Technique explanation
Teaching Explanation
Once we have calculated the values for our five "buckets" (from Lesson 17), we must combine them into a single number. Because each bucket (except the leftmost) represents a specific place value (units, tens, hundreds, etc.), it can only hold one digit. If a bucket has two digits, like 18, we keep the right digit (8) and "carry" the left digit (1) to the next bucket on the left. We always start this process from the right side and move left, adding the carry to the next bucket's total before deciding what to carry again.
Method Condition
This method is applicable when: 3-digit multiplication where one or more zone products exceed 9.
Standard Fallback
If this method is not suitable, use: Standard long multiplication.
Misconception & Correction
Misconception: Carrying the units digit and keeping the tens digit (e.g., in 18, keeping the 1 and carrying the 8). Correction: The units digit of any sum is the only part that "belongs" in that place value. All higher digits represent multiples of the next place value and must be moved.
Worked examples
Worked Examples
| Step | Example 1: 4 \ | 13 \ | 28 \ | 27 \ | 18 | Example 2: 6 \ | 11 \ | 12 \ | 9 \ | 2 |
|---|---|---|---|---|---|---|---|---|---|---|
| 1. Zone 1 (R) | Keep 8, Carry 1 | Keep 2, Carry 0 | ||||||||
| 2. Zone 2 | 27 + 1 = 28; Keep 8, Carry 2 | 9 + 0 = 9; Keep 9, Carry 0 | ||||||||
| 3. Zone 3 | 28 + 2 = 30; Keep 0, Carry 3 | 12 + 0 = 12; Keep 2, Carry 1 | ||||||||
| 4. Zone 4 | 13 + 3 = 16; Keep 6, Carry 1 | 11 + 1 = 12; Keep 2, Carry 1 | ||||||||
| 5. Zone 5 (L) | 4 + 1 = 5; Keep 5 | 6 + 1 = 7; Keep 7 | ||||||||
| Final Result | 56088 | 72292 | ||||||||
| Independent Check | 123 × 456 = 56088 | 212 × 341 = 72292 |
Always perform an independent check to verify your result.
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