1.1b Why 2 NegativesBecome Positive1.1b Why 2 NegativesBecome Positive
1.1b Why 2 NegativesBecome Positive1.1b Why 2 NegativesBecome Positive
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Adding Zeroes
•Suppose there are two types of chips:
•yellow chips are equal to +1
•red chips are equal to -1
•If you add both of them together, thepair will be equal to zero
+
1
-
1
+1
-1
+1
-1
When you add a pair together, you are adding nothing
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Multiplying Negative and Positive Numbers
•To understand why multiplying two negatives willbecome positive, we will start off with theseexamples
POSITVE X POSITIVE
Numberof groups
to add
How many chips
In each group
With 5 groups of 3 coins, we get 15 coins altogether
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Positive X Negative
Numberof groups
to add
3 red chips ineach group
With 5 groups of 3 red coins, we get 15 red coins altogether
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•Negative X Positive
Numberof groups
to take away
How many chips
In each group
First of all, there’s nothing on the table to take away!!
So we need to add pairs of zeros until we can take away 5 groups of 3 coins
+1
-1
After you have enough pairs on the table, take away 5 groups of 3 coins
Now you have 15 red coins left on the table
This means the product is -15
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•Negative X Negative
Numberof groups
to take away
3 red chips
in each group
First of all, there’s nothing on the table to take away!!
So we need to add pairs of zeros until we can take away 5 groups of 3 red coins
+1
-1
After you have enough pairs on the table, take away 5 groups of 3 red coins
Now you have 15 yellow coins left on the table
This means the product is 15
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Number Line:
•You can also use a number line to explain whymultiplying two negatives become positive
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
Facing Positive Direction
Facing Negative Direction
•You always begin at zero
•1st number tells you where to face
•2nd number tells you which way to hop
•When it’s positive move forward
•When it’s negative move backward
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Positive X Positive:
Positive X Negative:
Number ofhops facing
Positivedirection
Number of steps
in each hop
( 2 forward)
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
Number ofhops facing
Positive direction
Number of steps
in each hop
( 3 backwards)
-7
-6
-5
-4
-3
-2
-1
0
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Negative X Positive:
Negative X Negative:
Number ofhops facing
Negativedirection
Number of steps
in each hop
( 2 forward)
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
Number ofhops facing
Negativedirection
Number of steps
in each hop
( 4 backwards)
-7
-6
-5
-4
-3
-2
-1
0
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