Multiplying Three-Digit Number by Two-Digit Number

To multiply a three-digit number ($abc$) by a two-digit number ($ef$), you can break it down into smaller, more manageable multiplications. Treat the three-digit number as two groups, $a$ and $bc$.

Procedure:

1. Multiply the two-digit groups: $bc \times ef$. The last two digits of this product form the end of your final answer. Note the carry.
2. Multiply the leading digit of the three-digit number by the two-digit number, and add the carry: $a \times ef + \text{carry}$. This result forms the beginning of your final answer.

For example, $117 \times 15$: First, $17 \times 15 = 255$. The last two digits are 55, carry 2. Then, $1 \times 15 + 2 = 17$. The result is 1755. This often involves other tricks for the intermediate steps.