265 lines
15 KiB
Plaintext
265 lines
15 KiB
Plaintext
GwDGwDGwDGwDGwDGwDGwDGwDGwDGwDGwDGwDGwDGwDGwDGwDGwDGwDGwDGwDGwDGwDGwDGwDGwDGwD
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G G
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w _____ ____ 1 4 999 "uh-rith-muh-tick" w
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D // | \ 11 44 9 9 by Aardv@rk D
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* || ____ | || | 1 444 999 *
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G || || \ / | || | 1 4 9 issue #149 of "GwD: The American Dream G
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w \\___// \/\/ |____/ 111 4 999 with a Twist -- of Lime" * rel 05/05/05 w
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D D
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GwDGwDGwDGwDGwDGwDGwDGwDGwDGwDGwDGwDGwDGwDGwDGwDGwDGwDGwDGwDGwDGwDGwDGwDGwDGwD
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--- -- - -- --- -- - -- --- -- - -- --- -- - -- ---
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[This was written 10 years ago for my Algebra II class in high school. The
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teacher also taught remedial math, and I guess she was tired of it, so she
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made us write these lame descriptions of how to do math problems to help her
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out or something. We had to do "writing assignments" in every class; it's all
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about teaching to the standardized test that has a writing portion. We were
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supposed to write about how to do the four basic artithmetic operations with
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both positive and negative integers. It always struck me as odd that we were
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supposed to explain negative numbers but not fractions/decimals, since both of
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these concepts require understanding of one of the operations we were supposed
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to explain. How can you understand negative numbers if you don't know how to
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subtract? Seriously. That teacher was dumb; much dumber than the kids that
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were in HS and didn't know how to add.
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Anyway, this got a good grade, despite its condescension. -Aardv@rk]
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I hear you've been having some trouble with math. Well, don't you worry about
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that! I'm going to teach you math backwards and forwards so you'll never have
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trouble again. Adding, subtracting, multiplying and dividing will be a piece
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of cake if you follow my simple instructions. If you really don't know this
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stuff, you should probably quit using the computer and get to studying.
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You must start with addition. Addition is the simplest mathematical
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operation and the easiest to learn. It is simply putting two (or more) things
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together. For example, if you have two apples and I give you one more apple,
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how many apples do you have? There are three apples. If you do not
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understand this, count two of your fingers and then count one more. (If you
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do not know how to count, you are beyond help. Also, if you do not have
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fingers, well, umm, count beans or something.) The number sentence (it is
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called that because it is somewhat like a word sentence) for this is
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"2 + 1 = 3" because you had two apples and I gave you one more. What if you
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have three oranges and I give you three more? You have six oranges. The
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number sentence this time is "3 + 3 = 6". Now, let's try something a little
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bit harder. If you have six peanuts and I give you 3 more, how many peanuts
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do you have in all? You have nine peanuts. The number sentence this time is
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"6 + 3 = 9". Addition works the same way for larger numbers. When you add
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zero to a number, the number stays the same: "5 + 0 = 5". Addition is
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commutative. That means that "5 + 2 = 2 + 5 = 7". Basically, being
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commutative rocks nads. It means that the numbers to be added can be added in
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any order and give you the same result.
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"What about these 'negative numbers' I have heard so much about but have no
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idea what they are?" is probably what you are asking yourself right now.
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Well, I am not supposed to tell you what negative numbers are, even though I
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am supposed to tell you how to use them. Don't worry, it does not make any
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sense to me either. Addition with negative numbers is as follows:
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"5 + - 6 = -1" which is exactly the same thing as saying "5 - 6 = -1", turning
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it into a subtraction problem from an addition problem. Similarly,
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"-5 + -6 = -11" is the same as saying "-5 - 6 = -11". This has also turned it
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into a subtraction problem. See the next paragraph for help with subtraction.
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If you think you understand, move on to the next paragraph. If you feel that
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you need a little bit more practice, try these examples or the problems
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following the instructions on your own or ask your parents or teacher for
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help.
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Subtraction is a little bit more difficult than addition, but not much. You
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should think of subtraction as the opposite of addition. Let's go back to the
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apple example. You now have three apples, right? What if I take my apple
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back? I'm a mean bastard, huh? How many apples do you have then? If you
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think you would have 2 two apples, you are correct. The number sentence this
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time is "3 - 1 = 2". That may seem easy, but what will happen if I use a
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problem you haven't seen before? There are nine kids that you are friends
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with in your class. If two of them go to another class, then how many friends
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are left in your class? There are seven friends left in your class. The
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number sentence is "9 - 2 = 7". How about just a number sentence without
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things related to it? Try this number sentence and fill in the blank:
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"11 - 5 = __". Did you put "6" in the blank? You should have. If you
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didn't, they're all going to laugh at you. Negative numbers are just one
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small step beyond standard run of the mill everyday subtraction. If you
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subtract zero from a number, you get the same number: "4 - 0 = 4". Think of
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negative numbers as zero minus a positive number. For example, "0 - 4 = -4".
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Adding a negative number is the same thing as subtracting a positive number:
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"4 + -1 = 4 - 1 = 3". What about subtracting negative numbers? Subtracting
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negative numbers is addition. "5 - -2 = 5 + 2" because the "minus signs"
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cancel each other out. Think that the negative sign in front of a negative
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number changes whatever sign (+ or -) to the other sign (- or +). So,
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"-1 - -2 = -1 + 2 = 1" and "5 + -3 = 5 - 3 = 2". Negative numbers are tricky
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until you get the hang of using them. Subtraction is not commutative! I
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DON'T KNOW HOW MANY TIMES I'VE HAD TO EXPLAIN THIS PART. YOU'D BETTER
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REMEMBER IT! SERIOUSLY. Do you think you need to spend some more time on
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subtraction, or can we move on to multiplication? If you need some more help,
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do not be ashamed to try some of the provided problems or ask an adult for
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help. That's what we're here for. Sort of.
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Multiplication is nothing but addition on a large scale. If there are ten
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classrooms and each classroom has 20 students in it, how many students are
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there in all? You could count or use the number sentence
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"20 + 20 + 20 + 20 + 20 + 20 + 20 + 20 + 20 + 20 = ___"
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If you add all of these twenties the number you will get is 200. However,
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since you know that you are adding twenty ten times, you can say twenty times
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ten equals two hundred or "20 X 10 = 200". If you have seven pairs of socks,
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how many socks do you have? (There are two socks in a pair.) Use the number
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sentence "7 X 2 = __". If you put 14 in the blank, good job. If you
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didn't, well, try again. Remember that any number times one is that number:
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"3 X 1 = 3". Also, you must know that any number multiplied by zero is zero.
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Using the classroom problem, if there are zero classrooms with twenty students
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each, then how many classrooms students are there? If you said zero, you are
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right. If you didn't, pay better attention. This is shown by "20 X 0 = 0" or
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"0 X 20 = 0". Like addition, multiplication is commutative; you can put the
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numbers to be multiplied in any order and the result will not change:
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"3 X 4 = 4 X 3 = 12". You are now ready to move on to multiplication by
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negative numbers. There are four things you need to know to multiply using
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negative numbers: 1) a positive times a negative is always a negative; 2) a
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negative times a positive is always a negative (which, given commutativity, is
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the same thing as a positive times a negative, so I'm really just repeating
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myself for no reason); 3) a negative times a negative is always a positive; 4)
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any number times negative one (-1) switches signs but stays the same. (It is
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assumed that you know that a the product of the multiplication of two positive
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numbers is always positive.) To illustrate cases one and two: "3 X -4 = -12"
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and "-3 X 4 = -12". That's not too hard, now is it? Don't answer that. Case
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three, however, is very important. Remember that when multiplying, negative
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signs cancel, and you will never go wrong. For example: "-5 X -6 = 30" and
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"-10 X -2 = -20". Case four is also very important, though it is really
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just putting the other three cases into a specific situation. If you multiply
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a positive number by negative one you get the "negative version" of that number
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(put a negative sign in front of it): "5 X -1 = -5" or "-1 X 5 = -5".
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However, if you multiply a negative number by negative one, you get the
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"positive version" of that number: "-3 X -1 = 3". Now you should see what I
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mean by saying that the signs switch. Multiplication is a little harder than
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anything else we have covered. Division is the next operation. If you
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understand how to multiply, division will be very easy for you. If you don't,
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well, too bad, because it's what I'm covering next, anyway.
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Division is the last of the operations we need to discuss. Just as
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subtraction is the opposite of addition, division is the opposite of
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multiplication. Normally, the division symbol is something like this: o
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---
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o
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but there is no key for that on my keyboard, so I am going to use the "/"
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symbol instead, because it also means division. So now on to actually
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dividing! Isn't this fun? If you want to know how many threes there are in
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nine, use "9 / 3 = _". The answer to this problem is 3. You can check this
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by multiplying: "3 X 3 = 9". You have determined the correct answer. If you
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have 3 boxes of grapefruits and you know that there are 45 grapefruits in all,
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how many grapefruits are there per box (assuming, of course, that the
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grapefruits are evenly distributed...lacking this assumption, the correct
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answer is "not enough information")? You should divide forty-five by three:
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"45 / 3 = 15". There are fifteen grapefruits per box. Division is not
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commutative: "9 / 3 <> 3 / 9". (<> means "is not equal to" because the
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"greater than" and "less than" symbols are used. If a number is greater than
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or less than another number, it does not equal that number.) Division by
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negative numbers is easy. You just need to know: 1) if a negative number is
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divided by a positive number, the result is negative; 2) if a positive number
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is divided by a negative number, the result is negative; and 3) if a negative
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number is divided by a negative number, the result is positive. (It is
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assumed that you know that a positive number divided by a positive number
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results in a positive number.) Examples for cases 1 and 2 are:
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"-10 / 5 = -2" and "10 / -5 = -2". An example for case 3 (which is very
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important) is: "-4 / -2 = 2". Yet again, the negative signs cancel each
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other out. Division is easy, it just takes some practice.
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Do you think you understand better now? I hope so. Just remember the order
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of operations: 1) go from left to right in an equation; 2) do all
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multiplication and/or division problems before doing addition or subtraction
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problems. Now, all you need to do is practice. If you choose to take the
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quiz, give yourself five points for each problem you get right. Subtract 9
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points from your score for each problem you get wrong, in class UIL Number
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Sense scoring fashion. Information on how to order the answers to the quiz
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can be found immediately following the quiz. Good luck in school, and enjoy
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the challenge of math!
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NEXT LESSON: FRACTIONS...BE AFRAID...BE VERY AFRAID...
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______________________________________________________________________________
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PRACTICE PROBLEMS
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-----------------
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Addition
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--------
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1) 2 + 5 = __ 2) 3 + 7 = __ 3) 6 + 9 = __ 4) 7 + 6 = __ 5) 5 + 3 = __
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6) -2 + 5 = __ 7) -1 + -4 = __ 8) -6 + -9 = __
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Addition Bonus
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--------------
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10 + 11 + 3 + -3 = __
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______________________________________________________________________________
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Subtraction
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-----------
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1) 4 - 3 = __ 2) 7 - 5 = __ 3) 7 - 2 = __ 4) 6 - 4 = __ 5) 12 - 1 = __
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6) -4 - 3 = __ 7) 7 - -5 = __ 8) -7 - 2 = __ 9) -6 - -4 = __
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Subtraction Bonus
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-----------------
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11 - 8 - 2 - -3 = __
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______________________________________________________________________________
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Multiplication
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--------------
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1) 2 X 2 = __ 2) 3 X 5 = __ 3) 5 X 1 = __ 4) 6 X 2 = __ 5) 3 X 4 = __
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6) 2 X -2 = __ 7) -3 X -5 = __ 8) 5 X -1 = __
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Multiplication Bonus
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--------------------
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3 X 4 X 2 X -1 X -2 = __
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______________________________________________________________________________
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Division
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--------
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1) 9 / 3 = __ 2) 4 / 2 = __ 3) 7 / 1 = __ 4) 6 / 2 = __ 5) 10 / 2 = __
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6) 9 / -3 = __ 7) -4 / 2 = __ 8) -6 / -2 = __
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Division Bonus
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--------------
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12 / 2 / 3 / -1 = __
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______________________________________________________________________________
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DO NOT LOOK AT THE ANSWERS UNTIL YOU HAVE COMPLETED THE PROBLEMS
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______________________________________________________________________________
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Addition Answers
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----------------
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1) 7 2) 10 3) 15 4) 13 5) 8 BONUS -=- 21
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6) 3 7) -5 8) -15
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______________________________________________________________________________
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Subtraction Answers
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-------------------
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1) 1 2) 2 3) 5 4) 2 5) 11 BONUS -=- 4
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6) -7 7) 12 8) -9 9) -2
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______________________________________________________________________________
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Multiplication Answers
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----------------------
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1) 4 2) 15 3) 5 4) 12 5) 12 BONUS -=- -48
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6) -4 7) 15 8) -5
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______________________________________________________________________________
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Division Answers
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----------------
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1) 3 2) 2 3) 7 4) 3 5) 5 BONUS -=- -2
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6) -3 7) -2 8) 3
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______________________________________________________________________________
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/-----------------\
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|* Q * U * I * Z *|
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\-----------------/
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1) 1 + 3 - 2 = __ 2) 4 X 5 / 2 = __ 3) 1 + 1 + 3 - 2 = __ 4) 5 X 6 = __
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5) 2 + 3 - 4 + 1 = __ 6) 10 + 1 - 2 X 2 - 15 = __ 7) 4 + 5 + 3 - 2 = __
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8) 1 + 3 X 2 = __ 9) 1 + 1 + 6 - 5 + 2 = __ 10) 6 X 2 - -3 = __
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11) 1 - 3 + 8 + -2 X 3 = __ 12) 5 X 4 / -2 + 5 = __ 13) 5 - 6 / 3 X 4 = __
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______________________________________________________________________________
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For answers to the quiz send a self-addressed stamped envelope along with five
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American dollars to GwD Inc. at the address below.
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______________________________________________________________________________
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--- -- - -- --- -- - -- --- -- - -- --- -- - -- ---
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Issue#149 of "GwD: The American Dream with a Twist -- of Lime" ISSN 1523-1585
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copyright (c) MMV Aardv@rk/GwD Publications /---------------\
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copyright (c) MMV GwD, Inc. All rights reserved :HUMANITY SUCKS.:
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a production of The GREENY world DOMINATION Task Force, Inc. : GwD :
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Postal: GwD, Inc. - P.O. Box 16038 - Lubbock, Texas 79490 \---------------/
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FYM -+- http://www.GREENY.org/ - editor@GREENY.org - submit@GREENY.org -+- FYM
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GwDGwDGwDGwDGwDGwDGwDGwDGwDGwDGwDGwDGwDGwDGwDGwDGwDGwDGwDGwDGwDGwDGwDGwDGwDGwD
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