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Lattice Multiplication – Definition, Examples | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">Lattice MultiplicationLattice Multiplication – Definition, ExamplesTable of ContentsLattice Multiplication Definition of Lattice Multiplication

Lattice multiplication is a method of multiplication in which we use a lattice grid to multiply two or more large numbers. Unlike traditional long multiplication, this method uses a visual framework or structure resembling a lattice (a framework of crossed strips) to organize and simplify the multiplication process. The method works by breaking down the numbers being multiplied with the help of a lattice structure, making the multiplication process more visual and easier to understand.

To multiply an m-digit number by an n-digit number, we draw a lattice of order m×nm \times nm×n. The smallest grid used is a 2×22 \times 22×2 grid. Each digit of the first number is assigned to an individual column, while each digit of the second number is assigned to a row. The products of these digits are placed in the corresponding cells, and then numbers along diagonals are added to find the final product.

Examples of Lattice Multiplication Example 1: Multiplying Two Two-Digit Numbers Problem:

Find 23×3623 \times 3623×36 using lattice multiplication.

Step-by-step solution: Step 1, Draw the lattice. Since we are multiplying two two-digit numbers, we need to draw a 2×22 \times 22×2 grid.

2×2 lattice grid for multiplication

Step 2, Label the lattice. Assign each digit of 232323 to individual columns and each digit of 363636 to individual rows.

2×2 lattice grid for multiplication

Step 3, Multiply the numbers in the following pattern:

First row × First Column: 3×2=63 \times 2 = 63×2=6 First row × Second Column: 3×3=93 \times 3 = 93×3=9 Second row × First Column: 6×2=126 \times 2 = 126×2=12 Second row × Second Column: 6×3=186 \times 3 = 186×3=18

Write each product in the corresponding cell, with tens digit above the diagonal and ones digit below.

Step 4, Add the numbers in each diagonal. Start from the bottom right corner and work your way to the top left. If the sum is two digits, carry over the tens digit to the next diagonal.

Bottom right diagonal: 888 Middle diagonal: 2+9+1=122 + 9 + 1 = 122+9+1=12, write 222 and carry 111 Top left diagonal: 6+1=76 + 1 = 76+1=7 Final number: 828828828

2×2 lattice grid for multiplication

Step 5, Write the final product by reading the numbers from top left to bottom right: 828828828.

Therefore, 23×36=82823 \times 36 = 82823×36=828.

Example 2: Multiplying a Two-Digit Number by a One-Digit Number Problem:

Find the product of 979797 and 999 using lattice multiplication.

Step-by-step solution:

Step 1, Draw a 2×12 \times 12×1 grid since we're multiplying a two-digit number by a one-digit number.

Step 2, Label the grid with 999 and 777 on top (columns) and 999 on the left (row).

2×1 lattice grid for multiplication

Step 3, Multiply the numbers:

9×9=819 \times 9 = 819×9=81 7×9=637 \times 9 = 637×9=63 Write these products in their respective cells, with tens digit above diagonal and ones digit below.

Step 4, Add along the diagonals:

Bottom right diagonal: 333 Middle diagonal: 6+1=76 + 1 = 76+1=7 Top left diagonal: 888 Final number: 873873873 2×1 lattice grid for multiplication

Therefore, the product of 979797 and 999 is 873873873.

Example 3: Multiplying with Decimals Problem:

Find the product of 32.532.532.5 and 666.

Step-by-step solution: Step 1, Draw a 3×13 \times 13×1 grid for this multiplication. Label the columns with 333, 222, and 555 (the digits of 32.532.532.5) and the row with 666.

3×1 lattice grid for multiplication

Step 2, Multiply each digit: 3×6=183 \times 6 = 183×6=18 2×6=122 \times 6 = 122×6=12 5×6=305 \times 6 = 305×6=30 Write these products in the respective cells with tens digits above diagonals and ones digits below.

3×1 lattice grid for multiplication

Step 3, Add along the diagonals: Bottom right diagonal: 000 Second diagonal from right: 3+2=53 + 2 = 53+2=5 Third diagonal from right: 1+8=91 + 8 = 91+8=9 Top left diagonal: 111 Final number: 195195195

3×1 lattice grid for multiplication

Step 4, Place the decimal point in the answer. Since 32.532.532.5 has one decimal place and 666 has none, the product will have one decimal place. However, in this case, the decimal point falls after all the digits, so the answer is 195195195.

Therefore, 32.5×6=19532.5 \times 6 = 19532.5×6=195.

Comments(6)MMusicianFrankNovember 4, 2025I've been using lattice multiplication to teach my students. It's a great visual way that makes multiplying large numbers so much easier for them to grasp!

MCMs. CarterSeptember 17, 2025I’ve been struggling to help my kids with multiplication, but this lattice multiplication method made it so much easier! The step-by-step examples were super clear, and now they actually enjoy practicing. Thanks for such a helpful resource!

MCMs. CarterSeptember 10, 2025I’ve been struggling to teach my kids multiplication, but this lattice method made it so much easier! The grid really helps them stay organized, and the examples were super clear. Thanks for this resource!

NNatureLover25August 27, 2025I used the lattice multiplication method with my 5th grader, and it made multiplying big numbers so much easier for him! The grid system really helps organize the steps. Highly recommend it for visual learners!

MCMs. CarterAugust 20, 2025I’ve used the lattice multiplication method with my 5th grader, and it’s been a game-changer! The grid makes it easy to follow, especially for visual learners. Great explanation and examples here!

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