LR Multiplication & Splitting
Three routes to the same product: split by place value, round up and compensate, or factor into easier pieces. Pick whichever needs the fewest intermediate numbers.
1. The three routes
- Split: break the multiplier into place values. 4312 × 42 → 4312 × 40 + 4312 × 2.
- Round and compensate: use a nearby round multiplier, then subtract the excess. 68 × 52 → 68 × 50 + 68 × 2.
- Factor: replace one factor with smaller factors. 24 × 35 → 24 × 5 × 7.
The decision rule
Count the intermediate results each route needs. Choose the route with the fewest, and always multiply from the left so the leading digits of the answer are settled first.
Two special divisors behave better as multiplications: ÷25 = ×4 ÷ 100, ÷125 = ×8 ÷ 1000, ÷5 = ×2 ÷ 10. The full treatment is in the flagpole division lesson.
2. Worked examples
4312 × 42 — split
- 4312 × 40 = 172480
- 4312 × 2 = 8624
- 172480 + 8624 = 181104
- DS: DS(4312) = 1, DS(42) = 6 → 6; DS(181104) = 15 → 6 ✓
68 × 52 — round and compensate: 68 × 50 = 3400, 68 × 2 = 136 → 3536.
24 × 35 — factor: 24 × 5 = 120, 120 × 7 = 840.
3. Live demo
Watch the answer grow digit by digit
The demo is computed in your browser; nothing is sent anywhere.
4. Practice
- 4312 × 42 (split)
- 68 × 52 (round and compensate)
- 24 × 35 (factor)
- 96 × 25
- 7142 × 6
Answers
1) 181104. 2) 3536. 3) 840. 4) 2400 (96 ÷ 4 × 100). 5) 42852.
Previous lesson: LR Addition & Subtraction