Wednesday, April 4, 2012

Division My Way

My son is expected to do word problems where division is required, but his math book doesn't cover division in 3rd grade.  I don't like him using a calculator in math, but the division is more difficult than 12  :  3 = 4.
I started to teach him to do division problems and then looked for tutorials and could not find the method that I made up for him.  I wanted what he was doing to make sense so I explained it this way.  It turns out to be about the same amount of work as some of the other methods I've found, but it made sense to us.  I just thought I'd share it in case someone struggling with long division wants to try it this way too.

75  :  3 = ? We start with the problem and then rewrite it as 2 equations.  The 10's of the dividend on top and the 1's of the dividend on bottom.  The divisor stays the same.
7   :  3 = 2 R 1  then bring the remainder down and put it in front of the number from the 1's place
1 :  3 = 5  For the solution, put the top answer (minus remainder) back in the 10's place and the bottom answer in the 1's place and we know that 75  :  3 = 25

Another example without explanation:

54  :  2 = ?

 5  :  2 =                   ----->     5  :  2 = 2 R 1
 4  :  2 =                   ----->   14  :  2 = 7
so 54  :  2 = 27

If the first digit of the dividend is smaller than the divisor, we then just skip the first equation and keep the first 2 numbers together in our first equation.


121  :  11 = ?

12  :  11 = 1 R 1
11  :  11 = 1
so 121  :  11 = 11


rather than saying 1 :  11 = 0 R 1  in the first line and so on we just skipped this step.


or

104  :  8 = ?

10  :  8 = 1 R 2
24  :  8 = 3
so 104  :  8 = 13


This method is not for everyone.  My son thought it was super easy to learn, but my husband just glanced at it and said, "That is not how you do division!"  My discriptions may be hard to follow, but I think if you look at the last few problems closely, you can figure out our method.  It works for bigger problems as well and the end answer can still have a remainder.

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