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How to Add and Subtract
Positive and Negative Numbers

Numbers Can be Positive or Negative:

Negative Numbers (-) Positive Numbers (+)
(This is the Number Line, read about Using The Number Line)

"-" 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

This 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) ?

 

Subtracting a Negative is the same as Adding


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:

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 ... ?

It is also possible to have questions like:

What is 6 + (-3) ?
or what is 6 - (+3) ?

They are really the same! Both are subtraction:

Subtracting a Positive or
Adding a Negative
is
Subtraction


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.




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
Two like signs become a positive +(+) or 3+(+2) = 3+2 = 5
-(-) 6-(-3) = 6+3 = 9
       
Two unlike signs become a negative +(-) or 7+(-2) = 7-2 = 5
-(+) 8-(+2) = 8-2 = 6
       

Try These Exercises ...

Now try This Worksheet, and see how you go.

... or Play With It!

Try playing Casey Runner, you need to know the rules of positive and negative to succeed!