Division Basics • Topic 2 of 3

Division as Inverse of Multiplication

Multiplication and division are opposites. One undoes the other. If you multiply $3$ by $4$ to get $12$, then dividing $12$ by $4$ takes you back to $3$. Because of this, every multiplication fact gives you matching division facts.

Fact families. Three numbers that multiply and divide together make a fact family. For $3$, $4$ and $12$:

Multiplication	Division
$3\times4=12$	$12\div3=4$
$4\times3=12$	$12\div4=3$

Use your times tables to divide. To work out $42\div7$, just ask: "$7$ times what is $42$?" Since $7\times6=42$, the answer is $42\div7=6$. So learning the tables well makes division quick.

Check your division by multiplying back. To check $36\div6=6$, multiply: $6\times6=36$ — correct! This is the easiest way to be sure a division answer is right.

Why it helps: you do not need to learn division facts separately — they come free with the multiplication facts you already know.

Common mistake: getting the family the wrong way round. From $5\times6=30$ the divisions are $30\div5=6$ and $30\div6=5$, never $5\div30$.

DIVISION UNDOES MULTIPLICATION

        x 4                 / 4
    3 ------> 12         12 ------> 3

FACT FAMILY for 3, 4 and 12:

    3 x 4 = 12      12 / 3 = 4
    4 x 3 = 12      12 / 4 = 3

So if you know your times tables, you already know division!
   7 x 6 = 42   ->   42 / 7 = 6   and   42 / 6 = 7

Solved Examples

Worked Example

If $6\times4=24$, write the two matching division facts.

Solution

$24\div6=4$
$24\div4=6$
Answer: $24\div6=4$ and $24\div4=6$

Worked Example

Write the full fact family for $5$, $6$ and $30$.

Solution

$5\times6=30$, $\;6\times5=30$
$30\div5=6$, $\;30\div6=5$
Answer: those four facts

Worked Example

Use a times-table fact to find $42\div7$.

Solution

$7$ times what is $42$? $7\times6=42$.
So $42\div7=6$.
Answer: $6$

Worked Example

Find $56\div8$.

Solution

$8\times7=56$.
So $56\div8=7$.
Answer: $7$

Worked Example

Check whether $36\div6=6$ is correct.

Solution

Multiply back: $6\times6=36$.
It matches, so it is correct.
Answer: Yes, correct

Worked Example

Find $45\div9$ using your tables.

Solution

$9\times5=45$.
So $45\div9=5$.
Answer: $5$

Key Points

Multiplication and division are inverse (opposite) operations.
A fact family links three numbers, e.g. $3\times4=12$, $12\div3=4$, $12\div4=3$.
To divide, ask "what times the divisor gives the dividend?"
Knowing your times tables means you already know the division facts.
Check any division by multiplying the answer back.
Keep the family the right way round: from $5\times6=30$ you get $30\div5$ and $30\div6$.

Quick Check — 4 MCQs

Tap an option to check your answer0 / 4

Q1.Division is the opposite (inverse) of:

Explanation: Multiplication.

Q2.If $6\times4=24$, then $24\div6=$

Explanation: $4$.

Q3.To find $42\div7$, ask "$7$ times what is $42$?" The answer is:

Explanation: $6$.

Q4.You can check $36\div6=6$ by working out:

Explanation: $6\times6=36$.

Practice more MCQs → 📝 Assignment · 35 marks