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