Putting Multiplication Math Facts to Good Use!
It’s not far past memorizing your multiplication facts before you’re quickly confronted with bigger numbers. Multiplying multi-digit numbers is one of the first math operations that require an algorithm to complete, so it represents something of a milestone when learning arithmetic.
Fortunately, the steps for multiplying multiple digit numbers is straightforward and we’ll cover them right here.
Steps in the Standard Multiplication Algorithm
The most commonly taught way to multiply a multiple digit number is using the “standard algorithm” which involves multiplying each place value in order from right to left. This means every operation is a single digit math fact, which relies on your having memorized the multiplication table already.
We’ll multiply each place value from one of the numbers, and then add them up. So this algorithm can be thought of as “summed place value multiplication.” We’ll keep track of the intermediate multiplication steps below the problem in a “workspace” area, and then when we’re done those add up to get the final product.
The steps look something like this…
- Setup the numbers you are multiplying (the “multiplicands”) vertically.
- Start with the left-most digit from the lower number. To keep things simple, we’ll call this digit from the lower multiplicand the “lower digit.”
- Select the left most digit from the top multiplicand (the “top digit”).
- Multiply the lower digit by the top digit.
- Add any carried value recorded above the top digit from a previous step.
- Write the ones place value from that result below.
- If there’s a tens place in the result and there are more digits remaining in the top multiplicand, carry that tens digit over to what would be the next top digit. You’ll add it later when we get back to step 5 again for that digit.
- If there’s a tens digit in the result and there are NO MORE digits remaining in the top multiplicand, we need to handle that carry now. Just put that digit down in the workspace to the left of the digit you wrote in step 6.
- If there are more digits in the top multiplicand, select the next digit to the left as the new top digit and go back to step 4.
- Once you have completed cycling over the digits in the top multiplicand, select the next bottom digit from the bottom multiplicand and start multiplying the top multiplicand again at step 3.
- If there are no more digits left in the
