What Is Grid Method Multiplication? A Step-by-Step Guide

Imagine you are packing for a trip. If you just toss everything into your suitcase without organizing, it can get messy fast. 

But if you neatly separate your clothes, shoes, and accessories into different sections, everything fits perfectly, and packing becomes much easier.

Multiplication can feel the same way! 

When we try to solve a big multiplication problem all at once, it might seem tricky. But what if we could break it into smaller, easier steps? That’s where the grid method comes in.

In this guide, we’ll walk through this simple and effective way to multiply numbers step by step. 

Whether you’re just starting to learn multiplication or looking to get ahead in math, the grid method will make multiplying numbers feel as easy as packing a well-organized suitcase!

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What Is the Grid Method?

The grid method is a simple way to break down multiplication into smaller, easier steps. It’s like solving a puzzle—one piece at a time! 

You might also hear it called the box method or area method because we use a grid (or boxes) to organize our numbers before multiplying.

Imagine having to multiply big numbers like 25 × 15 or 56 × 112 without a calculator.

Instead of trying to solve it all at once, the grid method lets you split the numbers into tens and ones (or hundreds, tens, and ones for bigger numbers), multiply those smaller parts, and then add them all together to get the final answer. 

It’s like solving a puzzle—one piece at a time!

You May Also Like: How to Do Long Multiplication?

How Does the Grid Method Work?

To use the grid method, we follow these four simple steps:

1. Break Up the Numbers: Split each number into its place values (hundreds, tens, ones).

2. Draw a Grid: Create a box with the right number of rows and columns based on the place values.

3. Multiply Across the Grid: Multiply the numbers where each row and column meet.

4. Add Up the Results: Add up all the answers in the grid to get the final result.

It might seem like a lot at first, but once we go through an example together, it will all make sense!

Say we want to multiply 23 × 7—let’s see how the grid method helps us solve it step by step.

Step 1: Break Up the Numbers

Before multiplying, we split each number into its place values.

• We split 23 into 20 and 3 because 23 has two place values: tens (20) and ones (3). 

• The number 7 stays the same because it has just one place value.

Step 2: Draw a Grid 

Now, we get our grid ready:

Since 23 has two place values, we dedicate two columns (one for 20 and one for 3) to it. 

Since 7 has one place value, we dedicate one row to it. 

We also leave an extra column on the left for the × symbol to remind us we are multiplying.

x	20	3
7

Step 3: Multiply Across the Grid

Now, we multiply each number in the row by each number in the column:

• 20 × 7 = 140

• 3 × 7 = 21

We fill in the grid with these results:

x	20	3
7	140	21

Step 4: Add Up the Results

Now, we add the two results inside the grid:
140 + 21 = 161

So, 23 × 7 = 161.

And that’s it! 

Pretty simple, right?

Solved Examples

Now that we understand the grid method, we’ll explore how it works in different scenarios!

So far, we’ve seen how the grid method helps with smaller multiplications, but what happens when the numbers get bigger? The good news is that this method works just as well for two-digit by two-digit and even three-digit by two-digit multiplication.

Let’s see that in action!

Example 1: Multiplying a Two-Digit by a Two-Digit Number

We will multiply 34 × 12.  

Step 1: Break Up the Numbers

We split 34 into 30 and 4 because 34 has two place values: tens (30) and ones (4). 

The number 12 splits into 10 and 2 because it has tens (10) and ones (2).

Step 2: Draw a Grid

Since 34 has two place values, we create two columns (one for 30 and one for 4). 

Since 12 has two place values, we create two rows (one for 10 and one for 2). 

We also leave an extra column on the left for the × symbol to remind us we are multiplying.

x	30	4
10
2

Step 3: Multiply Across the Grid

Now, we multiply each number in the row by each number in the column:

• 30 × 10 = 300

• 30 × 2 = 60

• 4 × 10 = 40

• 4 × 2 = 8

We fill in the grid:

x	30	4
10	300	40
2	60	8

Step 4: Add Up the Results

Now, we add all the numbers in the grid:

300 + 60 + 40 + 8 = 408

So, 34 × 12 = 408.

Multiplying a Three-Digit by a One-Digit Number

Let’s multiply 145 × 6.

Step 1: Break Up the Numbers

We split 145 into 100, 40, and 5 because it has three place values: hundreds (100), tens (40), and ones (5).

The number 6 stays the same because it has only one place value.

Step 2: Draw a Grid

Since 34 has two place values, we create two columns (one for 30 and one for 4). 

Since 12 has two place values, we create two rows (one for 10 and one for 2). 

We also leave an extra column on the left for the × symbol to remind us we are multiplying.

x	100	40	5
6

Step 3: Multiply Across the Grid

Now, we multiply each number in the row by each number in the column:

• 100 × 6 = 600

• 40 × 6 = 240

• 5 × 6 = 30

We fill in the grid:

x	100	40	5
6	600	240	30

Step 4: Add Up the Results

Now, we add all the numbers inside the grid:

600 + 240 + 30 = 870

So, 145 × 6 = 870.

Multiplying a Three-Digit by a Two-Digit Number

Now, let’s see how the grid method helps when we’re multiplying 256 × 34.

Step 1: Break Up the Numbers

We split 256 into 200, 50, and 6 because it has three place values: hundreds (200), tens (50), and ones (6).

The number 34 splits into 30 and 4 because it has two place values: tens (30) and ones (4).

Step 2: Draw a Grid

Since 256 has three place values, we create three columns (one for 200, one for 50, and one for 6).

Since 34 has two place values, we create two rows (one for 30 and one for 4). 

We also leave an extra column on the left for the × symbol to remind us we are multiplying.

x	200	50	6
30
4

Step 3: Multiply Across the Grid

Now, we multiply each number in the row by each number in the column:

• 30 × 200 = 6000

• 30 × 50 = 1500

• 30 × 6 = 180

• 4 × 200 = 800

• 4 × 50 = 200

• 4 × 6 = 24

We fill in the grid:

x	200	50	6
30	6000	1500	180
4	800	200	24

Step 4: Add Up the Results

Now, we add all the numbers inside the grid. 

Since we’re working with large numbers, we can list them from biggest to smallest in order and use column addition to add them up.

   6000  

+ 1500  

+  800  

+  200  

+  180  

+   24  

------------

  8704  

• Add the ones: 0 + 0 + 0 + 0 + 0 + 4 = 4

• Add the tens: 0 + 0 + 0 + 0 + 8 + 2 = 10 (write 0, carry 1)

• Add the hundreds: 0 + 5 + 8 + 2 + 1 (carried) = 7

• Add the thousands: 6 + 1 = 8

So, the final answer is 256 × 34 = 8704.

Try It Yourself! Practice Grid Multiplication

Now it’s your turn! Use the grid method to solve these multiplication problems.

When you’re done, check how you did at the bottom of the guide.

Task 1: Two-Digit by One-Digit

Solve: 42 × 6

Task 2: Two-Digit by Two-Digit

Solve: 36 × 14

Task 3: Three-Digit by One-Digit

Solve: 125 × 8

Task 4: Three-Digit by Two-Digit 

Solve: 203 × 12

FAQs About the Grid Method Multiplication

Learning about the grid method of multiplication doesn’t come without questions. Here are the ones we usually get from students and parents.

1) When do students typically learn the grid method?

Most students learn the grid method in 3rd or 4th grade when they begin multiplying larger numbers and need a structured way to organize their work.

2) What if one of my numbers has a zero in it?

Zeros can seem confusing, but just treat them like any other number! If you’re multiplying 304 × 5, split 304 into 300, 0, and 4. The zero will create a 0 in the grid, which doesn’t change the final sum.

3) Can I use the grid method for multiplying decimals?

Yes! The grid method works for decimals just like it does for whole numbers. The key is to ignore the decimal points at first and multiply as if they weren’t there.

Once you have your final sum, count the total number of decimal places in the original numbers. Then, move the decimal point that many places from the right in your answer. 

For example, to solve 2.3 × 1.4, we first multiply 23 × 14, which gives 322. Since the original numbers have a total of two decimal places, we move the decimal two places from the right, giving us 3.22.

4) What are some common mistakes to watch out for when doing grid multiplication?

Here are a few things to be careful about:

• Forgetting a box: Make sure you multiply every part of each number.

• Skipping a step when adding: Always add all the numbers in the grid.

• Misplacing numbers: If you don’t line up place values correctly, the final sum will be wrong.

• Mixing up number breakdowns: Double-check that you’ve split numbers into tens, ones, or hundreds correctly before multiplying.

Master Grid Multiplication at Mathnasium of South Westminster

Mathnasium of South Westminster is a math-only learning center for K-12 students in Westminster, CO.

Using a proprietary teaching approach called the Mathnasium Method™, our specially trained math tutors offer face-to-face instruction in an engaging and supportive group environment to help students of all skill levels master any math class and topic, including grid method multiplication. 

Explore our approach to elementary school tutoring:

• 3rd grade math tutoring

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Each student begins their Mathnasium journey with a diagnostic assessment that allows us to understand their unique strengths and knowledge gaps. Guided by assessment-based insights, we develop personalized learning plans that will put them on the best path toward math mastery. 

Whether your student is looking to catch up, keep up, or get ahead in their math class, schedule an assessment, and enroll at Mathnasium of South Westminster today! 

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Pssst! Check Your Answers Here

Great job tackling the practice problems! Now, let’s check your work.

Task 1: 42 × 6 = 252

Task 2: 36 × 14 = 504

Task 3: 125 × 8 = 1000

Task 4: 203 × 12 = 2436