How to Use Box Multiplication Method

How to multiply 23 × 45 with a box

This is also called the grid method or an area model. The box organizes the distributive property: (20 + 3) × (40 + 5). Each cell represents one part of the total product. The table below is a calculation grid, not a drawing to scale.

1. Split the numbers by place value

Write 23 as 20 + 3 and 45 as 40 + 5. Use 20 and 3 as the column labels, and 40 and 5 as the row labels. Labeling a tens part as 2 or 4 would lose its value.

2. Multiply each row label by each column label

3. Add all four partial products

800 + 120 + 100 + 15 = 1,035. You can group the rows first: 800 + 120 = 920 and 100 + 15 = 115; then 920 + 115 = 1,035.

Check: 23 × 45 is close to 20 × 50 = 1,000. A result of 45 or 315 would be too small. The tens-by-tens box is 20 × 40 = 800, not 80.

A blank box multiplication template

Copy this grid onto paper. Put the expanded first number across the top and the expanded second number down the side. Fill every product cell, then add the four results.

For a three-digit factor, add a hundreds column. For example, 102 × 34 uses columns 100, 0, and 2 and rows 30 and 4. Its six cells are 3,000, 0, 60, 400, 0, and 8; their sum is 3,468. Keeping a zero column can help you track the empty tens place.

Can you use the box method with decimals?

Yes. Keep the actual decimal values in the labels. To multiply 23 × 4.5, split 23 into 20 + 3 and 4.5 into 4 + 0.5.

Add 80 + 12 + 10 + 1.5 = 103.5. Because the labels already use their true values, you do not shift the decimal again after adding.

Try the method yourself

Use the blank grid for 14 × 32, 26 × 43, and 12 × 2.5. Write the expanded factors before filling the boxes.

For more practice, choose multiplication in the free Grade 4 worksheet collection and work the problems with your own box grid. These are general multiplication worksheets, not pre-drawn box templates. Use the Grade 4 math learning hub to review related skills.

For a visual way to explore partial products, see The Math Learning Center’s Partial Product Finder.