



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 
