Arithmetic Operations
Long Multiplication – Full Step-by-Step Guide
Long multiplication is used when both numbers have two or more digits. It breaks the problem into smaller multiplications using the distributive property.
The Method
- Write the larger number on top, the smaller below.
- Multiply the entire top number by the ones digit of the bottom number.
- Write a zero as a placeholder and multiply the top number by the tens digit.
- Add the two partial products.
Worked Example: 43 × 27
Step by Step
Step 1: 43 × 7 = 301.
Step 2: 43 × 20 = 860 (write 43×2=86, then add one zero → 860).
Step 3: 301 + 860 = 1,161
Try It Step by Step: 43 × 27
Click through each step below to watch the two partial products build up and combine into the final answer.
Partial product (ones)
Partial product (tens)
43
×27
301
860
1161
43 × 27 = ?
Click Step 1 or Auto Play to begin multiplying 43 by 27!
43 × 27 = 1,161
Two partial products, added together, give the final answer.
Two partial products, added together, give the final answer.
Worked Example: 256 × 34
Three-digit × two-digit
256 × 4 = 1,024.
256 × 30 = 7,680.
1,024 + 7,680 = 8,704
Three-Digit Multiplier: 125 × 312
Advanced
125 × 2 = 250.
125 × 10 = 1,250.
125 × 300 = 37,500.
250 + 1,250 + 37,500 = 39,000
Key Takeaways
- Each row is one partial product: multiply by ones, then tens, then hundreds.
- Add one placeholder zero for the tens row, two for the hundreds row, etc.
- Add all partial products to get the final answer.
- Estimate to check: 43 × 27 ≈ 40 × 30 = 1,200 ✓
Practice: Long Multiply
Two multi-digit numbers are shown below. If you get it wrong (or leave it blank), we'll break it into partial products together.
Calculate the product.