The Bridge Method
Two-digit products in a single pass: first × first, the cross terms, last × last. Three columns, one answer, no intermediate products written down.
1. The three columns
- Left column: first digit × first digit.
- Middle column: the cross terms (a × d + b × c).
- Right column: last digit × last digit.
- Merge from the right, carrying anything over 9 into the neighbouring column.
Fixed path: 23 × 41
3 × 1 = 3; then 2 × 1 + 3 × 4 = 14 → write 4, carry 1; then 2 × 4 = 8, plus the carry = 9 → 943.
2. Worked examples
12 × 13
- Right: 2 × 3 = 6
- Middle: 1 × 3 + 2 × 1 = 5
- Left: 1 × 1 = 1
- Answer: 156
32 × 13 with a carry
- Right: 2 × 3 = 6
- Middle: 3 × 3 + 2 × 1 = 11 → write 1, carry 1
- Left: 3 × 1 = 3, plus carry = 4
- Answer: 416
3. Live demo
Type two numbers and see how the three columns merge
The demo is computed in your browser; nothing is sent anywhere.
4. Practice
- 12 × 13
- 32 × 13
- 41 × 23
- 54 × 32 — this one carries twice
- Write your own pair where the middle column exceeds 20
Answers
1) 156. 2) 416. 3) 943. 4) 1728 (4×2 = 8; 5×2 + 4×3 = 22 → 2 carry 2; 5×3 + 2 = 17 → 17|2|8). 5) e.g. 67 × 89: 63 cross = 6×9 + 7×8 = 110 → 110 carries twice.
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