The UT Method
Units and Tens as two separate lanes: one lane produces answer digits, the other produces the carry. Multi-digit multiplication becomes a leftward walk.
1. The core idea
- Units lane: the only lane that writes digits into the answer.
- Tens lane: computes only the carry, and hands it to the next column. It never mixes with the answer digits.
- Pair products: each column uses one cross-product pair (adjacent digit combinations) plus the carry coming in.
Good for: 3-digit × 2-digit, 4-digit × 2-digit (for example 4312 × 42). Not worth it for single digits — the multiplication tables are already faster.
Learn this after LR multiplication and the bridge method. Otherwise you will "recite the procedure" instead of computing numbers, and end up slower.
2. Start with two digits: 86 × 23 = 1978
- Right column (last × last): 6 × 3 = 18 → write 8, carry 1
- Middle column (cross sum + carry): 8 × 3 + 6 × 2 = 24 + 12 = 36, + 1 = 37 → write 7, carry 3
- Left column (first × first + carry): 8 × 2 = 16, + 3 = 19
- Answer: 1978
UT is simply the bridge method rewritten as "units lane / tens lane" — the arithmetic is identical, the bookkeeping is stricter.
3. Multi-digit × two digits: walk leftwards
With a 4-digit multiplicand you repeat the same two moves four times, moving one place left each time: compute the units digit, compute the carry. Below are the book's standard questions — try each one before you look at the answers.
4. Practice
- 86 × 23
- 68 × 74
- 213 × 34
- 5743 × 63 (challenge)
- 4312 × 42, then verify with DS
Answers
Three questions a day, computed with UT and then verified with DS. Within a week the carry stops being something you say out loud.
Previous lesson: The Vitruvian Man Method