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How It Works
The lattice method places digits along the top and right of a grid. Each cell holds a single-digit product split by a diagonal: tens above, ones below. You then sum along each diagonal from right to left, carrying when the total exceeds 9, to read off the final answer.
Example Problem
Multiply 34 × 13 with the lattice method:
- Grid cells: 3×1 = 0/3, 4×1 = 0/4, 3×3 = 0/9, 4×3 = 1/2.
- Sum diagonals right to left: 2, 9+4+1 = 14 (write 4 carry 1), 3+0+0+1 = 4, 0.
- Result: 442.
Frequently Asked Questions
What is lattice multiplication?
Lattice multiplication is a grid-based method that reduces multi-digit multiplication to single-digit products arranged in cells with diagonal lines. Summing along the diagonals produces the final answer. It dates back to at least the 13th century.
Is lattice multiplication faster than the standard algorithm?
It is not necessarily faster, but many students find it easier because it separates multiplication from addition and carries happen only during the diagonal sums, reducing errors.
Can the lattice method multiply numbers with different digit counts?
Yes. A 3-digit by 2-digit multiplication simply uses a 3×2 grid. For 245 × 13, you build a grid with 6 cells and sum 5 diagonals, giving 3,185.
Related Calculators
- Grid Multiplication Calculator — multiply using the box/area model.
- Addition Calculator — traditional column addition with shown work.
- Long Division Calculator — step-by-step long division.
- Fraction Multiplication Calculator — multiply fractions with step-by-step work.
- Statistics Calculator — compute mean, median, and standard deviation from data sets.