Division is in many ways the opposite of multiplication, or more technically, it is the inverse of multiplication. When we are given a division problem, say 6 ÷ 3, what we are asking is if we break apart 6, how many groups of 3 can we get and how many are left over. Below is an illustration using boxes.
We will start with 6 boxes:
Now since we want groups of 3, lets create a bin to put those in.
Now we must fill up the bin with 3 squares.
We can do this one more time filling up another bin.
Since we have no more squares left we count the number of bins it took. In this case we have 2 bins. so the answer to our problem is:
6 ÷ 3 = 2.
Terms
In the above division problem 15 ÷ 5 = 3 we say that 15 is the
Dividend, 5 is the
Divisor and 3 is the
Quotient.
Division as the inverse of Multiplication
Once you memorize
multiplication tables, any division problem whose dividend is an answer within the multiplication table for the divisor is pretty simple. For example if you have the problem 72 ÷ 8 , you can think what multiplied by 8 gives 72?... 9 of course!
Remainders
Sometimes a problem doesn't work out quite as nicely, lets take the following problem for example:
12 ÷ 5
We start out with 12 boxes:
We create our first bin and put 5 boxes in it. We can then put another 5 boxes into a second bin as so:
Unfortunately we have 2 boxes left over. The rule is that we can only create a new bin if we have enough boxes to fill it. In this case we don't so we simply say that we have a remainder of 2:
12 ÷ 5 = 2 remainder 2.
We can write this in different ways such as:
2 remainder 2
2r2
2 2/5
Notation
Division can be written many different ways. All of the following describe the same problem and are read as 15 divided by 5 equals 3:
