tag:blogger.com,1999:blog-2212741399857110313.post5750859036017987013..comments2024-03-11T11:13:12.066-05:00Comments on Homeschool and Etc.: Math Wars? Stop the Hate!Happy Elf Mom (Christine)http://www.blogger.com/profile/15047347624037697311noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-2212741399857110313.post-55495647459841597262008-07-18T20:46:00.000-05:002008-07-18T20:46:00.000-05:00Or you can highlight the word that you want the li...Or you can highlight the word that you want the link to be and then go to the hyperlink icon and put in the web address. After you hit OK then it should automatically put it in and when you publish the post it should put it in a different color.<BR/>Mine doesn't always change the color.Zimms Zoohttps://www.blogger.com/profile/07671798321373854716noreply@blogger.comtag:blogger.com,1999:blog-2212741399857110313.post-45856030225957740182008-07-18T19:39:00.000-05:002008-07-18T19:39:00.000-05:00There are only a few basic "Math Concepts" in simp...There are only a few basic "Math Concepts" in simple arithamatic and elementry algebra. If a person understands them, they know all the concepts of basic math. The rest of "Elementry Math" is learning to do arithamatic according to these basic concepts. Really, it is that simple folks. Below is a two page basic "Math Concepts" book. Enjoy:<BR/>"A Two Page Algebra Book"<BR/>By<BR/>Carl M. Bennett, BEE; MS(3)<BR/><BR/>Mathematics is a language for expressing precise, logical ideas. The basic language of mathematics is common Algebra.<BR/><BR/>Algebra is based on the definitions of two rules of how to “operate on” or combine two real numbers to form another real number, and five other definitions of the characteristics of these operations needed to make Algebra logically consistent and practical as a language of logical thought.<BR/><BR/>The first rule is called addition or the “+” operation on two real numbers.<BR/><BR/>For two real numbers a, and b, a + b is defined as the real number c which is equal to the combined value or “sum” of the numbers a, and b.<BR/>For example 3 + 5 is defined as 8 or 3 + 5 = 8.<BR/><BR/>The second rule is called multiplication or the “x” operation on two real numbers.<BR/><BR/>For two real numbers a, and b, a x b is defined as the real number c which is equal to the combined value or “sum” of the number b added to itself a times.<BR/>For example 3 x 5 is defined as (5 + 5 + 5) = 15.<BR/><BR/>To be logically consistent and practical, both of the above operations, addition (+) and multiplication (x) must have the four basic characteristics defined below.<BR/><BR/>1 - Both addition (+) and multiplication (x) must be “associative” in character.<BR/><BR/>This means that the order in which we associate and add the numbers a + b + c, gives the same real number. That is to say, if we first associate and add (a + b) and then add c, or we first associate and add (b + c) and then add a, we get the same real number.<BR/>For example, (3 + 5) + 7 = 15 gives the same result as 3 + (5 + 7) = 15.<BR/><BR/>This also means that the order in which we associate and multiply the numbers a x b x c, gives the same real number. That is to say, if we first associate and multiply (a x b) and then multiply by c, or we first associate and multiply (b x c) and then multiply by a, we get the same real number.<BR/>For example, (3 x 5) x 7 = 105 gives the same result as 3 x (5 x 7) = 105.<BR/><BR/>2 - Both addition (+) and multiplication (x) must be “commutative” in character.<BR/><BR/>This means that the order in which we add the numbers a, and b, gives the same real number. That is to say, if we add a + b, or we add b + a, we get the same real number.<BR/>For example, 3 + 5 = 8 gives the same result as 5 + 3 = 8.<BR/><BR/>This also means that the order in which we multiply the numbers a, and b, gives the same real number. That is to say, if we multiply a x b or multiply b x a, we get the same real number.<BR/>For example, 3 x 5 = 15 gives the same result as 5 x 3 = 15.<BR/><BR/>3 - Both addition (+) and multiplication (x) must have the “identity” characteristic.<BR/><BR/>This means that for addition (+), there must be a real number, I, when added to any real number a, always gives, a + I = I + a = a. For addition (+), this "identity" is I = 0.<BR/>For example 5 + 0 = 5.<BR/><BR/>This also means that for multiplication (x), there must be a real number, I, when multiplied by any real number a, always gives a x I = I x a = a. For multiplication (x) this "identity" is I = 1.<BR/>For example 5 x 1 = 1 x 5 = 5.<BR/><BR/>4 - Both addition (+) and multiplication (x) must have an “inverse” characteristic<BR/><BR/>This means that for addition (+), a real number b is the addition (+) “inverse” of any real number a, if and only if a + b = 0. The addition (+) “inverse” for any real number a, is the “negative of its real value”, defined as "minus a" or -a, since a + (-a) is always equal to the addition (+) "identity", I=0, that is to say a + (-a) = 0, for all real numbers a, of both positive or negative value.<BR/>For example (-5) + (-(-5)) = (-5) + 5 = 0.<BR/><BR/>For simplicity we often write –5 + 5 = 0 = 5 – 5, but 5 – 5 is mathematically, actually 5 + (-5). The “minus (-) notation” only tells us that -a, is the negative in value of a. Thus minus (-) is not actually a valid algebraic operation on two real numbers like addition (+) is, since the minus (-) operation is neither “associative” nor “commutative” as defined above.<BR/>For example, 7 - 6 = 1 is not the same as 6 - 7 = (-1).<BR/><BR/>This also means that for multiplication (x) a real number b is the multiplication (x) “inverse” of a real number a, if and only if a x b = 1. The multiplication (x) “inverse” for any real number a, is the reciprocal of its real value, defined as the real number (1/a), since a x (1/a) is always equal to the multiplication (x) "identity", I=1, for all real numbers except zero = 0.<BR/><BR/>Zero has NO multiplication (x) “inverse”, since (zero) x (any real number) = zero, thus not the multiplication (x) "identity", I=1, as required for zero to have a multiplication (x) “inverse”.<BR/><BR/>This is why "division by zero", for example, a x (1/0) or a /0, is NOT allowed in common Algebra.<BR/><BR/>For simplicity we often write, for example, 25 / 5 = 5, however; 25 / 5 is mathematically, actually 25 x (1/5) = 5. The "divide (/) notation" only tell us that a number is the “inverse” of a real number. Thus divide (/) is not actually a valid algebraic operation on two real numbers like multiplication (x) is, since the divide (/) operation is neither “associative” nor “commutative” as defined above.<BR/><BR/>For example, 8 / 2 = 4 is not the same as 2 / 8 = 0.25 or the rational, real number, one quarter, (1/4).<BR/><BR/>To be logically consistent and practical, both of the above operations, addition (+) and multiplication (x) must have the one additional basic joint characteristic as defined below.<BR/><BR/>5 - Multiplication (x) must be “distributive” over addition (+), that is,<BR/><BR/> a x ( b + c ) = (a x b) + ( a x c ) and ( a + b ) x c = (a x c ) + ( b x c ) for all real numbers.<BR/><BR/>The above "rules and characteristics" define common Algebra. Every logically and mathematically correct manipulation of any algebraic equation involves these "rules and characteristics" or a composite of them.<BR/><BR/>© Carl M. Bennett, 18 August 2006. May be reproduced only for educational and research purposes.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-2212741399857110313.post-47013868508645619362008-07-18T13:26:00.000-05:002008-07-18T13:26:00.000-05:00When you compose a post,there will be a chain look...When you compose a post,there will be a chain looking icon. Click on that and put the website address in it. Once you get it put onto your post that your making there will be this <> at the end. That is where you would type "this" or what ever you want to type. I hope that helps a little.<BR/><BR/>Aunt B. AKA Brandyaunt bhttps://www.blogger.com/profile/03012593264104061351noreply@blogger.com