# Why the Rules for Multiplying Integers Work ```MULTIPLYING INTEGERS
2 Possible Situations
The Signs are the Same
When the factors (2 numbers that you multiply) have the same sign, the
product (consider of multiplication) is positive.
Same
() x () = +
(+) x (+) = +
Example #1:
(+5) x (+6) = +30
or
(5) (6) = 30
Example #2:
Different
() x (+) = 
(+) x () = 
(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
or
6 + 8= 48
(+9) x (11) = 99
or
+9 x 11= 99
(Figure out that it is negative, then multiply 6 x 8)
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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
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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
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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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