Use Long Multiplication: Four Digits by Two Digits

Long multiplication is a written method for multiplying 4-digit numbers by a 2-digit number. 

Example => 2564 x 32

1 => First, write the larger number above the smaller number. Make sure that the ones and the tens columns line up.

2 => Multiply the ones digit of the bottom number by the ones digit of the top number. 2 × 4 = 8. Write 8 under the ones.

3 => Multiply the ones digit of the bottom number by the tens digit of the top number. 2 × 6 = 12. Write 2 on the line and carry the 1.

4 => Multiply the ones digit of the bottom number by the hundreds digit of the top number. 2 × 5 = 10. Add the 1 you carried to make 11. Write 1 in the 100s column and carry the 1.

5 => Multiply the ones digit of the bottom number by the thousands digit of the top number. 2 × 2 = 4. Add the 1 you carried above the 2 to make 5, then write 5 in the thousands column of the first answer row.

6 => Write a 0 in the ones column below the first product. Now, you’re multiplying by 30, instead of 3!

7 => Multiply the tens digit of the bottom number by the ones digit of the top number. 3 × 4 = 12. Write 2 on the line, then carry 1.

8 => Multiply the tens digit of the bottom number by the tens digit of the top number. 3 × 6 = 18. Add the 1 you carried over to equal 19. Write 9 on the line and carry the 1.

9 => Multiply the tens digit of the bottom number by the hundreds digit of the top number. 3 × 5 = 15. Add the 1 you carried over to equal 16. Write the 6 on the line and carry the 1.

10 => Multiply the tens digit of the bottom number by the thousands digit of the top number. 3 × 2 = 6. Add the 1 you carried over to equal 7. Write 7 on the second row answer line.

11 => Add both the rows of products using column addition.

Now try a few practice questions!