Trading or Regrouping, the New Borrow and Payback
Yes, the old fashioned borrow and pay back seems easy and tempting, but really, trading makes a lot of sense. If the number on top is too small to subtract the number below from, you change one from the next (higher) place value to ten of these units so you can subtract. If the next place has a zero, you will have to go up one more place.
You can not subtract 6 from 1 so you take one from the 3 in the tens place (which is one ten) and add that ten to the units. In fact, you are not changing the number. Then 11 units take away 6 leaves 5. Now 4 tens can not be subtracted from 2 tens, so we have to trade one of the 5 hundreds into tens (that’s ten tens) which gives us 12 tens from which to subtract 4 tens
leaving 8 tens. Then 4 hundreds take away 1 leaves three.
On the other hand, borrowing ten on a top number and paying back ten to a bottom number is also maintaining the value of the answer. The problem is that you are in effect increasing both numbers by ten. It’s like changing 82 – 37 to 92 – 47. Both equal 45.
