Concept 1 of 9
Long Multiplication at Scale
Today's big idea
One row per digit, and each row starts with one more zero than the row above.
Each row shifts one more zero than the row above it before you add them up.
How it works
👀 What's going on?
Two rows handled 243 x 26 last year. A stadium with 1,248 seats in each of 36 blocks needs the same method on bigger numbers. Nothing about the method changes. Only the rows get longer.
💡 Here's the trick
Look at the sum above. The first row is 1,248 x 6, and the second is 1,248 x 30, so it starts with a 0. That is the same two-row shape as before, just with a four-digit number on top. When the bottom number has three digits you get three rows, and each one starts with one more 0 than the row above it. A row for hundreds carries two zeros, because you are multiplying by 300 and the answer lands two columns to the left. Count the zeros off the place you are multiplying by and the rows line themselves up.
🪄 How to do it
- 1.Write one row per digit of the bottom number, as the sum above does.
- 2.Start each row with one more 0 than the row above it, then multiply.
- 3.Add every row together.
✍️ Try it
Work out 214 x 132. You will need a row for the 2, a row for the 30 and a row for the 100.
The rows are 214 x 2 = 428, then 214 x 30 = 6,420, then 214 x 100 = 21,400. Adding all three gives 28,248. The last row carries two zeros because 100 is hundreds, and it is also the largest by far.
⚠️ Watch out
You might be thinking a third row needs only one 0, the way the second row did. It needs two. Give the hundreds row a single 0 and 21,400 becomes 2,140. That drops your total by more than 19,000, and it still looks like a sensible answer.
🌟 Why this matters
Working out a year of something monthly, or the seats in a stadium, lands on numbers this size. The method also underpins the estimation questions where you round first and multiply the rounded values.
Exam tip: Write every row's zeros before you multiply anything, so the shape is right before the arithmetic starts.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“Work out 1,248 × 36 using the column method.”
- 1
One row per bottom digit
36 has two digits, so there are two rows: one for the 6, one for the 30.
- 2
Row 1 — the ones
1,248 × 6 = 7,488
- 3
Row 2 — start with a 0
This row is × 30, not × 3, so it opens with a 0. 1,248 × 30 = 37,440
- 4
Add the rows ✓
7,488 + 37,440 = 44,928
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
THE PROBLEM
1,248 × 36
?1,248 × 6
···1,248 × 30
This row multiplies by 6. How many zeros does it start with?
Quick check
✅ VERIFICATION
In the column method for 326 x 145, how many zeros does the row for the 1 start with?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Long Division with Bigger Numbers
The rung that fits nothing still needs its digit.