document.write( "Question 1208362: The math subtraction problem.\r
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Algebra.Com's Answer #846746 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "That's a great question.  Many people do not know why, because elementary\r\n" );
document.write( "teachers often just say \"You do it because it works\", or \"because I said so\"! \r\n" );
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document.write( "In short, it's not 9 you're changing the 0 to. You're adding 90 because that\r\n" );
document.write( "digit is in the placeholder for 10 times as much as the digit you're borrowing \r\n" );
document.write( "it for. When you can't borrow from the digit next door on the left, and have to\r\n" );
document.write( "borrow from two doors on the left, you borrow 100 instead of 10, so you dump the\r\n" );
document.write( "extra 90 that you didn't need to borrow on the zero that you couldn't borrow\r\n" );
document.write( "from.  \r\n" );
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document.write( "When you have to borrow from three doors over, you borrow 1000, which is\r\n" );
document.write( "borrowing 990 too much, so you dump 900 on the zero 2 doors over and 90 on the\r\n" );
document.write( "digit next door and add the remaining 10 to the digit you're borrowing it for.\r\n" );
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document.write( "The number of units (one, ten, hundreds, thousands, ten-thousands, etc.) \r\n" );
document.write( "which each digit tells how many of -- is always 10 times as much as how many\r\n" );
document.write( "units the digit just right of it tells how many of.\r\n" );
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document.write( "Normally when subtracting by hand, when the upper digit is smaller than the\r\n" );
document.write( "lower digit, we borrow 1 of the units from the digit just to the left of it,\r\n" );
document.write( "which is actually 10 units, and add 10 to the digit that was too small to\r\n" );
document.write( "subtract from, and then we reduce the digit just to the left by 1. \r\n" );
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document.write( "But sometimes the digit to the left is 0 and we can't borrow 10 from it.\r\n" );
document.write( "So we must go to the next digit to the left, and borrow 100 from it instead\r\n" );
document.write( "of 10 from the one next door. So we have over-borrowed.\r\n" );
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document.write( "We only wanted to borrow 10 units, not 100 units, so we need to get rid of \r\n" );
document.write( "the extra 90 that we borrowed.  \r\n" );
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document.write( "So we get rid of the extra 90 we borrowed by changing the digit (0) we couldn't\r\n" );
document.write( "borrow 10 from, to a 9. (It's really adding 90 to it because the units count 10\r\n" );
document.write( "times as much.) Then we take the remaining 10 and add it to the digit that was\r\n" );
document.write( "too small to subtract from.\r\n" );
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document.write( "Recap: We couldn't borrow 1 of the units from the digit just to the left (which\r\n" );
document.write( "would have been 10 of the units you needed) because it was 0.  So we borrowed 1\r\n" );
document.write( "from the next digit to the left (which is 100 of the units we needed to borrow).\r\n" );
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document.write( "We only needed to borrow 10, but we had to borrow 100 instead.  So we borrowed\r\n" );
document.write( "90 too much. So to get rid of the extra 90 units we borrowed, we added 9 to the\r\n" );
document.write( "0 we couldn't borrow from. Since that digit tells 10 times as many units as\r\n" );
document.write( "the digit we needed the 10 for, changing the 0 to 9 amounts to getting rid\r\n" );
document.write( "of the extra 90 we borrowed.  \r\n" );
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document.write( "Read what I wrote several times.  You'll get it.\r\n" );
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document.write( "[I heard that some third grade teacher told their students \"You change it to 9\r\n" );
document.write( "because you feel sorry for that placeholder since it only had 0. So you give it\r\n" );
document.write( "as much as you can to cheer it up, which is 9\" LOL]\r\n" );
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document.write( "Edwin
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