The ones row
To work out 24 × 36, split 36 into 30 + 6 and multiply 24 by each part. Each answer goes on its own row, and the two rows are added at the end.
Start with the ones digit of 36: 24 × 6. This is multiplying in columns: 4 × 6 = 24, so write 4 and carry 2 tens. Then 2 × 6 = 12, and the carried 2 makes 14. The first row is 144.
The gold 6 is the digit being multiplied by. The first row is 24 × 6 = 144.
The 3 is 3 tens
Next comes the 3 in 36. It is in the tens place, so it stands for 3 tens, which is 30. The second row is 24 × 30, not 24 × 3.
Work out 24 × 3 = 72, then multiply by 10: 24 × 30 = 720. In the column, write a 0 in the ones place first, then write 72 to the left of it. The 0 moves every digit of 72 one place to the left, and that is what multiplying by 10 does.
The second row is 24 × 30 = 720. The gold 0 holds the ones place, so 72 starts in the tens column.
Add the two rows
Add the two rows: 144 + 720 = 864. So 24 × 36 = 864.
Check with an estimate: 24 is about 20 and 36 is about 40, and 20 × 40 = 800. 864 is close to 800.
144 + 720 = 864.
Why there are two rows
The two rows are the two parts of 36. A rectangle 24 wide and 36 tall has an area of 24 × 36. Cut it across at 30, and it becomes two pieces: one 24 by 30, and one 24 by 6. The pieces are the two rows of the column method, and together they are the whole rectangle.
The piece 24 by 30 is 720, and the piece 24 by 6 is 144. Together they make 864.
The missing zero
Leaving out the 0 is the usual mistake. Then the second row is 72, and 144 + 72 = 216. The estimate says about 800, so 216 is far too small.
A three-digit number on top works the same way. For 125 × 23: 125 × 3 = 375, and 125 × 20 = 2500. Add the rows: 375 + 2500 = 2875.