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Breaking Down the Problem

To multiply two 2-digit numbers, such as 37 and 26, we use the distributive property to break down the problem into simpler parts. This method involves decomposing each number into tens and ones and then multiplying each part separately before combining the results.

Example: 37 x 26

1. Separate the Numbers by Place Value:37 can be broken down into 30 (three tens) and 7 (seven ones).
   26 can be broken down into 20 (two tens) and 6 (six ones).
   

2. Multiply Each Part:
   First, multiply the ones place: 37×637 \times 637×630×6=18030 \times 6 = 18030×6=180
   7×6=427 \times 6 = 427×6=42
   Add these products together to get the total for the ones place: 180+42=222180 + 42 = 222180+42=222.
   

3. Multiply the Tens Place:
   Next, multiply the tens place: 37×2037 \times 2037×2030×20=60030 \times 20 = 60030×20=600
   7×20=1407 \times 20 = 1407×20=140
   Add these products together to get the total for the tens place: 600+140=740600 + 140 = 740600+140=740.
   

4. Combine the Results:
   Finally, add the totals from the ones place and the tens place to get the final product:222+740=962222 + 740 = 962222+740=962.
   

By following these steps, we see that 37×26=96237 \times 26 = 96237×26=962.

Why This Method Works

The method works because it leverages the distributive property of multiplication, allowing us to break down complex multiplication problems into more manageable parts. By understanding and practicing this method, you'll find multiplying larger numbers becomes more intuitive and less error-prone.

Conclusion

Understanding and mastering the technique of multiplying two 2-digit numbers using partial products and the distributive property is a crucial skill in mathematics. With resources like Khan Academy's detailed video explanations and our supplementary flashcards and practice videos, you can enhance your learning and become more confident in your mathematical abilities.