Taking away three-digit numbers: Abacus lesson notes (ages 7+)

Ages 7+ · Abacus · Taking away

Taking away three-digit numbers

346 on the frame: three hundreds, four tens and six ones.

The big ideaStart at the ones. Any row with too few borrows from the row above.

How it works

The frame has three rows: hundreds on top, then tens, then ones.

Start at the ones. Any row with too few beads borrows from the row above.

Borrowing twice is just two trades, one after the other: a hundred trades for ten tens, then a ten trades for ten ones.

If the row above has nothing to lend, open the next row up first.

Three rows: ones, then tens, then hundreds.

Example 1: A page, strips and singles

346 - 158. Ones: 6 is too few for 8, so open a ten: 16 - 8 = 8 ones. Now 3 tens are left.
Tens: 3 is too few for 5, so open a hundred: 13 - 5 = 8 tens. Now 2 hundreds are left.
Hundreds: 2 - 1 = 1.
346 - 158 = 188

1 hundred, 8 tens and 8 ones are left: 188.

Example 2: Borrow once

482 - 157. Ones: 2 is too few for 7, so open a ten: 12 - 7 = 5 ones. Now 7 tens are left.
Tens: 7 - 5 = 2.
Hundreds: 4 - 1 = 3.
482 - 157 = 325

3 hundreds, 2 tens and 5 ones are left: 325.

Example 3: Borrow twice

531 - 247. Ones: 1 is too few for 7, so open a ten: 11 - 7 = 4 ones. Now 2 tens are left.
Tens: 2 is too few for 4, so open a hundred: 12 - 4 = 8 tens. Now 4 hundreds are left.
Hundreds: 4 - 2 = 2.
531 - 247 = 284

2 hundreds, 8 tens and 4 ones are left: 284.

Example 4: Nothing to lend

703 - 258. The tens row has nothing to lend, so open the hundred first: 6 hundreds and 10 tens.
Then open a ten: 9 tens and 13 ones.
Ones: 13 - 8 = 5. Tens: 9 - 5 = 4. Hundreds: 6 - 2 = 4.
703 - 258 = 445

4 hundreds, 4 tens and 5 ones are left: 445.

Words to know

borrow: Trade one bead down for ten on the row below.
too few: A row that has fewer beads than the number to take away.
hundreds row: The top row. Each bead is worth a hundred.
open: Slide a bead down to trade it for ten on the row below.

Watch out

Look at each row before you start: which rows are too short?
Work from the ones up to the hundreds, row by row.
After a row lends a ten, it has one fewer bead. Count that before you take away from it.

Try it

What is 375 - 142?
What is 462 - 138?
What is 541 - 267?
What is 602 - 345?

Answers: 1. 233 · 2. 324 · 3. 274 · 4. 257

Try at homeAsk a grown-up to help you sort a pile of cards or stickers into groups of one hundred, groups of ten, and singles. Give some to a friend. Which group did you have to open?

For grown-upsSort a pile of cards or stickers into hundreds, tens and singles. Give some away and ask which group your child had to open.

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