Division

Division is splitting into equal parts or groups.

It is the result of "fair sharing".


Example: there are 12 chocolates, and 3 friends want to share them, how do they divide the chocolates?

 
12 Chocolates   12 Chocolates Divided by 3

Answer: 12 divided by 3 is 4: they get 4 each.

Symbols

÷ /

We use the ÷ symbol, or sometimes the / symbol to mean divide:

12 ÷ 3 = 4
12 / 3 = 4

Let's use both symbols here so we get used to them.

Opposite of Multiplying

Division is the opposite of multiplying. When we know a multiplication fact we can find a division fact:

Example: 3 × 5 = 15, so 15 / 5 = 3.

Also 15 / 3 = 5.

Why? Well, think of the numbers in rows and columns like in this illustration:

Multiplication... ...Division
3 groups of 5 make 15... so 15 divided by 3 is 5
   
and also:
 
   
5 groups of 3 make 15... so 15 divided by 5 is 3.
   
 

So there are four related facts:

  • 3 × 5 = 15
  • 5 × 3 = 15
  • 15 / 3 = 5
  • 15 / 5 = 3

Knowing your Multiplication Tables can help you with division!

Example: What is 28 ÷ 7 ?

Searching around the multiplication table we find that 28 is 4 × 7, so 28 divided by 7 must be 4.

Answer: 28 ÷ 7 = 4

Names

There are special names for each number in a division:

dividend ÷ divisor = quotient


Example: in 12 ÷ 3 = 4:

  • 12 is the dividend
  • 3 is the divisor
  • 4 is the quotient

 

But Sometimes It Does Not Work Perfectly!

Sometimes we cannot divide things up evenly ... there may be something left over.

Example: There are 7 bones to share with 2 pups.

But 7 cannot be divided exactly into 2 groups,
so each pup gets 3 bones,
but there will be 1 left over:

We call that the Remainder.

Read more about this at Division and Remainders

Exercises

Try these division worksheets.