How Does Multiplication Works
Example 1 - 65 x 97
Here is the pictorial representation on how to multiply 2 numbers:
We need 4 multiplications in order to calculate the product of two 2-digit numbers!
Multiplying 3 digit into 2 digit numbers
Consider two numbers: 781 × 95 = 74,195.
Step 1: Multiply the digit in the ones place of the bottom number (95) by each digit of the top number (781) from right to left. Write the result, 3905, below the line.
Step 2: Multiply the digit in the tens place of the bottom number (9) by the top number, write the result, 7029, on the next line, ensuring it is shifted one place to the left as it represents tens. Add a 0 at the end to reflect its position.
Step 3: Add the intermediate results (3905 and 7029) to get the final answer, 74,195.
Example 3 - 367 X 251
When the bottom factor (multiplier) is a three-digit number, multiplying the digit in the hundreds place will produce a result followed by two zeros. Here’s another example to illustrate this.
$$ \begin{aligned} &\ \ 367 \\ \times &\ \ 251 \\ \hline &\ \ 367 \quad\quad \text{(Step 1: $367 \times 1$ from the ones place)} \\
- &\ 1835 \quad\quad \text{(Step 2: $367 \times 5$ from the tens place, shifted)} \\
- &\ 73400 \ \ \text{(Step 3: $367 \times 2$ from the hundreds place, shifted twice)} \\ \hline &\ 92117 \quad \ \text{(Add intermediate results to get the final product)} \\ \end{aligned} $$