How to Add and Subtract
Positive and Negative Numbers
Numbers Can be Positive or Negative
This is the Number Line:
Negative Numbers (−)  Positive Numbers (+) 
"−" 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
Balloons and Weights
Let us think about numbers as balloons (positive) and weights (negative):
This basket has balloons and weights tied to it:

Adding a Positive Number
Adding positive numbers is just simple addition.
We can add balloons (we are adding positive value) the basket gets pulled upwards (positive) 
Example: 2 + 3 = 5
is really saying
"Positive 2 plus Positive 3 equals Positive 5"
We could write it as (+2) + (+3) = (+5)
Subtracting A Positive Number
Subtracting positive numbers is just simple subtraction.
We can take away balloons (we are subtracting positive value) the basket gets pulled downwards (negative) 
Example: 6 − 3 = 3
is really saying
"Positive 6 minus Positive 3 equals Positive 3"
We could write it as (+6) − (+3) = (+3)
Adding A Negative Number
Now let's see what adding and subtracting negative numbers looks like:
We can add weights (we are adding negative values) the basket gets pulled downwards (negative) 
Example: 6 + (−3) = 3
is really saying
"Positive 6 plus Negative 3 equals Positive 3"
We could write it as (+6) + (−3) = (+3)
The last two examples showed us that taking away balloons (subtracting a positive) or adding weights (adding a negative) both make the basket go down.
So these have the same result:
 (+6) − (+3) = (+3)
 (+6) + (−3) = (+3)
In other words subtracting a positive is the same as adding a negative.
Subtracting A Negative Number
Lastly, we can take away weights (we are subtracting negative values) the basket gets pulled upwards (positive) 
Example: What is 6 − (−3) ?
6−(−3) = 6 + 3 = 9
Yes indeed! Subtracting a Negative is the same as adding!
Two Negatives make a Positive
What Did We Find?
Adding a positive number is simple addition ...
Positive and Negative Together ...
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
Subtracting a negative ...
Example: What is 14 − (−4) ?
14−(−4) = 14 + 4 = 18
The Rules:
It can all be put into two rules:
Rule  Example  

+(+)  Two like signs become a positive sign  3+(+2) = 3 + 2 = 5  
−(−)  6−(−3) = 6 + 3 = 9  
+(−)  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
Now Play With It!
Try playing Casey Runner, you need to know the rules of positive and negative to succeed! 
A Common Sense Explanation
And there is a "common sense" explanation:
If I say "Eat!" I am encouraging you to eat (positive)
If I say "Do not eat!" I am saying the opposite (negative).
Now if I say "Do NOT not eat!", I am saying I don't want you to starve, so I am back to saying "Eat!" (positive).
So, two negatives make a positive, and if that satisfies you, then you are done!
Another Common Sense Explanation
A friend is +, an enemy is −
+ + ⇒ +  a friend of a friend is my friend  
+ − ⇒ −  a friend of an enemy is my enemy  
− + ⇒ −  an enemy of a friend is my enemy  
− − ⇒ +  an enemy of an enemy is my friend 
A Bank Example
Example: Last year the bank subtracted $10 from your account by mistake, and they want to fix it.
So the bank must take away a negative $10.
Let's say your current balance is $80, so you will then have:
$80−(−$10) = $80 + $10 = $90
So you get $10 more in your account.
A Long Example You Might Like
Ally's Points
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:  9  
Ally's Mom discovers spilt milk:  9 − 3 = 6  
Then Dad confesses he spilt the milk and writes "undo". How do we "undo" a minus 3? 

So Mom calculates:  6 − (−3) = 6 + 3 = 9 
So when we subtract a negative, we gain points
(i.e. the same as adding points).
A few days later. Ally has 12 points.  
Mom adds 3 points because Ally's room is clean.  12 + 3 = 15  
Dad says "I cleaned that room" and writes "undo" on the chart. Mom calculates:  15 − (+3) = 12  
Dad sees Ally brushing the dog. Writes "+3" on the chart. Mom calculates:  12 + (+3) = 15  
Ally throws a stone against the window. Dad writes "−3" on the chart. Mom 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.
or
Adding a Negative
is
Subtraction
Try These Exercises ...
Now try This Worksheet, and see how you go.
And also try these questions: