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 To
develop the rules for adding signed numbers, we are going to introduce
Bill, the star running back on his school's football team. In all
of these situations the length of Bill's runs will be either a positive
number, where he has gained yards,
or a negative number which will indicate that Bill
lost yardage on his run.
 For
example:
+7 will indicate that he
gained 7 yards
-7 will indicate that
he lost 7 yards
Ready to Begin? Let's Try a Few...
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Adding 2 Positive Numbers
On Bill's first carry, he gained 4 yards. (+4)
On his next carry he gained 5 yards (+5)
To calculate his total yards for these two
carries we add +4
+ +5
Since both numbers are positive, his total is
+9 |
Here's Another Example...
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Adding 2 Negative Numbers
On Bill's next carry he lost 3 yards (-3)
and
he lost another 2 yards (-2) after
that.
This time when we find the total of these 2 carries we are adding 2
negative numbers.
-3 + -2
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-6 |
-5
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-4 |
-3
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-2 |
-1 |
0 |
1 |
2 |
3 |
4 |
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Looking at the number
line, we see that we start at -3 and
then move left 2 more until we arrive
at -5
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Let's Combine Positive and Negative
Numbers...
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Adding a Positive and Negative
Number Let's suppose
in this situation, Bill gains 8 yards (+8).
Then he loses 3 yards (-3) on the next
carry. Again, if we do this on a number line we would arrive at
+8
+ -3 =
+8
+ -3 = +5
Notice that in both cases the sum
equals the difference of the
absolute values
of both numbers
The sign is the same as is on the number with the
greatest value
l-8l
= 8 l+3l
= 3 |
Let's look at another example of this
rule...
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Remember the sign is
the same as the number with the greatest value.
+7
+ -2 = 7 - 2 =
+5
( + because 7 is +)
-12 + +8
= 12 - 8 = -4 ( -
because 12 is -)
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One More Possible Solution to Deal With
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What if Bill gains 6
yards (+6) on one carry,
and then loses 6 yards (-6)
on the next carry?
Do you see what happens when we total these two numbers?
+6
+ -6 = ?
Easy! The -6 cancels the +6 and the result is
zero!
+6
+ -6 = 0
In other words when adding numbers
that have equal absolute values but opposite signs, the
answer is
always zero!
+12 + -12 = 0
-31 + +31
= 0 |
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Let's Practice!
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