Pam's Scribe Post

 today's lesson:

January 8, 2014
 (all answers at the end of explanation)
 

       Integers not only have adding in them, but subtracting, or removing. A rule you must know is "Whenever something is not there, you must add a zero pair"
A stragety you can use when you want to recongnize when to say "and" (add or combine) or "remove" is when the equation is a double negative or it's a negative and a negative, if not, then always combine unless you remove a negative (negative and negative). When you have a negative and a negative, you must add a zero pair since that negative isn't there.

negative minus negative (with brackets)

 



For example, (-5) - (-6) =
For the words, it would be :
Owe 5 Remove Owe 6.

Since you are trying to remove (-6), you can't since there isn't so you do a zero pair.

++++++
- - - - - -     <--- This evens them out and then you remove the (-6) so you are left with positive 6.

Here  you would remove the (-6) since it's part of the equation.
Then you combine (-5) since integers is all about combining.

+ + + + + +
-  -  -  -  -

You have one positive left over, therefore, the answer is (+1) or have 1.

 

positive minus negative (no brackets)

 

And example for a positive minus negative equation is:

9 - 1 =

This may seem like a regular subtracting question, but it really is like saying (+ 9) - (-1).

The minus sign actually is part of the one since it means that the one is negative.

A way this might be easier is to say the equation out loud or put it in words like so:

             have 9, owe 1.

To show this you would have 9 positives (have is positive), and 1 negative (owe is negative).

 

+ + + + + + + + +

 -



The zero pair cancels one of the positives and one of the negatives, leaving behind only 8 positives. The answer would be (+8) or have 8.

negative minus negative ( first one has no brackets)

 

This may seem different from the first one, but it's all about how you look at it.

An example of this type is : -4 - (-6) =

The only difference for this is that the negative 4 doesn't have brackets.

In words this would be : Owe 4 REMOVE Owe 6.

In pictures or in integer chips this would be 6 zero pairs, removing the minus, and you add the positives with the negative which is negative 4.

 

-  -  -  -  -  -

+ + + + + +

 

Then COMBINE the positive 6 with the negative 4.

 

+ + + + + +

-  -  -  - 

 

Then you have 2 positives left over which gives you your answer of (+2). 

 

It goes with positive minus negative, example: 4-(-6)
 

positive minus negative (with brackets)

 

 

An example of positive minus negative would be:

7-(-6) =

In words this would be have 7 REMOVE owe 6. This a double negative, since there are two negatives together.

+ + + + + +
-  -  -  -  -  -

Then you combine the 6 positives together with the 7 positives, which equals 13.

 

Calculate with the zero pairs and you're done. You have one positive left over, and you answer is (+1) or have 1.

if that didn't work, here's a video. 



 

 







here's some more fun with subtracting integers (game)

 

 

Integers Subtracting Game

(if that didn't work try copying this link)

http://www.sheppardsoftware.com/mathgames/integers/FS_Integer_subtraction.htm

 

 

 

Good luck on your learning!