Ineed

-7- (-6)
explain how you could use a number line to find the difference.
what is the difference?

You can use a number line to subtract -6 from -7. The difference is -1.

Rules for Subtracting Integers

Date: 10/31/2001 at 10:41:08

From: Julie

Subject: Rules for subtracting integers

For my assignment I need to write rules for subtrating integers. I

don`t know where to get this information.

Date: 10/31/2001 at 16:58:52

From: Doctor Peterson

Subject: Re: Rules for subtracting integers

Hi, Julie.

I don't tend to use "rules"; it works better to base what I do on an

understanding of how things work. Let's look at how things work, and

then you can see if you can express that in a simple set of rules.

If we put two numbers on the number line, then when we subtract A

from B, we get the "directed distance" from A to B:

                        B-A

                +>

   <oo>

                A                 B

That is, B-A is the number you have to add to A in order to get B:

   A + (B-A) = B

If B > (is greater than) A, as shown, then B-A is a positive number

(the arrow goes to the right). But if B < (is less than) A, then the

difference will be negative:

                        B-A

                <+

   <oo>

                B                 A

In fact, B-A is exactly the opposite of A-B:

   B-A = -(A-B)

So you can subtract a larger number from a smaller one by subtracting

the other way around and sticking a negative sign on the answer.

That's a rule you can use.

Another fact you may want to use is that if you have a number in

between, the difference is the sum of the two intermediate

differences:

                        B-A           C-B

                +>>

   <ooo>

                A                 B         C

                +>

                             C-A

   C-A = (B-A) + (C-B)

Notice that I deliberately didn't indicate on the number line whether

A and B are positive or negative; I didn't show where zero is. That's

because this definition of subtraction doesn't care about that. But

when you actually try to subtract two numbers, it will matter. And 0

may play the role of A, B, or C in this picture. For example, if B is

zero, since 0-A is -A, and C-0 is just C, this says that

   C-A = -A + C

Since A is a negative number, -A is positive, and this gives a way to

subtract a negative number from a positive by just adding two positive

numbers, something you already know how to do.

There are three places where I could have put the zero, and each

corresponds to a different case you may want to consider when you

write your rules. Try writing a rule to find B-A in each of these

cases:

1. A and B are both positive:

                         A            B-A

                +>>

   <ooo>

                0                 A         B

                +>

                              B

2. A is negative and B is positive:

                         -A            C

                +>>

   <ooo>

                A                 0         B

                +>

                             B-A

3. A and B are both negative:

                        B-A           -B

                +>>

   <ooo>

                A                 B         0

                +>

                             -A

In each case, you will want to consider which number is larger (and in

case 2, that means which of the two is positive); I've only shown B

larger. This will give you six cases; you may find a way to simplify

your rules by combining related cases. Have fun finding a way to say

all this neatly! Really, it can all be done with those two little

"rules" I gave above:

   B-A = -(A-B)

and

   B - A = B + -A

Just put these together a little differently in each case.

Step-by-step explanation:

cheater

step-by-step explanation: