Carrying and borrowing are just trading blocks. Watch the numbers change as you trade 10 for 1.
Start here. Every number is made of blocks: single cubes (ones), long rods (tens), flat squares (hundreds) and big cubes (thousands). Adding means putting piles of blocks together. Subtracting means taking blocks away.
Carrying. When you add and a column ends up with 10 or more blocks, you cannot keep them there. Trade 10 of them for 1 block in the next column to the left. That trade is what we call carrying. The little +1 above the next column on the paper shows it.
Borrowing. When you subtract and a column does not have enough blocks, break 1 block from the next column to the left into 10 smaller blocks. That is borrowing. The paper shows a −1 on the column you borrowed from and a +10 on the column that received the blocks. If the next column is empty (as in 1000 − 1), you break from the one after that first.
Try this above. Press One with a carry and watch which column turns yellow. Switch to − and press One with a borrow. Then type 1000 and 1 in the boxes and see how many breaks it needs.
Carrying means trading 10 blocks in one column for 1 block in the next column to the left. It is also called regrouping.
Borrowing means breaking 1 block from the next column into 10 smaller blocks so you have enough to take away. The number stays the same. Only the blocks change.
Because the hundreds and tens columns are empty. You break the thousand into 10 hundreds, then 1 hundred into 10 tens, then 1 ten into 10 ones. Then you can take away 1 one.
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