Pre Algebra Like Terms
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Like Terms

 If we have 3 pizzas and we go and get 2 more pizzas we have 5 pizzas:

 3 Pizzas + 2 Pizzas = 5 Pizzas

 Letters in math work the same way as pizzas. 
 If we have 3X and we go and get 2X more, we have 5X:

 3 X + 2 X = 5 X

 Just think of the letter X like the word pizza. 
 5 was the number of pizzas we had. 
 5 is the number of X's we have.
 We can do subtraction like this too:

 6 X - 2 X = 4 X

 (Just like 6 pizzas - 2 pizzas = 4 pizzas)

 If somebody asked us you to add the number 6 and 3 pizzas, 
 you really couldn't do it. Numbers and pizzas don't mix. 
 The same goes for trying to add stuff like:

 3 X + 2

 We have 3 X's plus a silly 2. 
 You can't add them together.
 So 3X + 2 is just 3X + 2


If we tried to add 3 pizzas and 4 bowling balls, 

 all we would get is a big mess. 
 You really can't add different stuff like this together 
 and get anything that makes sense. 
 The same thing goes for different letters. 
 An X and a Y are as different as bowling balls and pizzas. 
 You just CAN'T add them together. 
 So ...

 3 X + 4 Y  is just 3 X + 4 Y

 Let's go back to stuff we can combine.
 What could we do with something like this:

 3 X + 4 Y + 2 X - 6 + 7 + 3Y

 We have 2 different X things in that mess. 
 We can combine the two of them:

 3 X + 2 X = 5 X

 Along with the rest of the glob we now have:

 5 X + 4 Y - 6 + 7 + 3Y

 We can combine the Y's. 4Y + 3Y = 7Y. 
 So we now have:

 5 X + 7 Y - 6 + 7

 We can also combine the -6 and the +7
 -6 + 7 = 1 (Start at - 6 and go up 7). 
 That means we now have.

5 X + 7 Y + 1 

 Now, all the things that had the same letter (or no letter) 
 have been combined. 
 That means we're done.
 When two or more things have the same letter (or no letter) 
 we call them:


 A Term means any number, letter, or group of numbers and letters 
 that are separated from other things by a + or a -.
 Like means any term that has the same letter or letters. 
 The same exponent on the letter or letters. Or no letters at all.

   copyright 2005 Bruce Kirkpatrick

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