Division Example

You might be asking whether or not division is capable of being simplified with number sense.  Well, it is!  It's trickier, I admit, but you can take division problems and break it down somewhat to make the process simpler if you can keep track of everything in your head.  I present this image containing an example, I will explain the process afterward:

Yes, 138/6 is not an easy problem to do in your head normally.  Like the image describes, though, 6 can be broken up into 3 and 2.  Its easier to divide 138 by 2 than it is by 3, which is why 2 goes first.  That said, it still isn't that easy to divide 138 by 2, so now 138 is broken up into parts: 120, 10 and 8.  Why 120 and 10 and not just 130?  Try dividing 13 by 2, its not a whole number.  130 divided by 2 would be but it's still much easier to divide 120 by 2 than 130 by 2.

Once those three parts are halved, they are recombined to get 69.  That 69 is then divided by the leftover 3.  Like in the last problem, 69 is broken up into 60 and 9 to be divided by 3, a relatively simpler task than before.  The two results are then recombined to get 23.  Both parts of 6 - 2 and 3 - have been accounted for, so 138 divided by 6 gives you an answer of 23.

You might make the argument that doing this problem on paper, the way you were taught in school, might be faster.  True, but you would only have learned a method (long division), doing these exercises in your head helps you learn the actual numbers and the relationships between each number like 2 or 3, or in previous examples 10 or 100, and being able to use them in operations that do not explicitly follow set rules or guidelines.  If you're freely able to calculate these operations in your head, even slowly, you've got yourself a solid foundation of number sense.