Division Basics • Topic 1 of 3

Division as Fair Sharing

What is Division?

Division means splitting a number into equal groups. It is the opposite of multiplication (putting equal groups together). The division sign is $\div$.

Two ways to think about division

1. Sharing equally. "Share $12$ sweets among $3$ children" — how many does each get? Deal them out one by one until none are left: each child gets $4$. So $12\div3=4$.

2. Making equal groups. "How many groups of $3$ are in $12$?" Take groups of $3$ away: $12\to9\to6\to3\to0$, that is $4$ groups. So $12\div3=4$ again.

The words we use

Word	Meaning	In $12\div3=4$
Dividend	the number being shared	$12$
Divisor	how many groups (or group size)	$3$
Quotient	the answer	$4$

Division is repeated subtraction. $12\div3$ asks how many times you can take $3$ away from $12$. You can do it $4$ times, so the answer is $4$.

Special division facts:

Any number $\div 1$ is itself: $7\div1=7$.
Any number $\div$ itself is $1$: $7\div7=1$.
$0$ shared into any group is $0$: $0\div5=0$.

Real life: sharing chocolates equally, putting the same number of books on each shelf, or making equal teams.

Common mistakes to avoid:

Order matters in division: $12\div3$ is not the same as $3\div12$.
The groups must be equal — sharing only counts if every group gets the same amount.

FAIR SHARING:  12 sweets shared equally among 3 children

   Child 1:  o o o o
   Child 2:  o o o o      Each child gets 4.
   Child 3:  o o o o      So  12 / 3 = 4

MAKING EQUAL GROUPS:  how many groups of 3 are in 12?

   [o o o] [o o o] [o o o] [o o o]   -> 4 groups
   So  12 / 3 = 4  again.

REPEATED SUBTRACTION:  12 - 3 - 3 - 3 - 3 = 0   (took 3 away 4 times)

Solved Examples

Worked Example

Share $12$ sweets equally among $3$ children. How many does each child get?

Solution

Share into $3$ equal groups: $12\div3$.
Each child gets $4$.
Answer: $4$ sweets each

Worked Example

Find $20\div5$.

Solution

How many $5$s make $20$? $5,10,15,20$ — that is $4$.
Answer: $4$

Worked Example

Find $15\div3$.

Solution

Share $15$ into $3$ equal groups.
Each group has $5$.
Answer: $5$

Worked Example

How many groups of $4$ are in $16$?

Solution

$16\div4$: take away $4$ four times ($16,12,8,4,0$).
Answer: $4$ groups

Worked Example

Find $18\div6$.

Solution

Share $18$ among $6$.
$6\times3=18$, so each gets $3$.
Answer: $3$

Worked Example

$24$ pencils are packed equally into $4$ boxes. How many pencils in each box?

Solution

$24\div4=6$.
Answer: $6$ pencils in each box

Key Points

Division splits a number into equal groups; the sign is $\div$.
It can mean "share equally" or "make equal groups" — both give the same answer.
Dividend $\div$ divisor $=$ quotient (e.g. $12\div3=4$).
Division is repeated subtraction.
Any number $\div1=$ itself; any number $\div$ itself $=1$; $0\div n=0$.
Order matters: $12\div3$ is not the same as $3\div12$.

Quick Check — 4 MCQs

Tap an option to check your answer0 / 4

Q1.The division sign is:

Explanation: $\div$.

Q2.$12\div3=$

Explanation: Each of $3$ groups gets $4$.

Q3.In $20\div5=4$, the quotient is:

Explanation: The answer is the quotient.

Q4.Any number divided by $1$ is:

Explanation: Itself.

Practice more MCQs → 📝 Assignment · 35 marks