Wednesday, March 27, 2013

Open Array Model for Divison

Decompose (break apart) the numbers into easier numbers (landmark numbers such as 10, 100, 1000) and then compose (put together) the partial products.
Here is an example of an open arrary model for division.   Solve 1,525 / 12.
Using benchmark numbers, how many groups of 12 are in 1,525?  I know that 1000 x 12 is 12,000.  That is way too big.  If I multiply 100 x 12, that is 1200.  That is less than 1525.  I can put the 100 above the rectangle array and then put 1200 in a sectioned off portion of the array.  On my scratch paper, I need to subtract 1200 from 1525.  I now have 325 left.  I cannot make another 100 groups, so I choose a smaller benchmark number.  I can make 10 groups of 12 which is 120.  Again, I put the 10 above the rectangle and put 120 in another sectioned off portion of the array and also subtract it from my balance of 325.   I repeat this process until I cannot make any more groups of 12.  The quotient is the total of the partial quotients that are above the array.  The remainder (if any) is my remaining balance.