What the small one is

Before you read anything

$347 + 285$. Try it in your head first, honestly, and notice where you lose it.

Then set it out in columns — and before you work it out, say roughly how big the answer will be.

Ten tens, going next door

Fourteen tens is more than the column holds. Ten of them tie into one hundred and move a column to the left, and the hundred and forty never changes.

That is the small 1. Not a mark, not a rule — a hundred, standing in the column where hundreds live.

The same move you already know

:x nutshell-exchange

Ten of one size traded for one of the next size up. The amount does not change; only how it is held does.

Module 3 tied ten ones into a ten. This is the same :exchange with bigger pieces, and it will be the same one again in the thousands. There is only ever this one move.

Backwards, it is a bundle opened

$503 - 176$. There are three ones and you need six, so a ten is opened: four tens and thirteen ones. And there were no tens to open, so a hundred was opened first.

Musa

wrote 4 tens and 13 ones, and left the tens digit alone

The opened ten is gone. If thirteen ones arrive, the tens column has to go down by one — otherwise the number quietly grew.

Say how big first

Columns fail silently. A slipped digit gives a wrong answer that looks exactly as tidy as a right one, so the guess you made at the start is the only thing that will catch it.

Check yourself

Six to try

Estimate first, every time. Two of these ask what the carry or the borrow actually is, and those are the ones worth slowing down for.

1

Roughly, without working it out: $296 + 545$ is nearest to?

2

$216 + 506$

3

$798 + 315$

4

Adding $352$ and $492$ in columns puts a small $1$ at the top of the hundreds column. What is that $1$?

5

$233 - 146$

6

Taking $4$ from the ones of $53$: there are not enough. What happens?

Carrying and borrowing · page 1 of 2 Print it

Carrying and borrowing · page 2 of 2 Print it

Show that you have it

The hardest kind

Both of these need a bundle opened, and one of them needs a hundred opened before a ten can be. Write down every exchange you make.

1

$540 - 357$

2

$516 - 449$

Next: Why the second row shifts The whole thing on one page