Pre Algebra Division With Remainders
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Leftovers
Division With Remainders

 
 Say you wanted to divide 5 pizzas into 2 equal piles. 
 How many are in each pile?
 

 
 We have a problem. 
 We can put two pizzas in each pile, 
 but we have one left over. 
 What do we do with it? 
 
 We could just call it a leftover or remainder.
 We could say 5 divided by 2 equals 2 with 1 left over.
 
 That's OK, I guess. But it's not a real answer. 
 The real answer is to cut that last pizza in half!
 

 
 Now we have the same amount in each pile. 
 There's NOTHING left over!
 
 So how much is in each pile?
 
 In each pile we have 2 whole pizzas plus 1 piece out of 2.
 
 Hey, that last part sounds like a FRACTION!
 
 It sure does. 
 We have ...

 

 You might not don't know how to add these two things together 

 to make one number (yet). 
 For now, just write them next to each other like this: 
 

 
 This thing is made up of a whole number AND a fraction. 
 We call it a MIXED NUMBER.
 
 Since we are big time math types now, 
 we can write:
 

 
 Example:
 
 Divide 7 into 3 equal piles:
 

 

 
 Did you catch that 1/3 part?
 
 Here's a toughie ...
 
 Example:
 
 Divide 8 into 3 equal piles:
 

 
 Oops! This time we have 2 left over. 
 What do we do?
 
 If we had only 1 left over we could cut it into 3 equal pieces. 
 Then put 1 piece in each pile. 
 Here we do that to each one of the 2 that are left over:
 

 
 So what do we have in each pile?
 

 
 We can add those pieces together:
 

 
 So when we divide 8 into 3 piles, 
 we have ...
 

 
 OK, here's the deal ...
 
 We had 2 left over. 
 We divided them into 3 piles. 
 The parts in each pile added up to:
 

 
 HERE'S A NEWS FLASH ...

 

 That's how leftovers always work!

 
 Example:
 
 Divide 2 into 5 piles:
 

 
 In each pile we have:
 

 
 So when we do 2 divided into 5 piles, 
 we get:
 

 
 Pop Quiz:
 
 What do we get if we divide 3 into 7 piles?
 

 
 

   copyright 2005 Bruce Kirkpatrick

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