### Teacher Guide to Division

Division is very similar to multiplication. In fact, you could say it is multiplication in reverse. Whereas multiplication is used to add together multiples of the same number, division is used to determine how many pieces are in a whole.

EXAMPLE #1:

Imagine that you have 100 jelly beans (called the "dividend") that you want to hand out to 5 (called the "divisor") of your friends, but you want to make sure that each friend gets the same amount as everyone else - you would use division to calculate that.

So, 100 jelly beans divided by 5 friends equals 20 jelly beans each.

The result (20 jelly beans) is referred to as the "quotient".

How does "division" work?

In division, you are basically subtracting a number repeatedly until there is nothing left. Using the example above, you could have made sure than each friend got the same amount of jelly beans by handing one jelly bean out at a time to each friend. However, doing so would have taken a long time.

Division makes the process easier and faster. You calculate how many times one number (the "divisor") goes into another (the "dividend") by subtracting the divisor from the dividend until nothing remains.

What if there is some left over that is too small to make up a divisor?

It is okay if the numbers do not divide into one another perfectly. Any remaining amount is referred to as the remainder.

EXAMPLE #2:

If you were dividing 9 by 2, you would find that you can take 2 away from nine 4 times, however, you would be left with 1:

 9 divided by 2 equals 4 plus 1 dividend divisor quotient remainder

The remainder is basically a portion of the divisor and it can be expressed as such - this is called a fraction. In this example, the remainder (1) is half the amount of the divisor (2), so it would be expressed as ½ and added to the quotient, making the quotient expressed in fractions 4 ½. Verbally, this would be expressed by saying that 2 (the divisor) goes into 9 (the dividend) 4 ½ times.

How do you check your work?

You can find out whether your calculations were correct by working backward. Using Example #2, you would know that you are correct because the divisor (2) multiplied by the quotient (4) plus the remainder (1) equals the dividend (9).