Multiplying two 2-digit numbers might seem daunting at first, but with a systematic approach, it can be quite straightforward! Here’s a step-by-step guide to help you through the process.
Step 1: Write the Numbers Vertically
Start by writing the two numbers you want to multiply one above the other, just like you would with standard long multiplication. For example, if you are multiplying 23 by 45, it should look like this:
23 x 45
Step 2: Multiply the Bottom Number’s Ones Digit
Take the ones digit of the bottom number (5 in this case) and multiply it by each digit of the top number (23). Start from the right:
- 5 x 3 = 15 — write down 5 and carry over 1.
- 5 x 2 = 10 + 1 (the carry) = 11 — write down 11 to the left of the 5.
Your first result should look like this:
23 x 45 ______ 115
Step 3: Multiply the Bottom Number’s Tens Digit
Now, take the tens digit of the bottom number (4) and multiply it by each digit of the top number (23), just like before. However, remember to shift the result one position to the left since we are now multiplying the tens place:
- 4 x 3 = 12 — write down 2 below the line, shifting it one position to the left.
- 4 x 2 = 8 + 1 (the carry from earlier) = 9 — write down 9 in the next position to the left.
Your second result should look like this:
23 x 45 ______ 115 +920
Step 4: Add the Two Results Together
Now, simply add the two partial results:
115 + 920 ______ 1035
So, 23 x 45 = 1035!
Final Thoughts
It may initially seem complex, but with practice, this method of multiplying 2-digit by 2-digit numbers will become second nature. Try it out with different sets of numbers to gain confidence and speed!