Column Subtraction — Borrowing, the Other Way
Column addition carries a ten forward when a column overflows. Column
subtraction runs into the opposite problem: a column that doesn't have enough
to give. 342 - 168 — start at the ones column, 2 - 8. You can't take 8 away
from 2 and stay in single digits. Something has to come from next door.
See it first
The ones column only has 2, but needs to give up 8. Break one ten into ten loose ones — now there are 12 to work with, and 3 tens left.
Borrowing: one ten becomes ten ones
Here's the fix. The tens column of 342 has a 4 in it — four tens. Break one of those tens apart into ten ones, and lend it to the ones column:
3 14 2 (the 4 became a 3, and the 2 became 12)
- 1 6 8Now the ones column is 12 - 8 = 4, easily. The tens column shrank from 4 to
3 — because it gave one of its tens away.
Finishing the subtraction
Continue column by column, the same as before, checking each one for whether it needs to borrow:
2 13 12 one more borrow: the hundreds' 3 lends a ten to the tens
3 4 2
- 1 6 8
--------
1 7 4Tens column: 3 (after lending) - 6? Still not enough — so the hundreds
column lends its neighbor a ten too: the tens become 13, and 13 - 6 = 7.
Hundreds: 2 - 1 = 1. 342 - 168 = 174.
❓ Cross-question — "Does the value of the number actually change when you borrow?" No — that's the whole point. 342 is exactly the same amount whether you write it as 3 hundreds + 4 tens + 2 ones, or 3 hundreds + 3 tens
- 12 ones. Borrowing just rewrites the number in a form where each column has enough to subtract — nothing is created or lost.
🎯 Your turn
Work out 604 - 258 by columns, borrowing wherever a column comes up short —
watch what happens when the digit you're borrowing from is itself a 0.
Then explain, in the exercise below, where the borrowed ten actually comes
from.