how this works, but first remember:
Positive Negative
= 0
Also, Multiplication is just a shortcut for repeated addition.
+3 x +4 means ‘add’ 3 groups of 4
We use the first sign, for +3 as addition… it tells you what to do with the groups.
One group of 4
Added to another group of 4
Added to a third group of 4 = 12
Remember the language. Example: +6 x +5 means ‘add’ 6 groups of +5
What happens when the signs are different?
+3 x –4 = “add” 3 groups of –4
+ + = -12
Now let’s look at the first number being negative.
Since +3 x –4 = “add” 3 groups of –4
Then -3 x +4 = “take away” 3 groups of +4
________________________________________________
Remember that any equal number of - and + integers equals 0 (zero)
= 0
________________________________________________
Start at zero… then
-3 x +4 = “take away” 3 groups of +4
When we ‘take away’ 3 groups of positive 4 we are left with -12
_______________________________________________
And now… Why is a negative times a negative = a positive?
Start at zero…
=0
–3 x –4 = “take away” 3 groups of -4
When we ‘take away’ 3 groups of negative 4 we are left with +12
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