This lattice multiplication worksheet helps students master double-digit multiplication using the grid method.

Let’s solve each multiplication problem using lattice multiplication. I’ll go step by step for each one, then give the final answers.

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Problem 1: 38 × 29
*(Already solved in example — answer is 1102)*
We’ll skip this since it’s given.

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Problem 2: 12 × 34

Set up a 2x2 grid (since both are 2-digit numbers).

Top row: 1 and 2
Right column: 3 and 4

Fill each box with product of top digit and right digit:

- Top-left: 1 × 3 = 03 → write 0 above diagonal, 3 below
- Top-right: 2 × 3 = 06 → 0 above, 6 below
- Bottom-left: 1 × 4 = 04 → 0 above, 4 below
- Bottom-right: 2 × 4 = 08 → 0 above, 8 below

Now add along diagonals from bottom-right to top-left:

Diagonal 1 (bottom-right): 8 → write 8
Diagonal 2: 6 + 4 + 0 = 10 → write 0, carry 1
Diagonal 3: 3 + 0 + 0 + 1 (carry) = 4
Diagonal 4 (top-left): 0 → but we don’t write leading zero

So reading left to right: 4, 0, 8 → 408

✔ Check: 12 × 34 = (10+2)(30+4) = 300 + 40 + 60 + 8 = 408 ✔️

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Problem 3: 81 × 30

Grid: top digits 8, 1; right digits 3, 0

Boxes:

- 8×3 = 24 → 2/4
- 1×3 = 03 → 0/3
- 8×0 = 00 → 0/0
- 1×0 = 00 → 0/0

Add diagonals:

Bottom-right diagonal: 0 → 0
Next: 0 + 0 + 0 = 0
Next: 4 + 3 + 0 = 7
Next: 2 + 0 = 2
Top-left: 0 → ignore

Result: 2, 7, 0, 0 → 2430

✔ Check: 81 × 30 = 81 × 3 × 10 = 243 × 10 = 2430 ✔️

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Problem 4: 26 × 56

Grid: top 2,6; right 5,6

Boxes:

- 2×5 = 10 → 1/0
- 6×5 = 30 → 3/0
- 2×6 = 12 → 1/2
- 6×6 = 36 → 3/6

Add diagonals:

Bottom-right: 6 → 6
Next: 0 + 2 + 3 = 5
Next: 0 + 3 + 1 + 1 = 5? Wait — let's label positions clearly.

Actually, better to draw mentally:

Diagonals (from bottom-right up):

1. Only bottom-right cell lower triangle: 6 → sum = 6
2. Next diagonal: bottom-left lower (0) + top-right lower (2) + bottom-right upper (3) → 0 + 2 + 3 = 5
Wait — no, standard lattice adds along diagonals going from bottom-right to top-left, combining upper and lower parts appropriately.

Let me reorganize:

Label cells:

Cell A (top-left): 2×5 = 10 → upper=1, lower=0
Cell B (top-right): 6×5 = 30 → upper=3, lower=0
Cell C (bottom-left): 2×6 = 12 → upper=1, lower=2
Cell D (bottom-right): 6×6 = 36 → upper=3, lower=6

Now diagonals (starting from bottom-right corner, moving up-left):

Diagonal 1: only D’s lower part → 6
Diagonal 2: D’s upper (3) + C’s lower (2) + B’s lower (0) → 3 + 2 + 0 = 5
Diagonal 3: C’s upper (1) + B’s upper (3) + A’s lower (0) → 1 + 3 + 0 = 4
Diagonal 4: A’s upper (1) → 1

So digits: 1, 4, 5, 6 → 1456

✔ Check: 26 × 56
26 × 50 = 1300
26 × 6 = 156
Total = 1300 + 156 = 1456 ✔️

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Problem 5: 71 × 23

Grid: top 7,1; right 2,3

Cells:

A (7×2)=14 → 1/4
B (1×2)=02 → 0/2
C (7×3)=21 → 2/1
D (1×3)=03 → 0/3

Diagonals:

1. D lower: 3
2. D upper (0) + C lower (1) + B lower (2) → 0 + 1 + 2 = 3
3. C upper (2) + B upper (0) + A lower (4) → 2 + 0 + 4 = 6
4. A upper (1) → 1

Digits: 1, 6, 3, 3 → 1633

✔ Check: 71 × 23
70×23 = 1610
1×23 = 23
Total = 1610 + 23 = 1633 ✔️

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Problem 6: 53 × 72

Grid: top 5,3; right 7,2

Cells:

A (5×7)=35 → 3/5
B (3×7)=21 → 2/1
C (5×2)=10 → 1/0
D (3×2)=06 → 0/6

Diagonals:

1. D lower: 6
2. D upper (0) + C lower (0) + B lower (1) → 0 + 0 + 1 = 1
3. C upper (1) + B upper (2) + A lower (5) → 1 + 2 + 5 = 8
4. A upper (3) → 3

Digits: 3, 8, 1, 6 → 3816

✔ Check: 53 × 72
50×72 = 3600
3×72 = 216
Total = 3600 + 216 = 3816 ✔️

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Final Answer:
12 × 34 = 408
81 × 30 = 2430
26 × 56 = 1456
71 × 23 = 1633
53 × 72 = 3816