ADDING AND SUBTRACTING INTEGERS
ADDING AND SUBTRACTING INTEGERS
|Rules for Addition |
|Positive + Positive |Positive |
|Positive + Negative |Depends |
|Negative + Positive |Depends |
|Negative + Negative |Negative |
Numbers Can be Positive or Negative:
|[pic] |
|Negative Numbers (-) |Positive Numbers (+) |
|(This is the Number Line, read about Using The Number Line) |
|[pic] |[pic] |
|"-" is the negative sign. |"+" is the positive |
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 addtion.
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)
But what happens if we have negative numbers ... ?
For example, what is 6 - (-3) ?
|[pic] |Subtracting a Negative is the same as Adding |
|[pic] |Ally can be naughty or nice. So Ally's parents have said |
| |"If you are nice we will add 3 points (+3). If you are naughty, we take away 3 points (-3). When you |
| |reach 30 Points you get a toy." |
| |Ally starts the day with 9 Points: |
|[pic] |Ally's Mum discovers spilt milk: | |
| |9-3 = 6 | |
| | | |
| | | |
| | | |
| | | |
| |Then Dad confesses he spilt the milk and writes "undo". Mum calculates: | |
| |6-(-3) = 6+3 = 9 | |
| | | |
So if you subtract a negative, you gain points
(ie the same as adding points).
What About Positive and Negative Together ... ?
You can also have questions like:
What is 6 + (-3) ?
or what is 6 - (+3) ?
They are really the same! Both are subtraction:
|[pic] |Subtracting a Positive |
| |or |
| |Adding a Negative |
| |is |
| |Subtraction |
|[pic] |A few days later. Ally has 12 points. | |
| | | |
| | | |
| | | |
| | | |
| | | |
| |Mum adds 3 points because Ally's room is clean. | |
| |12+3 = 15 | |
| | | |
| | | |
| | | |
| | | |
| |Dad says "I cleaned that room" and writes "undo" on the chart. Mum calculates: | |
| |15 - (+3) = 12 | |
| | | |
| | | |
| | | |
| | | |
| |Dad sees Ally brushing the dog. Writes "+3" on the chart. Mum calculates: | |
| |12 + (+3) = 15 | |
| | | |
| | | |
| | | |
| | | |
| |Ally throws a stone against the window. Dad writes "-3" on the chart. Mum calculates: | |
| |15 + (-3) = 12 | |
| | | |
See: both "15 - (+3)" and "15 + (-3)" result in 12.
So:
It doesn't matter if you subtract positive points
or add negative points,
you still end up losing points.
Now, Here Are The Rules
| |Rule | |Example |
|[pic] |Two like signs become a positive sign |+(+) |3+(+2) = 3 + 2 = 5 |
| | |-(-) |6-(-3) = 6 + 3 = 9 |
| | | | |
|[pic] |Two unlike signs become a negative sign |+(-) |7+(-2) = 7 - 2 = 5 |
| | |-(+) |8-(+2) = 8 - 2 = 6 |
| | | | |
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, so they become a negative sign.
5+(-2) = 5 - 2 = 3
Answer: 5+(-2) = 3
Example: What is -6+(+3) ?
+(+) are like signs, so they become a positive sign.
-6+(+3) = -6 + 3
Start at -6 on the number line, move forward 3, and you end up at -3
Answer: -6+(+3) = -3
Example: What is 25-(-4) ?
-(-) are like signs, so they become a positive sign.
25-(-4) = 25+4
Start at 25 on the number line, move forward 4, and you end up at 29
Answer: 25-(-4) = 29
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