Multiplying Two Numbers Ending in 5

When multiplying two numbers that both end in 5 (e.g., $a5$ and $b5$), there is a specific trick based on whether the sum of the leading digits ($a+b$) is even or odd.

• If $a+b$ is even, the last two digits of the answer are 25.
• If $a+b$ is odd, the last two digits of the answer are 75.

The rest of the answer is found by calculating $a \times b + \lfloor \frac{a+b}{2} \rfloor$.

For $45 \times 85$: $a+b = 4+8=12$ (even), so the end is 25. The rest is $4 \times 8 + \frac{12}{2} = 32+6 = 38$. Answer: 3825.

For $35 \times 85$: $a+b = 3+8=11$ (odd), so the end is 75. The rest is $3 \times 8 + \lfloor \frac{11}{2} \rfloor = 24+5 = 29$. Answer: 2975.