Integers Inetegers are all the whole numbers and their opposites. Examples of intgers are -10,-9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9,10 There are 4 opperations that can be performed with integers Multiplication Adding Subtracting Divivsion First lets start with subtracting integers Subtacting integers is very easy if you follow all the rules from the box of RULES The rules of subtracting 1. The first step to solving a problem with integers is to simlify the problem. 11. To simlify a problem you need to know two rules... Two negetives next to each other make a positive

A positive next to a negative makes a positive 111. The second thing you need to subtract integers, is just subtract 1v.There are some rules you need to know before you can subtract. When you subtract from a negative number you are really adding, but when you get your answer you have to put a negative sign in front of it. Now you have learned the rules of subtraction, lets try some problems to test you understanding Before we try solve problems on our own, lets do some examples. Example Box 1. First lets try to solve -(-4) -3 The first thing you need to to do is simiply this problem into the simplist form you can think of

So in this case you would simipfy -(-4) -3 into 4-3

Now you have to subtract

After you did everything your answer should be...

1 2. If you still confused than lets try another problem Your problem is -5-10

As you already know the first step to solving integers is to simplify the problem, in this case the problem is already simplified

Now you have to subtract

Now remember negative numbers are very difiant so instead of subtracting change all the negative to positives so the equation looks like this,5+10 and add

You should have got 15,now put a neagtive sign in front of 15, so it s like this:-15 and thats your answer There are many was to solve a integer problem, one of the them is drawing a picture l 3. Now lets try one more problem together In this problem we are going to subtract form a positive

Your problem is-(-9)-10

This simplifies to 9-10

To subtract this you have to first subtract till zero so the equation becomes 0-1 then remove the zero and you get your answer-1 If you're confused then using counters There is another way to subtract integers 4-7 is your problem 1. Draw 4 positive signs because 4 is positive

2. Then draw 7 negative signs because 7 is negative

3.Now you have to cancel the signs Your look like this should paper ++++ ------- 1.4-7 To cancel signs you have to eliminate the two different signs at the same time

When there are either no more negative or positives signs left you are done

Your answer is the number of signs remaining, so if there are 2 negatives remaining then your aswer is -2 Now paper should look like this 4-7 ++++ ------- //// //// Answer:-3 1. In this picture I'm canceling out signs When you cancel one sign you have to cancel the other sign Your next problem is -(-6)+78 1.First simplify the problem to 6+78

2.Then draw 6 positive signs because 6 is positive

3.Draw 78 positive signs because 78 is positive 1. 4-7 ++++ //// ------- //// 2.6+78 ++++++ ++++++ ++++ ++++++++++++++++++++ ++++++++++++++++++++ ++++++++++++++++++++ ++++++++=84 P.S.Drawing a picture is a really good statergy for large numbers

I would suggest using this statery very rarely

Drawings pictues takes a long time and is not always reliable so just do this the relgular way unless you don't know how to do it with pictues Summary 1. So far you have learned how to solve equations tha involve subtraction using pictures and numbers Now I'm going to test your understanding Test#1 Rule:If you subtract a negative from a negative that result is a negative

R ule:When you subtract a positive from a positive, the answer can be anything

Rule: When you subtract a numger the result is the same as adding the oppisite of tha number number

Ex.8-2=6 or8+-(-2)

Key Concept:

To subtract a integer add its opposite 1.-3-8 or-(+3)-(+8)

2.4-5or -(-4)

3.+4-1or4+(-1)

4.-6-(-6)or-6+6

5.-9-(-4)or9+4

6.7-5or-(-7)-(+5)

7.-1-5=-(+1)-5

8.-7-(-5)or-7+5

9.-8-(-4)or-8+4

10.-(-10)-(-5)or10+5

11.-6-2or-(+5)-(+4)

12.-4-2or-(+4)-(+2) Answers 1.-1 1.-11

2.-1

3.3

4.0

5.-5

6.-2

7.-6

8.-2

9.-4

10.15

11.-8

12.-6 Adding integers is easy if you follow the rules Rules of Addition 1.The sum of 2 positive integers is is always positive.

the sum of two negatives is always negative

Ex. 5+1=6 -5+(-1)=-6 2.The sum of a positive integer and a negative integer can be anything

Ex. 5+(-1)=-6 -5+1=-4 -5+5=0 3.When you add 2 negative numbers...

First change all the negative numbers to positive numbers

Once you have your answer,put a negative in front of it 4.When you add two positives...

You well add them(you should already know how to do that so I don't think need to explain) 5.When you add a positive to a negative... When you add to a negative number, you have to convert both the numbers to positives and subtract

Then add a negative sign to your answer Lets try this with pictures 1.Your problem is 4+(-7)

1.-16+8 Process to do addition with integers...

First you have to simplify the problem

Then add

After that, check your work The Process ++++ ------- First draw the signs Then cross out the signs one at at a time, so it looks like this //// ++++ ------- //// You have three 3 negative signs left, so the answer is -3 First draw the signs ---------------- ++++++++ //////// //////// Because there are 8 minus signs left, the answer is -8 Lets try some problems Examples 1.3+1or3-(-1)=4 2.4+2or-(-4)+2=6

3.-3 + (-5)or-3 -5=-8

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