2-Digit by 2-Digit Multiplication

Multiplying 2-digit by 2-digit numbers might seem daunting, but with the right approach and understanding of the process, you can become proficient in no time. In this guide, we’ll explain the process of 2-digit by 2-digit multiplication step by step, so you can quickly learn and master this essential skill.

2-Digit by 2-Digit Multiplication

Step 1: Arrange the Numbers

Write the two numbers you want to multiply, one below the other, aligning them to the right. Draw a horizontal line beneath them. This arrangement will make the multiplication process easier to follow.

Example:

  23
  17
-----

Step 2: Multiply the Ones Digit of the Bottom Number

Begin by multiplying the ones digit of the bottom number (the second number) with the ones digit of the top number (the first number). Write the result below the horizontal line, aligning it to the right.

Example:

  23
  17
-----
   21

In this example, we multiplied 7 (ones digit of 17) by 3 (ones digit of 23) and got 21. We then wrote the 21 below the horizontal line.

Step 3: Multiply the Ones Digit of the Bottom Number with the Tens Digit of the Top Number

Now, multiply the ones digit of the bottom number with the tens digit of the top number. Write the result to the left of the previous result, carrying over any tens if necessary. Ensure the result starts directly under the tens digit of the previous result, (i.e. 4 in 14 is under 2 in 21)

Example:

Here, we multiplied 7 (ones digit of 17) by 2 (tens digit of 23) and got 14. We wrote the 14 to the left of the 21.

Step 4: Place a Zero

Since we’re moving on to the tens digit of the bottom number, we need to place a zero in the next row starting from the right hand side. This is because we’re now working with tens, not ones.

Example:

Step 5: Multiply the Tens Digit of the Bottom Number with the Ones Digit of the Top Number

Next, multiply the tens digit of the bottom number with the ones digit of the top number. Write the result to the left of the zero we just placed.

Example:

In this example, we multiplied 1 (tens digit of 17) by 3 (ones digit of 23) and got 3. We then wrote the 3 to the left of the zero.

Step 6: Multiply the Tens Digit of the Bottom Number with the Tens Digit of the Top Number

Now, multiply the tens digit of the bottom number with the tens digit of the top number. Write the result to the left of the previous result.

Example:

Here, we multiplied 1 (tens digit of 17) by 2 (tens digit of 23) and got 2. We wrote the 2 to the left of the 3.

Step 7: Add the Results

Finally, add the numbers you obtained in steps 2-6, and write the sum below another horizontal line.

Example:

  23
  17
-----
   21
  14
  230
-----
  391

In this example, we added the numbers in the rows below the horizontal line:

21 (from step 2)

140 (from step 3)
30 (from step 5)
200 (from step 6) = 391

The final result of our 2-digit by 2-digit multiplication is 391.

Recap of 2-Digit by 2-Digit Multiplication

To summarize the process of 2-digit by 2-digit multiplication, follow these steps:

Arrange the numbers one below the other, aligning them to the right.
Multiply the ones digit of the bottom number with the ones digit of the top number, and write the result below the horizontal line.
Multiply the ones digit of the bottom number with the tens digit of the top number, and write the result to the left of the previous result.
Place a zero in the next row as you move on to the tens digit of the bottom number.
Multiply the tens digit of the bottom number with the ones digit of the top number, and write the result to the left of the zero.
Multiply the tens digit of the bottom number with the tens digit of the top number, and write the result to the left of the previous result.
Add the results obtained in steps 2-6 to get the final answer.