Multiplication: Whole Numbers
Multiplication can be thought of as repeated addition. So, if you multiply a number by another number , this is the same as adding the number over and over again times. (Or adding over and over again times). For example:
Another way to think of whole number multiplication is to visualize objects arranged in a rectangle, with rows and columns.
Note that there are dots in the figure.
The Standard Algorithm
To multiply a multi-digit number by a one-digit number using the standard algorithm, write the two numbers on top of each other, with the ones digits vertically aligned and the multi-digit number on top.
Multiply the ones digit of the top number by the bottom number. Write down the ones digit of the result. If the result is greater than , carry the tens digit, as you do when adding.
Here, , so
Now multiply the tens digit of the top number by the bottom number, and add the carried digit to the result. Here, , and then we add to get . Since is less than , we don't have to carry this time.
Finally, multiply the hundreds digit of the top number by the bottom number. Here, .
To multiply two multi-digit numbers , write the number with more digits on top. For example, to multiply by , we write
First multiply the top number by the ones digit of the bottom number, as explained above. , so write down the and carry the :
is 36, plus is , so write down the 8 and carry the :
is , plus is . There are no more digits to carry, so write down .
Next, we need to multiply the top number by the tens digit of the bottom number. Since we're actually multiplying by , not by , we write down a as a place holder.
is , so write down a .
is , so write down an .
is , and there are no more digits to carry, so write down the .
The final step is to add the two results.