Lattice Multiplication Worksheets - Math Monks - Free Printable

Let’s solve each multiplication problem using lattice multiplication. Since we’re doing 2-digit by 2-digit, each grid is a 2x2 square with diagonals.

We’ll go one by one and fill in the grids mentally (or on paper), then add along the diagonals to get the final answer.

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Problem 1: 11 × 63

Break it down:
- Top row: 1 and 1
- Right column: 6 and 3

Fill the boxes:
- Top-left: 1×6 = 06 → write 0 above diagonal, 6 below
- Top-right: 1×3 = 03 → 0 / 3
- Bottom-left: 1×6 = 06 → 0 / 6
- Bottom-right: 1×3 = 03 → 0 / 3

Now add diagonally from bottom right:

Diagonal 1 (bottom right): 3
Diagonal 2: 6 + 0 + 0 = 6
Diagonal 3: 0 + 0 + 3 = 3? Wait — let me redraw this carefully.

Actually, better to do it step by step properly.

Lattice for 11 × 63:

Grid:

1 1
┌──────────┐
6 │ 0/6 │ 0/3 │
├─────┼─────┤
3 │ 0/6 │ 0/3 │
└─────┴─────┘

Now add diagonals from bottom right:

Rightmost diagonal: only 3 → 3
Next diagonal: 6 (from top-right) + 0 (from bottom-left) + 0 (from top-left lower)? Wait — no.

Standard way: diagonals go from bottom-right to top-left.

Label positions:

Top row: A B
Bottom row: C D

Where:
A = 1×6 = 06 → tens=0, units=6
B = 1×3 = 03 → tens=0, units=3
C = 1×6 = 06 → tens=0, units=6
D = 1×3 = 03 → tens=0, units=3

Now diagonals:

Start from bottom right: D's units → 3
Then next diagonal: D's tens + C's units + B's units → 0 + 6 + 3 = 9
Then next: C's tens + B's tens + A's units → 0 + 0 + 6 = 6
Then leftmost: A's tens → 0

So reading from left to right: 0, 6, 9, 3 → but leading zero doesn’t count → 693

Wait — that can’t be right because 11×63 should be 693? Let me check: 10×63=630, plus 1×63=63 → 630+63=693. Yes!

So 11 × 63 = 693

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Problem 2: 21 × 59

Break into digits: 2,1 and 5,9

Grid:

2 1
┌─────┬─────┐
5 │10/0 │ 5/0 │ ← 2×5=10, 1×5=5
├─────┼─────┤
9 │18/0 │ 9/0 │ ← 2×9=18, 1×9=9
└─────┴─────┘

Wait — actually, in lattice, you split each product into tens and units.

So:

Top-left: 2×5 = 10 → write 1 above diagonal, 0 below
Top-right: 1×5 = 5 → 0 above, 5 below
Bottom-left: 2×9 = 18 → 1 above, 8 below
Bottom-right: 1×9 = 9 → 0 above, 9 below

Now diagonals from bottom right:

Diag 1 (rightmost): 9
Diag 2: 8 (from bottom-left lower) + 5 (from top-right lower) + 0 (from bottom-right upper) → wait, no.

Better labeling:

Positions:

A (top-left): 2×5 = 10 → tens=1, units=0
B (top-right): 1×5 = 5 → tens=0, units=5
C (bottom-left): 2×9 = 18 → tens=1, units=8
D (bottom-right): 1×9 = 9 → tens=0, units=9

Diagonals (starting from bottom right):

1. D_units = 9
2. D_tens + C_units + B_units = 0 + 8 + 5 = 13 → write 3, carry 1
3. C_tens + B_tens + A_units + carry = 1 + 0 + 0 + 1 = 2
4. A_tens = 1

So number is 1, 2, 3, 9 → 1239

Check: 20×59 = 1180, 1×59=59 → 1180+59=1239 ✔️

So 21 × 59 = 1239

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Problem 3: 23 × 90

Digits: 2,3 and 9,0

Grid:

2 3
┌─────┬─────┐
9 │18/0 │27/0 │ ← 2×9=18, 3×9=27
├─────┼─────┤
0 │ 0/0 │ 0/0 │ ← 2×0=0, 3×0=0
└─────┴─────┘

Products:

A: 2×9=18 → 1/8
B: 3×9=27 → 2/7
C: 2×0=0 → 0/0
D: 3×0=0 → 0/0

Diagonals:

1. D_units = 0
2. D_tens + C_units + B_units = 0 + 0 + 7 = 7
3. C_tens + B_tens + A_units = 0 + 2 + 8 = 10 → write 0, carry 1
4. A_tens + carry = 1 + 1 = 2

So digits: 2, 0, 7, 0 → 2070

Check: 23×90 = 23×9×10 = 207×10 = 2070 ✔️

So 23 × 90 = 2070

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Problem 4: 47 × 32

Digits: 4,7 and 3,2

Grid:

4 7
┌─────┬─────┐
3 │12/0 │21/0 │ ← 4×3=12, 7×3=21
├─────┼─────┤
2 │ 8/0 │14/0 │ ← 4×2=8, 7×2=14
└──────────┘

Split:

A: 4×3=12 → 1/2
B: 7×3=21 → 2/1
C: 4×2=8 → 0/8
D: 7×2=14 → 1/4

Diagonals:

1. D_units = 4
2. D_tens + C_units + B_units = 1 + 8 + 1 = 10 → write 0, carry 1
3. C_tens + B_tens + A_units + carry = 0 + 2 + 2 + 1 = 5
4. A_tens = 1

Digits: 1, 5, 0, 4 → 1504

Check: 47×30=1410, 47×2=94 → 1410+94=1504 ✔️

So 47 × 32 = 1504

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Problem 5: 49 × 58

Digits: 4,9 and 5,8

Grid:

4 9
┌─────┬─────┐
5 │20/0 │45/0 │ ← 4×5=20, 9×5=45
├─────┼─────┤
8 │32/0 │72/0 │ ← 4×8=32, 9×8=72
└─────┴─────┘

Split:

A: 4×5=20 → 2/0
B: 9×5=45 → 4/5
C: 4×8=32 → 3/2
D: 9×8=72 → 7/2

Diagonals:

1. D_units = 2
2. D_tens + C_units + B_units = 7 + 2 + 5 = 14 → write 4, carry 1
3. C_tens + B_tens + A_units + carry = 3 + 4 + 0 + 1 = 8
4. A_tens = 2

Digits: 2, 8, 4, 2 → 2842

Check: 50×58=2900, minus 1×58=58 → 2900-58=2842 ✔️

So 49 × 58 = 2842

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Problem 6: 18 × 72

Digits: 1,8 and 7,2

Grid:

1 8
┌─────┬─────┐
7 │ 7/0 │56/0 │ ← 1×7=7, 8×7=56
├─────┼─────┤
2 │ 2/0 │16/0 │ ← 1×2=2, 8×2=16
└──────────┘

Split:

A: 1×7=7 → 0/7
B: 8×7=56 → 5/6
C: 1×2=2 → 0/2
D: 8×2=16 → 1/6

Diagonals:

1. D_units = 6
2. D_tens + C_units + B_units = 1 + 2 + 6 = 9
3. C_tens + B_tens + A_units = 0 + 5 + 7 = 12 → write 2, carry 1
4. A_tens + carry = 0 + 1 = 1

Digits: 1, 2, 9, 6 → 1296

Check: 18×70=1260, 18×2=36 → 1260+36=1296 ✔️

So 18 × 72 = 1296

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Problem 7: 46 × 15

Digits: 4,6 and 1,5

Grid:

4 6
┌─────┬─────┐
1 │ 4/0 │ 6/0 │ ← 4×1=4, 6×1=6
├─────┼─────┤
5 │20/0 │30/0 │ ← 4×5=20, 6×5=30
└─────┴─────┘

Split:

A: 4×1=4 → 0/4
B: 6×1=6 → 0/6
C: 4×5=20 → 2/0
D: 6×5=30 → 3/0

Diagonals:

1. D_units = 0
2. D_tens + C_units + B_units = 3 + 0 + 6 = 9
3. C_tens + B_tens + A_units = 2 + 0 + 4 = 6
4. A_tens = 0

Digits: 0,6,9,0 → 690

Check: 46×10=460, 46×5=230 → 460+230=690 ✔️

So 46 × 15 = 690

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Problem 8: 41 × 90

Digits: 4,1 and 9,0

Grid:

4 1
┌─────┬─────┐
9 │36/0 │ 9/0 │ ← 4×9=36, 1×9=9
├─────┼─────┤
0 │ 0/0 │ 0/0 │ ← 4×0=0, 1×0=0
└──────────┘

Split:

A: 4×9=36 → 3/6
B: 1×9=9 → 0/9
C: 4×0=0 → 0/0
D: 1×0=0 → 0/0

Diagonals:

1. D_units = 0
2. D_tens + C_units + B_units = 0 + 0 + 9 = 9
3. C_tens + B_tens + A_units = 0 + 0 + 6 = 6
4. A_tens = 3

Digits: 3,6,9,0 → 3690

Check: 41×90 = 41×9×10 = 369×10 = 3690 ✔️

So 41 × 90 = 3690

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Problem 9: 80 × 92

Digits: 8,0 and 9,2

Grid:

8 0
┌─────┬─────┐
9 │72/0 │ 0/0 │ ← 8×9=72, 0×9=0
├─────┼─────
2 │16/0 │ 0/0 │ ← 8×2=16, 0×2=0
└─────┴─────┘

Split:

A: 8×9=72 → 7/2
B: 0×9=0 → 0/0
C: 8×2=16 → 1/6
D: 0×2=0 → 0/0

Diagonals:

1. D_units = 0
2. D_tens + C_units + B_units = 0 + 6 + 0 = 6
3. C_tens + B_tens + A_units = 1 + 0 + 2 = 3
4. A_tens = 7

Digits: 7,3,6,0 → 7360

Check: 80×90=7200, 80×2=160 → 7200+160=7360 ✔️

So 80 × 92 = 7360

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Final Answer:
1. 693
2. 1239
3. 2070
4. 1504
5. 2842
6. 1296
7. 690
8. 3690
9. 7360