Division: Three Forms

Contributor: Erika Wargo. Lesson ID: 12098

Many opinions are divided on whether or not math is fun or useful. We make it both in this lesson, using practical examples and a chance to showcase your division talents! Learn the three forms, too!


Fractions and Operations

learning style
personality style
Beaver, Golden Retriever
Grade Level
Intermediate (3-5)
Lesson Type
Skill Sharpener

Lesson Plan - Get It!

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  • How do you divide 15 potatoes between 2 people?

You mash 'em!

  • But really, how would you divide them?

You are in charge of making gift bags for your friends that come to your party.

It's only fair if everyone has the same amount of candy in their bag. You have 30 pieces of candy and five friends. How many pieces does each friend get?

To play this out, you will need 30 pieces of candy (or any other object) and five bags (or other containers). Begin by sharing, or dividing, the candy into the bags so everyone has the same. After you are done, discuss these questions with your parent or teacher:

  • How many pieces of candy did you start with?
  • How many bags do you have?
  • How many pieces of candy are in each bag?
  • Is there any candy left?
  • How did you make sure everyone is getting the same amount?

Since the problem asked you to take a total number and divide it into equal groups, you solved a division problem. When you are looking for a missing factor, it is called division. Division is the inverse, or opposite, of multiplication. In this division problem, the missing factor could have been found by thinking, "Five times what number equals 30?" The missing number is six because 5 x 6 = 30.

Division can be shown in several ways. Here are three ways to show "Twelve divided by four."

  4 12  
  12 ÷  4  
  • In the first example, a division box is used.
  • In the second example, a division sign is used.
  • The third example shows a division bar. It looks like a fraction, doesn’t it?
  • To solve longer division problems, you would usually use the division box.

Three numbers are involved in every division problem. It is important to know the names of those numbers:

  1. The number being divided is called the dividend.
    12 ÷ 4 = 3
    12 is the dividend (In the example above, the candy represents the dividend.).
  2. The number by which it is divided is called the divisor:
    12 ÷ 4 = 3
    4 is the divisor (The bags, or number of guests, represent the divisor.).
  3. The answer to the division problem is called the quotient.
    12 ÷ 4 = 3
    3 is the quotient (In the example, the quotient is the number candies in each bag [or received by each guest]).

The chart below shows you the different ways to write division and the location of each number:


Positions of Divisor, Dividend, and Quotient

Division Box   quotient    
divisor dividend    
Division Sign dividend ÷ divisor = quotient
Division Bar dividend = quotient    


Keep this information handy and let’s go practice solving division problems in the Got It? section!

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