Multiplying Numbers Close to 100

Trick / Shortcut
Multiplying Numbers Close to 100
Topic
Multiplication
How It Works

To multiply two numbers, $N_1$ and $N_2$, that are close to 100:

  1. Find the difference of each number from 100: Let $x = N_1 - 100$ and $y = N_2 - 100$. (These can be positive or negative).
  2. First part (Left side): Add one number to the difference of the other from 100. For example, $(N_1 + y)$ or $(N_2 + x)$. This will be the leading digits of the answer.
  3. Second part (Right side): Multiply the two differences: $x \times y$. This forms the last two digits of the answer.
  4. Combine the parts. If $x \times y$ is a single digit, prepend a 0 (e.g., $8$ becomes $08$). If $x \times y$ is $\ge 100$, carry over the hundreds digit to the first part.

Combined Calculation: $(N_1 + y) \times 100 + (x \times y)$

Example

$97 \times 96$:

  1. Differences from 100: $x = 97 - 100 = -3$ $y = 96 - 100 = -4$
  2. Left part: $(97 + (-4)) = 93$. (Alternatively, $96 + (-3) = 93$).
  3. Right part: $x \times y = (-3) \times (-4) = 12$.
  4. Combine: Place 93 on the left, and 12 on the right. Result: $\textbf{9312}$

$102 \times 103$:

  1. Differences from 100: $x = 102 - 100 = +2$ $y = 103 - 100 = +3$
  2. Left part: $(102 + 3) = 105$.
  3. Right part: $x \times y = (+2) \times (+3) = 6$. (Write as $06$).
  4. Combine: Place 105 on the left, and 06 on the right. Result: $\textbf{10506}$

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