Skip to content
QQuanta KidsBy IIT & ISB Alumni
Sign up
← Back to Addition & Subtraction
1Story Translators2The Hopping Map3Number Smashers4The Column Stack5The Missing Piece6The Rewind Button7Estimate & Check

Concept 3 of 7

Number Smashers: The Partition Method

Free
1

Today's big idea

Big numbers are easier in pieces, whichever way you are going.

Split by place value, then add the matching pieces or take the chunks away in stages.

2

How it works

👀 What's going on?

Add 4,250 + 3,180 in your head and it feels like juggling four things at once. Take 3,180 back off 7,430 and it feels the same. Big numbers are hard to hold whole, whichever way you are going. So do not hold them whole. Smash them into place-value pieces and deal with one piece at a time.

💡 Here's the trick

ADDING · pair the matching pieces💥THOUSANDSHUNDREDSTENS4,2503,180+4,0003,00020010050807,000300130130 is over 100, so it spills up7,000 + 300 + 130 = 7,430SUBTRACTING · smash only the 3,180, then take its chunks off7,4304,4304,3304,250− 3,000− 100− 80back on 4,250, exactly where the adding started

Look at the picture above. It shows the same two numbers twice. In the top half both are smashed and the matching rooms are added, giving 7,000, 300 and 130, which join to 7,430. In the bottom half only the 3,180 is smashed, and its chunks come off 7,430 one at a time. Taking 3,000, then 100, then 80 walks you straight back to 4,250, where the adding began.

🪄 How to do it

  1. 1.Break a number apart by place value, the way the picture above smashes it into rooms.
  2. 2.Adding, smash both numbers and add the matching pieces, then join the chunk answers.
  3. 3.Subtracting, smash only the number being taken away, then remove its chunks one at a time.

✍️ Try it

First add 3,624 + 2,158. Then work out 7,463 − 3,185. The second one needs the other move.

For the sum, pair the pieces: 5,000, then 700, then 70, then 12. Joining those gives 5,782, and the 12 shows a pair can spill into the next room. For the difference, smash only the 3,185 and take it off in stages. From 7,463 take 3,000 to reach 4,463. Then 100 leaves 4,363, then 80 leaves 4,283, then 5 leaves 4,278.

⚠️ Watch out

You might be thinking subtraction pairs the pieces off in the same way. Try that on 7,463 − 3,185 and the tens hand you 60 take away 80. There is no way to write that down here. Smash only the number you are taking away, then remove its chunks in stages.

🌟 Why this matters

This is how people work out prices in their head at a shop, thousands first, then the small change. Knocking 3,000 off a bill in one go, then the rest, is the same habit. Splitting a big job into pieces you can hold works far beyond maths.
Exam tip: Partitioning is the foundation under every mental-maths shortcut for big numbers.

3

Watch me solve one

Quanta solves it

“Watch how I think through one of these — then you try.”

THE PROBLEM

“3,620 + 2,540 — add by smashing each into pieces.”

  1. 1

    Smash 3,620 🔨

    Split by place value: 3,000 + 600 + 20.

  2. 2

    Smash 2,540 🔨

    Split it too: 2,000 + 500 + 40.

  3. 3

    Add matching pieces

    Thousands: 5,000. Hundreds: 1,100. Tens: 60.

  4. 4

    Glue them back

    5,000 + 1,100 + 60 = 6,160

  5. 5

    Now the other way 🔄

    Take the 2,540 back off. Smash only the 2,540, because pairing pieces would ask for 20 − 40.

  6. 6

    Chunks off in stages ✓

    6,160 −2,000→ 4,160 −500→ 3,660 −40→ 3,620

Now you try one — same steps, different story 👇

4

See it in action

⚡ Time to play!

Tap each digit to smash it into its place-value piece — every room counts!

🔨 tap the digits

🔨 tap the digits

5

Quick check

✅ VERIFICATION

To work out 8,540 − 2,300 by smashing, what should you do?

⚡ Finish the activity above first to answer.

Keep going!

Up next: The Column Stack

Carry and borrow your way through columns full of empty rooms.

Concept 4 of 7 →