Multiplying and Dividing positive and negative integers.notebook
6 =
3 -
-7(7)
?
12 - 2 = ?
4(-1
e
eg
1)
nt
4 x 8 =
Remember that multiplication is repeated addition. 3 2 means to add 3 groups of 2.
7
Now you can write +2
+2
+2
=
?
lyi
Mu
Multiplying Integers with the Same Sign
rs -9
I
ng
March 10, 2015
p
?
lti
= 6
3 x
3 - 3
3 2 = ___ + ___ + ___ = ___
­10
­9
­8
­7
­6
­5 ­4
­3
­2
­1
0
1
2
3
4
5
6
7
8
9
10
So 3 2 = _____
= ?
?
Mar 7­9:23 AM
Mar 7­9:42 AM
So what about multiplying a negative times a negative???
It's all about direction. Lets look at it using a number line.
Here we have Baby Steven taking his firsts steps. He takes 2 paces at a time and does this three times, so he moves 2 steps x 3 = 6 steps forward:
Multiplying Integers with Different Signs
You can use repeated addition to find 3 (­2).
­2
­2
­5 ­4
­3
­2
Now you can write
­10
­9
­8
­7
­6
­2
­1
0
1
2
3
4
5
6
7
8
9
10
Now, Baby Steven can also step backwards (he is a clever little guy). His dad puts him back at the start and then Steven steps backwards 2 steps, and does this three times:
3 (­2) = ____ + ____ + ____
= ____.
So 3 (­2) = ____
Once again Steven's dad puts him back at the start, but facing the other way. Steven takes 2 steps forward (for him!) but he is heading in the negative direction. He does this 3 times:
Back at the start again (thanks Dad!), still facing in the negative direction, he tries his backwards walking, once again taking two steps at a time, and he does this three times:
So, by walking backwards, while facing in the negative direction, he moves in the positive direction.
Mar 7­9:44 AM
So here are the rules for multiplying Integers:
• Multiplying two positive integers gives you a positive product.
• Multiplying a positive integer and a negative integer gives you a negative product.
• Multiplying two negative integers gives you a positive product.
Mar 7­8:07 PM
Try these:
1. 5 5
5. 12 (­2)
2. 4(11)
6. 4(­6)
3. ­1(­9)
7. ­10(­6)(0)
4. ­7 (­8) 8. ­7 (­5) (­4) You can use the Magic Triangle to help you remember:
+
­
­
Mar 7­8:23 PM
Mar 7­8:29 PM
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