How to Multiply Two Digit Number Without Calculator

Method 1: Break It Down

This method involves breaking down the multiplication into simpler parts using place value. Here's how it works:

1. Multiply the tens digit of the first number by the tens digit of the second number.
2. Multiply the tens digit of the first number by the ones digit of the second number.
3. Multiply the ones digit of the first number by the tens digit of the second number.
4. Multiply the ones digit of the first number by the ones digit of the second number.
5. Add all the partial products together.

This method works well for numbers where one digit is 1, making some multiplications easier.

Method 2: Use the Distributive Property

The distributive property allows you to break down multiplication into simpler additions and subtractions. Here's how to apply it:

1. Express one of the numbers as a sum or difference of simpler numbers.
2. Multiply each simpler number by the other number.
3. Add or subtract the results.

This method is particularly useful when one of the numbers is close to a round number.

Method 3: The Lattice Method

The lattice method is a visual approach that uses a grid to organize the multiplication process. Here's how it works:

1. Draw a grid with one more row and column than the number of digits in your numbers.
2. Write the digits of the first number along the top and the second number along the side.
3. Multiply each digit from the top by each digit from the side and write the results in the grid.
4. Add the numbers diagonally to get the final product.

Worked Examples

Example 1: 24 × 36

Using the break it down method:

1. 2 × 3 = 6 (tens × tens)
2. 2 × 6 = 12 (tens × ones)
3. 4 × 3 = 12 (ones × tens)
4. 4 × 6 = 24 (ones × ones)
5. 6 + 12 + 12 + 24 = 54

The final answer is 864.

Example 2: 17 × 25

Using the distributive property:

1. 17 × (20 + 5) = (17 × 20) + (17 × 5)
2. = 340 + 85 = 425

The final answer is 425.