Concept 3 of 10
The Column Method: Long Multiplication
Today's big idea
The column method is the four-room grid folded into two stacked rows.
243 x 6 sits above 243 x 20, and the 0 is what makes the second row tens.
How it works
👀 What's going on?
The four-room rectangle works, but drawing it every time is slow, and for 243 x 26 the rooms get cramped. The column method is the same four rooms folded into two tidy lines. Nothing new is happening, it is just written faster.
💡 Here's the trick
Look at the two rows above. The top row multiplies 243 by the 6, and the bottom row multiplies 243 by the 20. Those are the same pieces the rectangle would have given you, just stacked instead of spread out. The bottom row is the reason for that 0 on the end. You are multiplying by 20, not by 2, so the answer lands one whole column to the left. Write the 0 first and every digit after it sits in the right place. Add the two rows and you have 243 x 26 = 6,318.
🪄 How to do it
- 1.Multiply the top number by the ones digit, the way the rows above do.
- 2.Write a 0 in the ones column, then multiply the top number by the tens digit.
- 3.Add your two rows together.
✍️ Try it
Work out 154 x 32. Do the row for 2 first, then the row for 30.
The first row is 154 x 2 = 308. The second row is 154 x 30, so write a 0 and then 154 x 3 = 462, giving 4,620. Adding 308 and 4,620 gives 4,928. Notice the second row is much bigger, because it counts thirty 154s and not three.
⚠️ Watch out
You might be thinking the 0 at the start of the second row is just decoration. It is doing the real work. Leave it out and 4,620 collapses into 462, so your total drops to 770 instead of 4,928. The 0 is what says this row counts tens.
🌟 Why this matters
Twenty-six boxes at 243 rupees each is one of these, and so is working out how many seats a hall holds from its rows. Two short rows and one addition beats juggling a big number in your head.
Exam tip: Write the 0 before you multiply, not after, so you can never forget it.
See it in action
⚡ Time to play!
THE PROBLEM
243 × 26
The four-room rectangle already knows this answer. The column method just folds each side of it into one row.
TOP ROW
the two rooms for the 6
BOTTOM ROW
the two rooms for the 20
Quick check
✅ VERIFICATION
In the column method for 137 x 24, what is the second row before you add?
⚡ Finish the activity above first to answer.
Keep going!
Up next: The Chunking Claw
Share candies fairly using big chunks first.