Division Explained
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Division as Repeated Subtraction
Division is the reverse of multiplication.
In multiplication, we want to know the total of groups of numbers.
In the example below, we want to know the total of 4 groups of 8.
In division, we want to divide the total into a few groups and we want to know how many are in each group.
In the example below, we want to know how many are in each group if we divide 72 into 4 equal groups?
Vocabulary of Division
Division with Remainder
Long Division
Watch the video for an overview of Division.
Division can also be explained this way: We want to divide the total into groups of a certain number and we want to know how many groups there are.
In the example below, we want to know how many groups of 4 can we get from 36?
Print and cut out these cards.
Divide Into Equal Groups
Here is how you teach your child to divide a number into equal groups.
Let's divide 12 into 3 equal groups. How many are in each group?
Give your child 12 counters (I'll use seashells to illustrate) and divide them this way:
- Start with 12.
(It's not necessary to line them up.)
2. Take one piece and put it aside.
3. Take another piece and put it in a second pile.
4. Take the next piece and put it in a third pile.
Now we have 3 piles or groups.
5. Put the fourth piece back in the first pile.
Continue putting a piece into each group till all 12 counters are used up.
You'll end up with 4 counters in each group so 12 divided into 3 is 4.
Write it this way: 12 ÷ 3 = 4
Divide into Groups of a Number
Here is another way to divide.
Divide 12 into groups of 3. How many groups would I get? In other words, how many 3's go into 12?
Give your child 12 counters, then divide them in this way:
1. Start with 12.
2. Group them into three's.
You will end up with 4 groups.
Once again, 12 divided into 3 is 4. Or 4 groups of 3's goes into 12.
Write it this way: 12 ÷ 3 = 4
Division as Repeated Subtraction
Another way to think of division is by repeated subtraction.
For example 12 ÷ 4 means how many times can you subtract 4 from 12?
Summary
Vocabulary of Division
Division with Remainder
Long Division
Factors, Greatest Common Factor
Division Game
Here are some division task cards to play with your child. Print and cut out these cards. Have a group of counters handy for your child to use.
Shuffle the cards and place them in a stack, face down in the center of the table.
Open the top card. Everyone writes out their working. Then take turns to explain how they got the answer.
Use the different methods shown above so your child understands that there are many ways of working out the answer to a question.
Divisibility Rules
If you want to know whether a number can be divided by another number, you can apply some divisibility rules. That is, there are some short cuts to know whether a number can be divided by 2, 3, 4 and so on.
Here are some of these rules.
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