Multiplying Two Numbers Near 100

This trick simplifies multiplying two numbers that are close to 100 (or 1000, etc.).

• Both numbers over 100: For $103 \times 108$, the last two digits are the product of the differences from 100 ($3 \times 8 = 24$). The first part of the answer is one number plus the other's difference from 100 ($103+8=111$). Answer: 11124.
• Both numbers under 100: For $97 \times 94$, the last two digits are the product of the differences from 100 ($3 \times 6 = 18$). The first part is one number minus the other's difference from 100 ($97-6=91$). Answer: 9118.
• One over, one under 100: For $103 \times 94$, the last two digits are $100 - (3 \times 6) = 82$. The first part is the larger number, minus the smaller's difference from 100, minus 1 ($103-6-1=96$). Answer: 9682.