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:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

the ratio of red paint to blue paint is always 9/7. that means that, whatever x's value, (4x+12)/(4x-4) has that same ratio. so, set up an equation and cross-multiply to solve for x:

9/7 = (4x+12)/(4x-4)

9(4x-4) = 7(4x+12)

36x - 36 = 28x + 84

8x - 36 = 84

8x = 120

x = 15