Start with the ones
To work out 247 × 3 in columns, write 247 and put the 3 under its ones digit. Then multiply each digit of 247 by 3, one column at a time, starting with the ones.
Ones: 7 × 3 = 21. 21 ones are 2 tens and 1 one. Write the 1 in the ones column of the answer, and carry the 2 tens: write a small 2 above the tens column.
7 × 3 = 21. The 1 is written in the ones column, and the carried 2 sits above the tens.
Multiply, then add the carry
Tens: 4 × 3 = 12, which is 12 tens. Add the 2 tens carried from the ones: 12 + 2 = 14 tens. 14 tens are 1 hundred and 4 tens, so write 4 in the tens column and carry 1 hundred above the hundreds column.
Multiply first, then add the carry. Adding the carry first, 4 + 2 = 6 and then 6 × 3 = 18, multiplies the carried tens by 3 a second time.
4 × 3 = 12, and the carried 2 makes 14. The 4 is written in the tens column, and 1 hundred is carried.
The last column
Hundreds: 2 × 3 = 6, and the carried 1 makes 7. Write 7 in the hundreds column. So 247 × 3 = 741.
Check with an estimate: 247 is about 250, and 250 × 3 = 750. 741 is close to 750.
2 × 3 = 6, and the carried 1 makes 7. The answer is 741.
Where the carries come from
Multiplying in columns is multiplying by splitting, written down. 247 is 200 + 40 + 7, so 247 × 3 = 200 × 3 + 40 × 3 + 7 × 3 = 600 + 120 + 21 = 741.
Each column works out one of those parts. The 21 from the ones has 2 tens in it, and the carry moves them into the tens column. The 120 from the tens has 1 hundred in it, and the next carry moves it into the hundreds column.
247 is split into 200, 40 and 7, and each part is multiplied by 3.
Four digits
A longer number takes more columns and the same steps. For 1324 × 4: 4 × 4 = 16, so write 6 and carry 1 ten. 2 × 4 = 8, and the carried 1 makes 9. 3 × 4 = 12, so write 2 and carry 1 thousand. 1 × 4 = 4, and the carried 1 makes 5. So 1324 × 4 = 5296.
A carry that is left out makes the answer too small. If the carried thousand is forgotten, the answer comes out as 4296, one thousand short.
1324 × 4 = 5296. One ten is carried from the ones, and one thousand is carried from the hundreds.