Setting up a multiplication problem

Multiplying by a single-digit number

Write the larger number at the top and the smaller number at the bottom, aligned to the right. Multiply each digit of the top number by the corresponding digit at the bottom, starting with the ones, carrying over as you would when adding.

Example: 47 × 6

• Units: 7 × 6 = 42 -> write 2, carry 4
• Tens: 4 × 6 = 24, plus the carry 4 = 28 -> write 28

Result: 47 × 6 = 282

Multiplying by a multi-digit number

When the second number has several digits, you first multiply by each digit separately, shifting each row one place to the left (as you are multiplying by tens, hundreds, etc.), then add up all the intermediate results.

Example: 34 × 26

• 34 × 6 = 204 (units column)
• 34 × 20 = 680; written as 34 × 2 = 68, shifted one place to the left (so 680)
• Add together: 204 + 680 = 884

Answer: 34 × 26 = 884

Complete example: 123 × 45

• 123 × 5 = 615
• 123 × 40 = 4920 (123 × 4 = 492, shift one place)
• Addition: 615 + 4920 = 5535

Result: 123 × 45 = 5535

Pitfalls to avoid

• Forgetting to shift the second row (and subsequent rows) one place to the left.
• Making mistakes with the carry-overs in the multiplication, which can exceed 9 (for example, 8 × 9 = 72).
• Adding up the intermediate results incorrectly at the end.