Let us find 224 divided by 3. This basically means that we want to separate 224 into 3 EQUAL groups. Our quotient will
tell us how many goes into each group.
Now, forget about math for a moment. How would you do this without math? Say you had a bucket of Lego pieces, and you
wanted to put them (for some crazy reason) into three smaller buckets, each with the same number of pieces. How would you go
about doing this without math?
I would take out three pieces and put one into each group. Then I would take out three more pieces and put one in each
group. I would continue this until I had used all the pieces. This is EXACTLY how long division works, with one exception:
because of place value, our job is made easier, and a bit harder conceptually. We have the constriction (and the advantage)
of having to group our pieces into hundreds, tens, and ones (i.e., groups of one hundred pieces, groups of ten pieces, and
groups of one piece).
Look at the empty groups above and imagine that, instead of 224, you had 3 hundreds and 3 ones. You would not waste your
time separating this amount into 303 little pieces and putting one piece into each group until the pieces were gone. You
would see that you could put 1 hundred and 1 one in each group. So grouping the pieces into chunks larger than one, using
place value for example, can be helpful.
We cannot divide 2 hundreds into 3 groups and leave any of the hundreds intact, so we start by breaking up the hundreds
into tens.
When we separate those 22 tens into 3 groups, we get 7 tens (70) in each group and 1 ten (and 4 ones) left over.
You can see it right there in the algorithm. If we guess 8 tens in each group, we have used more than we were allotted
from the beginning, so we put 7 in the quotient. This means we use 3 times 7, or 21, of the tens, and we have 22 minus 21,
or 1, ten left over.
Again, we cannot leave the tens intact and divide, so we have to break up the 1 ten into 10 ones. This gives us 14 ones.
Now we can do the piece by piece counting. Notice though that one only has to count out 14 pieces instead of 224 pieces.
And, of course with mathematics, we do not have to count out anything.
We put 4 ones in each group, which means we use 3 times 4, or 12, ones, and we have 14 minus 12, or 2, ones left over.
We can either call this R2, or we can split each of the leftover ones into thirds and place two thirds into each group.