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
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 Questions
- Calculate 36 × 24.
- Calculate 87 × 45.
- Calculate 124 × 23.
- A garden centre sells 148 pots per day. How many in 32 days?
- Calculate 305 × 47.