Pre Algebra Long Division
Math-Prof HOME Pre Algebra Table of Contents Ask A Question PREV NEXT

Fancy Division
Long Division

 
 There is another way that we can write division problems. Say we have:
 

 21 3

 Another way to do this is:
 Write down the 3 and the 21 next to each other, 
 like this:

 

 

 
 And draw a line that goes between the numbers and over the 21, 
 like this:
 

 

 
 Now we're ready to start. 
 Since what we're dividing by is a 3, 
 we need to think about dividing things into 3 piles.
 
 Start with the first number under the lines (the 2). 
 Can we divide 2 into 3 piles evenly?
 

 

 
 What do you mean evenly?
 
 I mean with whole numbers, not fractions.
 
 No, we can't.
 
 Can we divide it up so that there is at least 1 whole one in each pile?
 

No, we can't. 

 
 OK, then we go on. 
 Look at the next number under the lines too.
 

 

 
 Can we divide 21 into 3 piles evenly?
 
 I think so:
 

 

 
 So there are 7 in each pile. Write 7 above the 1 in 21.
 

 

 
 Now multiply the number on the top (the 7) 
 times the number on the left (the 3).
 Write the answer under the 21,
 

 7 x 3 = 21

 

 

 
 Subtract the number you just wrote down from the number above it.
 

 

 
 Since we got zero as the answer when we subtracted, we're done. 
 21 divided by 3 equals 7. 
 The answer is the number at the top.
 
 OK, so the dividing up 21 into 3 piles way of doing things 
 is going to get old real fast. 
 
 Did you notice that 3 x 7 = 21? 
 That means when we're doing these instead of writing the piles, 
 we can just say "3 times WHAT is 21." 
 If you know the times tables up that far, it's easy.
 
 Try Another One:
 
 Example:
 
 What is 224 divided by 8?
 

 

 
 Compare the 8 to the first number under the lines:
 

 

 
 8 is bigger than 2. 
 There's no whole number that:
 

 8 (that number) = 2

 
 That means we look at the next number under the lines too:
 

 

 
 Is 22 bigger than 8? Yes! we're in business! 
 Figure out how many 8's there are in 22.
 

 1 8 = 8

 

 2 8 = 16

 

 3 8 = 24

 
 OK, 2 x 8 is smaller than 22. 3 x 8 is bigger than 22. 
 What do we do now?
 
 2 is the biggest number that we can use and stay less than 22. 
 That means we use 2.
 
 Write the 2 at the top. 
 Write it above the second 2 under the lines.
 

 

 
 It goes above THAT
 because we have used both of the 2's under the line to get it.
 
 Now multiply the number at the top (the 2) times the number at the left (the 8).
 
 Write the answer at the bottom.
 2 x 8 = 16 so:
 

 

 
 We wrote the 16 under the 22 because we used the 22 to get it.
 Now subtract the 16 from the 22. 
 (22 - 16 = 6)
 

 

 
 We can't get any more 8's out of that 6. The 6 needs help. 
 It can get help from the last number in the 224. 
 The 4 that's still sitting up under the lines. 
 Bring it down next to the 6 at the bottom.
 

 

 
 Now the 6 is a 64. 
 How many 8's are there in 64?
 

 1 8 = 8

 
 2 8 = 16
 
 3 8 = 24
 
 4 8 = 32
 
 5 8 = 40
 
 6 8 = 48
 
7 8 = 56
 
 8 8 = 64
We have a WINNER! 
 
 8 x 8 = 64. Write the 8 at the top next to the 2 and above the 4. 
 

 
 Multiply the new number at the top (the 8) times the number at the left (the 8)
 and write that at the bottom. 
 (8 x 8 = 64, I think we've seen that somewhere before.)
 

 
 Now subtract that number from the number above it.
 

 

 
 We're all out of numbers, so we're done. 
 The answer is the number at the top. 
 224 divided by 8 equals 28.
 

 224 8 = 28

 

   copyright 2005 Bruce Kirkpatrick

Math-Prof HOME Pre Algebra Table of Contents Ask A Question PREV NEXT