http://www.mathsisfun.com/positive-negative-integers.html
How to Add and Subtract
Positive and Negative Numbers
Numbers Can be Positive or Negative:
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| Negative Numbers (−) | Positive Numbers (+) |
| (This is the Number Line, read about Using The Number Line) | |
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| “−” is the negative sign. | “+” is the positive sign |
No Sign Means Positive
If a number has no sign it usually means that it is a positive number.
Example: 5 is really +5
Adding Positive Numbers
Adding positive numbers is just simple addition.
Example: 2 + 3 = 5
is really saying
“Positive 2 plus Positive 3 equals Positive 5”
You could write it as (+2) + (+3) = (+5)
Subtracting Positive Numbers
Subtracting positive numbers is just simple subtraction.
Example: 6 − 3 = 3
is really saying
“Positive 6 minus Positive 3 equals Positive 3”
You could write it as (+6) − (+3) = (+3)
Balloons and Weights
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This basket has balloons and weights tied to it:
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Here is what adding and subtracting positive numbers looks like:
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You can add balloons (you are adding positive value)
the basket gets pulled upwards (positive)
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You can take away balloons (you are subtracting positive value)
the basket gets pulled downwards (negative)
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Now let’s see what adding and subtracting negative numbers looks like:
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You can add weights (you are adding negative values)
the basket gets pulled downwards (negative)
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And you can take away weights (you are subtracting negative values)
the basket gets pulled upwards (positive)
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That last one was interesting … subtracting a negative made the basket go up
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Subtracting a Negative is the same as Adding |
Example: What is 6 − (−3) ?
6−(−3) = 6 + 3 = 9
Example: What is 14 − (−4) ?
14−(−4) = 14 + 4 = 18
We also found that taking away balloons (subtracting positives) or adding weights (adding negatives) both made the basket go down.
And Positive and Negative Together …
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Subtracting a Positive or Adding a Negative is Subtraction |
Example: What is 6 − (+3) ?
6−(+3) = 6 − 3 = 3
Example: What is 5 + (−7) ?
5+(−7) = 5 − 7 = −2
The Rules:
It can all be put into two rules:
| Rule | Example | ||
|---|---|---|---|
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Two like signs become a positive sign | +(+) | 3+(+2) = 3 + 2 = 5 |
| −(−) | 6−(−3) = 6 + 3 = 9 | ||
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Two unlike signs become a negative sign | +(−) | 7+(−2) = 7 − 2 = 5 |
| −(+) | 8−(+2) = 8 − 2 = 6 | ||
They are “like signs” when they are like each other (in other words: the same).
So, all you have to remember is:
Two like signs become a positive sign
Two unlike signs become a negative sign
Example: What is 5+(−2) ?
+(−) are unlike signs (they are not the same), so they become a negative sign.
5+(−2) = 5 − 2 = 3
Example: What is 25−(−4) ?
−(−) are like signs, so they become a positive sign.
25−(−4) = 25+4 = 29
Example: What is −6+(+3) ?
+(+) are like signs, so they become a positive sign.
−6+(+3) = −6 + 3 = -3
Start at −6 on the number line, move forward 3, and you end up at −3