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It is sometimes very hard to understand the process of multiplication and operations with really big figures. There are a leading number of ways of carrying out the multiplication process but the lattice method is one of the most visual methods which is very convenient. It is based on a grid that allows transforming a multiplication problem into several small multiplications.
The lattice method helps to understand how to multiply multi-digit numbers as it suggests carrying out each multiplication separately with the numbers collected in a grid. It is also known as the lattice multiplication method or lattice math method.
This guide seeks to help readers understand the principle of the lattice method, its operating procedure, and its application with the help of some samples.
What Does the Lattice Method Imply?
The lattice method represents the method where people solve multiplication problems visually. Instead of multiplying two big numbers at one shot, it becomes a necessity to draw a grid and carry out the multiplication of each number separately. In a grid, each cell has a diagonal line. The tens from the product are written above the diagonal while the units are written below it and after the multiplication
For example, instead of trying to solve a large multiplication problem in your head, the lattice method gives every multiplication step its own space.
Quick Answer
The lattice method is a grid-based technique for multiplying numbers. It separates individual multiplication products into tens and ones and then adds the numbers along diagonal lines to find the final answer.
How Does Lattice Method Multiplication Work?
Lattice method multiplication entails the use of a very easy to understand concept:
- First, we write down the numbers that need to be multiplied.
- Then we go ahead and build a grid that reflects the number of digits.
- Doing this requires us to draw diagonal lines across the boxes.
- Next, we need to carry out our multiplication by multiplying digit pairs.
- After getting the results from our multiplication we need to input them in the boxes correctly.
- Then we add the digits according to the diagonal lines to give us the final answer.
The method is useful for students practicing multiple digit multiplication as the grid provides clarity during the process.
How to Use the Lattice Method Step by Step
Let’s look at the process more closely.
Step 1: Write the Numbers
Suppose we want to solve:
23 × 14
Write 23 across the top of the grid and 14 along the side.
Because both numbers have two digits, we need a 2 × 2 grid.
Step 2: Draw the Lattice Grid
Draw a square divided into four smaller boxes. Then draw a diagonal line through each box.
These diagonal lines help separate the tens and ones places.
Step 3: Multiply Each Pair of Digits
Now multiply each digit from the top number by each digit from the side number.
For 23 × 14, calculate:
- 2 × 1 = 2
- 3 × 1 = 3
- 2 × 4 = 8
- 3 × 4 = 12
Write each answer in its corresponding box.
For a one-digit answer, you can write 0 in the tens position. For 12, write 1 in the tens position and 2 in the ones position.
Step 4: Add Along the Diagonals
Once every box is filled, start adding the numbers along the diagonal lines.
This combines the partial products according to their place values.
For our example:
23 × 14 = 322
You can check the answer using traditional multiplication:
23 × 14 = 23 × 10 + 23 × 4
= 230 + 92
= 322
The answer is the same.
Lattice Method Example: 23 × 14
Let’s summarize the example:
Problem:
23 × 14
Partial products:
- 2 × 1 = 02
- 3 × 1 = 03
- 2 × 4 = 08
- 3 × 4 = 12
After placing these products in the lattice and adding the diagonal values, we get:
322
This example shows why the lattice method can be helpful. Instead of handling the entire multiplication problem in several lines, each small multiplication has a clear location.
Another Lattice Multiplication Example: 123 × 24
Now let’s try a larger problem:
123 × 24
The first number has three digits and the second has two digits, so you create a 3 × 2 lattice.
Multiply each digit:
Multiply by 2
- 1 × 2 = 2
- 2 × 2 = 4
- 3 × 2 = 6
Multiply by 4
- 1 × 4 = 4
- 2 × 4 = 8
- 3 × 4 = 12
Place these products in the appropriate boxes and add the diagonal values.
The final answer is:
123 × 24 = 2,952
You can verify it with traditional multiplication:
123 × 20 = 2,460
123 × 4 = 492
2,460 + 492 = 2,952
Recommended Reading: What is a 15 out of 20?
Why Does the Lattice Method Work?
lattice multiplication is not a trick. It involves the same multiplication and place value concepts as traditional methods of multiplication.Each box indicates multiplication of two digits. The diagonal lines make it easier to make sure the tens and the ones are in their right places.
At the end you add up the digits along all diagonals, which gives you the total of the partial products.
What Is the Lattice Boltzmann Method?
The phrase lattice Boltzmann method may come up while looking for lattice method, but it signifies something completely diferente. The lattice Boltzmann method (LBM) is a computational method that is used in science and engineering in order to model fluid flows and other phenomena. It has some roots in statistical physics and finds application in fluid mechanics as well as computational modeling applications.
The lattice Boltzmann method should not be confused with the lattice multiplication method that is taught in elementary schools.
In other words:
Lattice method: An illustrative technique of multiplication; Lattice Boltzmann method: A computational technique for modeling physical effects. The two approaches bear the term “lattice,” but they refer to completely different processes.
Conclusion
The lattice multiplication technique is a handy graphic technique for solving multiplication problems because the technique of putting individual products into a grid and summing them up diagonally splits a complex multiplication process into several steps. Lattice multiplication is a great technique when you are learning multi-digit multiplication and place value, as any other technique, this one requires training.
Try first with easy tasks, like 23 x 14, and then proceed to more difficult numbers, the main thing is to know what is going on with each step and not just to remember how it is done in the grid. Practice and you will see that multiplication becomes simpler.
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