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0 times table division facts

division

0 times table division facts

Connect multiplication and division so children can use the 0 table to solve sharing and grouping questions.

Quick answer

When you divide any number by 0, you can't do it – it's impossible! But when you divide 0 by any number (except 0), the answer is always 0.

Learning outcome

By the end of this page, you will understand that 0 divided by any number (except 0) equals 0, and that dividing any number by 0 is not possible.

Success signs:

You can explain why 0 ÷ 5 = 0
You can tell someone that 10 ÷ 0 cannot be done
You can solve simple division problems involving 0
You can explain the difference between 0 ÷ 5 and 5 ÷ 0

Why this matters

Understanding division with zero helps you solve problems in real life and prepares you for more advanced maths. You might need to know that you can't split something into zero parts, or that if you have zero cookies and try to share them among friends, each friend gets zero cookies. This idea is important for understanding bigger maths later on, like fractions, algebra, and working with numbers in science and engineering.

How it works

Division is about sharing or grouping things equally. When we divide, we ask:

How many groups can we make?
How many items are in each group?

When we divide 0 by any number, we are asking:

If we have 0 things, and we try to share them into some number of groups, how many things are in each group?

Since there are no things to share, each group gets 0 things.

But when we try to divide any number by 0, we're asking:

If we have some number of things, and we try to split them into 0 groups, how many things are in each group?

This is impossible because you can't make 0 groups!

Examples you can see

Example 1: Sharing Zero Cookies

Imagine you have 0 cookies. You want to share them equally among 4 friends.

How many cookies does each friend get? 0 ÷ 4 = 0

Since there are no cookies, each friend gets 0 cookies.

Example 2: Zero Apples in 3 Boxes

You have 0 apples and you want to put them into 3 boxes.

How many apples go in each box? 0 ÷ 3 = 0

Since there are no apples, each box has 0 apples.

Example 3: Impossible Sharing

You have 6 oranges and want to put them into 0 boxes.

How many oranges go in each box? 6 ÷ 0 = impossible

There's no way to put oranges into 0 boxes!

Example 4: The 0 Times Table in Reverse

Think about multiplication facts with 0:

0 × 5 = 0
0 × 10 = 0
0 × 1 = 0

When we reverse these to division:

0 ÷ 5 = 0
0 ÷ 10 = 0
0 ÷ 1 = 0

Try it as a mini adventure

Adventure: The Zero Island

You are a space explorer on a mysterious island called Zero Island. On this island, everything is about the number zero!

First time: You find 0 treasure chests. You try to share them equally among 3 friends. How many chests does each friend get? 0 ÷ 3 = 0
Second time: You collect 0 seashells and want to put them in 6 shells. How many shells do you put in each? 0 ÷ 6 = 0
Third time: You have 8 golden coins and want to split them among 0 treasure hunters. What happens? 8 ÷ 0 = impossible!
Fourth time: You find 0 stars in the sky and want to give them to 2 astronauts. How many stars does each astronaut get? 0 ÷ 2 = 0

As you explore, you learn that on Zero Island, dividing by zero is like trying to make a sandwich with no bread – it just doesn't work!

Common mistakes

Mistake	Why it happens	Correct answer
Thinking 0 ÷ 5 = 5	Children might confuse division with addition, thinking 0 + 5 = 5	0 ÷ 5 = 0
Thinking 5 ÷ 0 = 5	Children might think that since 5 ÷ 5 = 1, then 5 ÷ 0 = 5	5 ÷ 0 is impossible
Confusing 0 ÷ 5 and 5 ÷ 0	Children might not understand that order matters in division	0 ÷ 5 = 0, but 5 ÷ 0 = impossible
Thinking 0 ÷ 0 = 0	Children might think that if both numbers are zero, it should work	0 ÷ 0 is undefined (not a number)

Parent and carer guide

Help your child understand zero division by:

Using everyday examples like sharing cookies or toys
Reinforcing that 0 ÷ any number (except 0) = 0
Explaining that dividing by 0 is impossible, not just "we don't know"
Using the multiplication connection: if 0 × 5 = 0, then 0 ÷ 5 = 0
Encouraging them to draw pictures or use objects to understand
Being patient if they make mistakes – it's normal to get confused!

Ask questions like:

What happens when you have 0 apples and try to share with 4 friends?
Can you think of a time you had 0 of something?
Why can't we divide by zero?

Remember: Don't worry if your child doesn't get it straight away. This is a tricky concept that takes time to understand!

Practice questions

What is 0 ÷ 2? Answer: 0
What is 0 ÷ 10? Answer: 0
What is 0 ÷ 1? Answer: 0
What is 0 ÷ 7? Answer: 0
What is 0 ÷ 15? Answer: 0
What is 5 ÷ 0? Answer: Impossible
What is 12 ÷ 0? Answer: Impossible
What is 100 ÷ 0? Answer: Impossible
What is 0 ÷ 9? Answer: 0
What is 0 ÷ 3? Answer: 0

FAQ

Why can't you divide by zero?

Dividing by zero doesn't work because it's like trying to split something into no parts. You can't make zero groups, so the question doesn't make sense.

What is 0 divided by any number?

Zero divided by any number (except 0) always equals 0. This is because if you have nothing to share, each group gets nothing.

Can you divide zero by zero?

No, 0 ÷ 0 is undefined. It's not a number and doesn't make mathematical sense.

How does this connect to multiplication?

Division is the opposite of multiplication. If 0 × 5 = 0, then 0 ÷ 5 = 0. This helps us understand how numbers work together.

Why is learning this important?

Understanding zero division helps you solve real problems and prepares you for more advanced maths like algebra and fractions. It also helps you understand why some mathematical operations are not allowed.