The Standard Multiplication Algorithm

The standard algorithm is like a high-speed shortcut for multiplication. Instead of adding a number over and over, we break the problem into smaller, easier steps based on place value. We always work from right to left, starting with the ones place, then moving to the tens, hundreds, and finally the thousands. By focusing on one column at a time, we can solve massive problems with simple multiplication facts. Think of each column as a separate 'mini-problem' that contributes to the final big answer.

What happens when a 'mini-problem' results in a number larger than 9? We use regrouping (also called carrying). If you multiply the ones and get $15$, you can't fit two digits into one column. You write the $5$ in the ones place and 'carry' the $1$ (which represents 10) over to the top of the tens column. After you multiply the tens, you simply add that carried number to the result. This ensures every digit stays in its proper place value home.

Before you do the hard work, it helps to guess the 'ballpark' answer. This is called estimation. To estimate, round your 4-digit number to the nearest thousand. For example, if you are multiplying $3,982 \times 4$, round $3,982$ up to $4,000$. Since $4,000 \times 4 = 16,000$, your final answer should be close to $16,000$. If your calculated answer is $1,592$, you know you missed a place value!