Mastering 3-Digit Multiplication

Understanding 3-Digit Multiplication

3-digit multiplication can seem intimidating at first, but with a systematic approach, it can be quite manageable! Let’s break it down step by step. We'll use the example of multiplying 345 by 276.

Step 1: Write the numbers vertically

Write the numbers one under the other, aligning them by the rightmost digit:

     345
   x 276

Step 2: Multiply the bottom number by each digit of the top number

Start with the rightmost digit of the bottom number (6 in this example). Multiply it by each digit of the top number (345), starting from the right side:

• 6 × 5 = 30 (write down 0, carry over 3)
• 6 × 4 = 24 (add the carry over 3: 24 + 3 = 27, write down 7, carry over 2)
• 6 × 3 = 18 (add the carry over 2: 18 + 2 = 20, write down 20)

This gives:

     345
   x 276
   ------
    2070  (this is 6 multiplied by 345)

Step 3: Repeat for the next digit

Next, take the middle digit of the bottom number (7). Since this is actually in the tens place, we’ll multiply by 10.

• 7 × 5 = 35 (write down 5, carry over 3, but add a 0 to the end as it’s in the tens place)
• 7 × 4 = 28 (add the carry over 3: 28 + 3 = 31, write down 1, carry over 3, but add one 0)
• 7 × 3 = 21 (add the carry over 3: 21 + 3 = 24, write down 24 with 0 added)

So you should write:

     345
   x 276
   ------
    2070
   2415 0 (shift one place to the left)

Step 4: The final digit

Now, move to the leftmost digit of the bottom number (2). This represents 200:

• 2 × 5 = 10 (write down 0, carry over 1, add two 0s for the hundreds place)
• 2 × 4 = 8 (add the carry over 1: 8 + 1 = 9, then append a 0)
• 2 × 3 = 6 (append two 0s, since this is in the hundreds place)

So write:

     345
   x 276
   ------
    2070
   24150
 + 69000  (add two 0s and note it down)

Step 5: Add up all the rows

Now, add all the results together:

     2070
   24150
 +69000 
   ------
   95220

So, 345 × 276 = 95220.

Helpful Tips

• Practice regularly: The more you practice, the more comfortable you will become with 3-digit multiplication.
• Break it down: Always take your time and break the multiplication into manageable parts.
• Check your work: After completing your multiplication, it can be useful to check your work by using a calculator or estimating the answer to see if your result is reasonable.
• Use graph paper: This can help keep your numbers aligned correctly.
• Know the multiplication tables: Strong foundational knowledge of basic multiplication facts can speed up the process significantly.

By mastering these steps, you’ll gain confidence in tackling larger multiplications. Happy multiplying!