document.write( "Question 208369: what property is 7+(-7)=0 \n" ); document.write( "
Algebra.Com's Answer #157610 by Edwin McCravy(20056) $\"\"$ $\"About$
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document.write( "7+(-7)=0  demonstrates the \"additive inverse property\"\r\n" );
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document.write( "Here's what you need to know:\r\n" );
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document.write( "THE ADDITIVE IDENTITY IS 0\r\n" );
document.write( "There is just one \"do-nothing\" number for addition. \r\n" );
document.write( "This is 0 because when you add 0 to a number it \"does \r\n" );
document.write( "nothing\" for you get the same number back, so adding \r\n" );
document.write( "zero does nothing but give you IDENTICALLY the same \r\n" );
document.write( "number you started with. Every other number besides 0 \r\n" );
document.write( "does something when you add it, but not 0.  So 0 is the \r\n" );
document.write( "additive identity.  (There is also a multiplicative \r\n" );
document.write( "identity, 1, because it does nothing when you multiply\r\n" );
document.write( "by it.  So 0 is the additive identity, and 1 is the \r\n" );
document.write( "multiplicative identity.  But right now for this problem \r\n" );
document.write( "we only need to talk about the additive identity.)  \r\n" );
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document.write( "THE ADDITIVE INVERSE OF A NUMBER\r\n" );
document.write( "The additive inverse is the \"IDENTITY-MAKER\", or in the \r\n" );
document.write( "case of addition, the additive inverse.  Every number has \r\n" );
document.write( "just one \"IDENTITY-MAKER\" number under addition. The \r\n" );
document.write( "number 7 has the IDENTITY MAKER -7 because when you add \r\n" );
document.write( "the number -7 to the number 7 that makes 0, which is the \r\n" );
document.write( "IDENTITY for addition. (There are also multiplicative \r\n" );
document.write( "inverses, which are \"ONE-MAKERS\". (The multiplicative \r\n" );
document.write( "inverse of  is  because when you multiply \r\n" );
document.write( " by  you get the IDENTITY for multiplication. \r\n" );
document.write( "But right now for this problem we only need to talk about \r\n" );
document.write( "the additive identity and the additive inverse). \r\n" );
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document.write( "Question:  What do you have to add to 7 to make zero,\r\n" );
document.write( "           (which is the \"do-nothing\" number for addition?)  \r\n" );
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document.write( "Answer: You need to add -7 to make zero, the do-nothing number \r\n" );
document.write( "        for addition.\r\n" );
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document.write( "Therefore -7 is the additive inverse of 7.  And 0 is the\r\n" );
document.write( "additive identity.\r\n" );
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document.write( "So when you add the ADDITIVE INVERSE -7 to 7, you get \r\n" );
document.write( "the identity 0, or 7+(-7)=0   \r\n" );
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document.write( "Another word for \"ADDITIVE INVERSE\" is \"OPPOSITE\", formed \r\n" );
document.write( "by changing the sign.\r\n" );
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document.write( "---\r\n" );
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document.write( "Question:  What do you have to multiply 7 by to make one,\r\n" );
document.write( "           (which is the \"do-nothing\" number for \r\n" );
document.write( "           multiplication?)  \r\n" );
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document.write( "Answer: You need to multiply  by  to make \r\n" );
document.write( "        one, the do-nothing number for addition.\r\n" );
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document.write( "Therefore  is the muclipicative inverse of 7.  And 1 is the\r\n" );
document.write( "additive identity.\r\n" );
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document.write( "So when you multiply 7 by the MULTIPLICATIVE INVERSE of 7, you get \r\n" );
document.write( "the identity 1, or x   \r\n" );
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document.write( "Another word for \"MULTIPLICATIVE INVERSE\" IS \"RECIPROCAL\",\r\n" );
document.write( "formed by INVERTing it. (That's where they got the name \r\n" );
document.write( "\"INVERSE\" in the first place, but they borrowed it for\r\n" );
document.write( "addition too. \r\n" );
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document.write( "TMI?  Depends on how deep your teacher goes!\r\n" );
document.write( "Edwin
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