Lattice multiplication

key notes :

✨ What is Lattice Multiplication?
  • Lattice multiplication is a special method of multiplying large numbers.
  • It uses a grid (lattice) to organize numbers and make multiplication easier.
  • Each box of the grid is divided diagonally to help place tens and ones clearly.
✨ Wha📝 Steps to Do Lattice Multiplication

Draw the lattice grid

  • Make a box with as many columns as digits in one number.
  • Make as many rows as digits in the other number.
  • Draw diagonals in each small box from top right to bottom left.

Write the numbers

  • Write one number across the top (one digit per column).
  • Write the other number down the right side (one digit per row).

Multiply each pair of digits

  • Fill each box with the product of the column and row digits.
  • Write the tens digit above the diagonal and the ones digit below the diagonal.

Add along the diagonals

  • Starting from the bottom right, add the numbers along each diagonal.
  • If the sum is more than 9, carry over to the next diagonal.

Write the final answer

  • Read the answer from the bottom left to the top right.
📊 Example

Multiply 23 × 45

  1. Draw a 2-column × 2-row grid.
  2. Write 23 on the top, 45 on the right side.
  3. Multiply each digit:
    • 2 × 4 = 8 → write as 08 in the box.
    • 2 × 5 = 10 → write 1 and 0.
    • 3 × 4 = 12 → write 1 and 2.
    • 3 × 5 = 15 → write 1 and 5.
  4. Add along diagonals.
  5. Final answer = 1035.
🎯 Why Use Lattice Multiplication?
  • Keeps work neat and organized.
  • Helps avoid mistakes with place value.
  • Makes big multiplications easier.
🌟 Key Points for Students
  • Always draw the diagonals carefully.
  • Write tens and ones in the correct triangles.
  • Add carefully along the diagonals.
  • Practice makes you faster!

Learn with an example

😃 Use the lattice method to find 35×62. Calculate the sum of each diagonal. Your answers for the sums will fill in the answer for the product.
35×62=?,???

Step 1

To multiply two numbers using the lattice method, make a table with the digits of the first factor along the top and the digits of the second factor down the right. Draw diagonal lines from the top right to the bottom left of each box in the table.

Step 2

Multiply the digits and enter their products in the table. The diagonal in each box separates the digits in each product. For 1-digit products, put a 0 to the left of the diagonal.

Step 3

Sum each diagonal starting from the bottom right. Make sure to carry for sums greater than 10. Here are the first two diagonals shown:

Find the sums for the rest of the diagonals. Pay attention to the carried digit.

Step 4

Rewrite these sums as a string of digits in order from top to bottom, then left to right. This is the product of the original factors.

So, 35×62=2,170.

😀 Use the lattice method to find 24×40. Calculate the sum of each diagonal. Your answers for the sums will fill in the answer for the product.
24×40=???

Step 1

To multiply two numbers using the lattice method, make a table with the digits of the first factor along the top and the digits of the second factor down the right. Draw diagonal lines from the top right to bottom left of each box in the table.

Step 2

Multiply the digits and enter their products in the table. The diagonal in each box separates the digits in each product. For 1-digit products, put a 0 to the left of the diagonal.

Step 3

Sum each diagonal starting from the bottom right. Make sure to carry for sums greater than 10. Here are the first two diagonals shown:

Find the sums for the rest of the diagonals.

Step 4

Rewrite these sums as a string of digits in order from top to bottom, then left to right, dropping the leading zero. This is the product of the original factors.

So, 24×40=960.

Let’s practice!