AMC 8 2025 Fast Multiplication Trick for 106×107 | Quick Explanation
Learn a fast “Chinese method” shortcut to multiply numbers like 106×107 in seconds. See why it matches long multiplication and when it works.
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What you'll learn
- Multiply 106×107 quickly using a digit shortcut
- Verify the shortcut by connecting it to long multiplication
- Recognize when the method works for numbers near 100
- Reduce calculation time on AMC 8-style arithmetic
About this lesson
Want to multiply 106×107 without writing long multiplication? In this clip, you’ll see a quick shortcut often taught in Chinese math classes. We compare it to the standard American long-multiplication steps so you can trust the result. Use it to speed up mental math on AMC 8-style problems.
You can multiply 106×107 quickly by using the “near 100” shortcut: add 106 and 7 to get 113, then multiply the last digits 6×7=42, giving 11342.
How do you multiply 106×107 quickly without long multiplication?
Notice both numbers are 100 plus a small number: 106=100+6 and 107=100+7. Add one number to the other’s last-digit offset: 106+7=113 (this forms the leading part). Then multiply the offsets: 6×7=42 (this forms the last two digits). Combine them to get 11342.
This matches long multiplication because (100+6)(100+7)=10000+100(6+7)+42=10000+1300+42=11342. Practice this pattern for numbers close to 100 to speed up AMC 8 calculations.
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