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DIVISION (Under current development: August 2026)

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DIVISION means cutting one big group into several smaller groups.

You do this when you DIVIDE a number with another number.

Division is different from addition and subtraction.

 

Addition raises the total number of items you have.

Addition:12 + 4= 16. Sixteen total items in 1 group.

 

Subtraction lowers the total number of items you have.

    Subtraction:12 - 4= 8. Eight total items in 1 group.

 

After dividing items, you have the same number of items (total) that you started with, just in more groups.

Division: 12 4= 3. Twelve total items, placed into 3 groups of 4 items in each group.    

The below picture shows 10 items divided into 2 groups.

The answer is 5.

You have separated ten items into two groups of five.

5 items in group one + 5 items in group two = 10 total items

 

Different Division Signs !

You may see a DIVISION problem written with one of several different DIVIDE signs.

The above picture shows the divide sign:

Each style means the same thing:

 DIVIDE the large number to make a smaller number

Below we show you three common division signs used in the United States.

When you see / you will divide the first number with the second number:

12/3 = means: Divide 12 into 3 parts.

The answer is 4 parts. 12/3 =4

Every number in a division problem has a special math name.

 

These three Division math words are:

Dividend = The big number you start with (the total number of items).

Divisor = How many groups you are making from the one big group.

Quotient = The answer (how many items will be in each group).

Here is an example:

Division (Divide)

How many of your 12 cookies will each friend get.

Dividend: The total number you start with (12 cookies).

Divisor: The number of friends getting cookies (3 friends).

Quotient: The final answer (4 cookies for each friend).

 

Each person in the photo above gets four cookies.

12 is the Dividend (total cookies).

3 is the Divisor (plates).

4 is the Quotient (cookies per plate).

Do you remember that in multiplication

4 times 3 is 12 ( 4 X 3 = 12 ) ?

Then you already know how division works.

Your teacher may call it  a "Fact Family",

because the numbers are related in multiplication, addition, and division.

When you Multiply

4 X 3 = 12

When you Add numbers

4 + 4 + 4 = 12   

When you Divide

12/3 = 4

 

Below stories are in progress. August 1, 2026   Taylor

First working on stories, then making a graphic to fit each story

Problem 1: Finding the Group Size

The Story:

 

yadda yadda yadda

How to solve it: Pass out the ____, one by one, until they are all gone.

The Math Sentence:   15 \  4 =

The Answer: Each person gets ----------

# 2 of 3

🧸 Problem 2: Finding the Number of Groups

The Story:
Mary has of 12 dolls.

She wants to put them into plastic bags.

Each bag will hold 3 dolls.

How many plastic bags does Mary need to fit all of her dolls into the bags?

text

show 12 dolls

        👇            👇            👇            👇

    [ Bag 1 ]     [ Bag 2 ]     [Bag 3 ]     [ Bag 4 ]

 

How to solve it: Count out a group of 3 dolls and put them in a bag.

Keep making groups of 3 until all 12 dolls are packed. Then, count the bags!

The Math Sentence:12 / 3 = 4

The Answer: Mary needs 4 bags

Your teacher may also call this a "Fair Share", because each group is the same size or number.

 

Three  Ways to Think About Division

Fair Share is everyone gets an equal share

Equal Grouping: You have a total number of cookies and want to share them equally among a set number of friends.

Not Equal Grouping:

show graphic 15 divided by 4

You have a total number of cookies and want to give them away. Using division you will see how many friends will get cookies and how many cookies for each friend. One group may not be the same size as the other groups. For instance you have 15 cookies and 4 friends. Four people could get three cookies but one person would only get two cookies.   4+4+4+3 = 15

EXPLAIN how to handle remainders when numbers don't divide perfectly

Maybe make some worksheets that can be printed at home from PC.

  IN PROGRESS

 

 

Here is a detailed explanation of step 1 to step 7 that may help you better understand this long division.

It is not easy to see immediately how many times 3 is contained into 462. It may not be easy also to see how many times 3 is contained into 46. However, it is fairly easy to see that 3 is contained into 4 once.

Therefore, we do this in step 1 and put the 1 above the 4.

In step 2, we multiply 1 by 3 and subtract the answer or 3 from 4.

In step 3, we bring down the 62. Now, we need to find out how many times 3 is contained in 162. Still, it may not be obvious, so we will try to find out instead how many times 3 is contained into 16.

This is done in step 4 and we see that 3 is contained into 16 five times. We put the 5 above the 4.

In step 5 , we multiply 5 by 3 and subtract the answer or 15 from 16.

In step 6 , we bring down the 2.

In step 7 , we try to find out how many times 3 is contained into 12.

3 × 4 = 12, so 3 is contained into 12 four times.

Finally, we put the 4 above the 6.

The answer is 154. We can also say that 3 is contained into 462 one hundred fifty-four times.

Notice that the same division can be done faster if you can find out how many times 3 is contained into 46. 46 contains 3 fifteen times. Then, you can finish the problem in 4 steps as shown below:

 

When the dividend is bigger than 100, the answer may not be obvious. In this case you need to do long division in order to find the quotient. Study the following example (462 ÷ 3) carefully. 

Some day, I might even get around to writing this example. But today is not that some day.

Tom