Lesson 11:  Basic Division

Many students don't realize that division is nothing more than repeated subtraction.  It's a shortcut so that we don't have to subtract the same number many times over.  Division is also the opposite of multiplication.  This lesson will teach you the basics, and later lessons will teach you more.

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 division problem:  At a party, you have 15 cookies, and you want to give 3 cookies to each child.  How many children can get cookies?  One way to solve this problem is with subtraction.  We could start with 15 cookies, and then keep subtracting 3 cookies, until we run out of cookies.  Then we can see how many times we subtracted.  If we did that we would see that we could subtract 5 times.  That means that 5 children could get 3 cookies each.  That wasn't too tedious, but what if there had been 138 cookies?  We would certainly need a better method, and that method is division.  Division is nothing more than repeated subtraction.  It could also be thought of as taking a large quantity, and splitting it up into groups of equal size. 

The problem above could be represented with symbols by writing 15 ÷ 3, or 15 / 3, which is read as "fifteen divided by three."  It can also be written as a fraction (see left).  To solve this example, we need to start with 15, and see how many times we can subtract 3.  A shortcut would be to just break 15 into groups of 3, and see how many groups you can make.  If you try this using counters, you'll see that you can make 5 groups. 

It's important to be able to divide small numbers in your head quickly, and a good way to do this is by working with flashcards, either store-bought or homemade.  When you divide, the answer is called the quotient.  The number that you are dividing by is called the divisor, and the number that is being divided is called the dividend.  Of those terms, the most important one to remember is quotient.   

Later you'll learn how to divide larger numbers, as well as numbers which will not divide evenly, and will have a remainder left over.  For now, just practice dividing small numbers that divide evenly.  For example:  12 / 6 = 2, because you can divide 12 into two groups of six.  16 / 4 = 4, because you can break up 16 into four groups of four. 

Note that division is the opposite of multiplication.  We know that 3 x 4 = 12.  That means that 3 groups of 4 equals 12, or 4 groups of 3 equals 12.  We could use this knowledge to help us do division using these numbers.  For example to do 12 / 3, we can count how many groups of 3 we can make out of 12, and we'd see that the answer is 4.  We could count how many groups of 4 we can make out of 12, and we'd see that the answer is 3.  Experiment using counters to see that multiplication and division are opposites, or what are called inverse operations.

It's important to understand that division is not commutative, the way that multiplication is.  The order in which we divide two numbers matters.  For example, 15 / 3 is not the same as 3/ 15.  You'll learn more about this later, but for now just remember that addition and multiplication are commutative, but subtraction and division are not. 

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