Lesson 10:  Basic Multiplication

Many students don't realize that multiplication is nothing more than repeated addition.  It's a shortcut so that we don't have to add the same number many times over.  This lesson will teach you the basics.

Don't forget to watch the embedded video clip for this lesson at the bottom of the page.  Please be sure to read the embedded video information and disclaimer.

Here is a typical multiplication problem:  There are 5 children at a party, and each child will be given 3 cookies.  How many cookies are needed?  One way to solve this problem is with addition.  We could do 3 + 3 + 3 + 3 + 3, to get 15.  That wasn't too tedious, but what if there had been 172 children?  We would certainly need a better method, and that method is multiplication.  Multiplication is nothing more than repeated addition. 

The problem above could be represented with symbols as 3 x 5, which is read as "three times five".  That means that we need to add up 5 groups of 3, or we need to add 3 five times.  It's important to be able to multiply small numbers in your head quickly, and a good way to do this is by working with flashcards, either store-bought or homemade.  Another way to study multiplication is to make and use a multiplication table:

x	1	2	3	4	5	6
1	1	2	3	4	5	6
2	2	4	6	8	10	12
3	3	6	9	12	15	18
4	4	8	12	16	20	24
5	5	10	15	20	25	30
6	6	12	18	24	30	36

Take a look at the table above.  Here's how we use it.  To multiply two numbers, find the first number down the first column (in bold).  Then find the second number along the top row (in bold).  Find the square where that row and column intersect, and that will be the result of multiplying those two numbers.  The result is called the product.

There are many interesting things that we can learn from the table.  First, notice that I did not include zeros on the table.  This is because multiplying by zero is easy.  The answer is always 0.  Zero groups of anything is always zero, since there just aren't any of them. 

Another thing we can see is that multiplication is commutative, just like addition.  It doesn't matter the order in which we multiply two numbers.  For example, 3 x 5 is the same as 5 x 3.  Experiment using counters to see why 3 groups of 5 is the same quantity as 5 groups of 3.  You'll learn more about this later.

Finally, notice that as we move across a row, we are just counting multiplies of the first number in that row.  This is because multiplying is just repeated addition.  For example.  One four is 4.  Two fours is 8.  Three fours is 12, etc.  We're just counting by that number, which is to say that we're listing multiplies of that number.  It's very important for you to be able to count multiplies of a number very quickly, since this comes up often.

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