Maths Facts
0 times table and division by zero are not the same
A safe age-appropriate warning that multiplying by zero is fine, while dividing by zero is a different and much later idea.
Quick answer
Multiplying any number by zero always gives zero, but dividing by zero is not allowed in maths. The 0 times table is easy to learn, but division by zero is a special rule that children don't need to worry about yet.Learning outcome
By the end of this page, you will understand that multiplying any number by zero always gives zero, and that division by zero is not allowed in maths. You will also be able to solve simple multiplication problems with zero and know why some maths problems cannot be done. Success signs:- You can say that 0 x 5 = 0
- You can explain that you cannot divide by zero
- You can solve 0 x 7 = ?
- You can show that 0 x 0 = 0
Why this matters
Understanding the 0 times table is important because it helps you solve bigger maths problems later. It also helps you know what to do when you see zero in a maths problem. Knowing that you can't divide by zero helps you avoid silly mistakes in more advanced maths. In real life, you might use zero when sharing, counting, or even when playing games!How it works
Multiplying by zero is like having no groups of anything. If you have 0 apples in each of 5 bags, you still have 0 apples in total. When you multiply by zero, you are saying, "I have zero groups of something", so the answer is always zero. Division by zero is different. It's like trying to share 10 sweets between 0 friends. That doesn't make sense because there are no friends to share with. In maths, this is not allowed.Examples you can see
Let's look at some examples of the 0 times table:| 0 x 0 | 0 x 1 | 0 x 2 | 0 x 3 | 0 x 4 | 0 x 5 | 0 x 6 | 0 x 7 | 0 x 8 | 0 x 9 | 0 x 10 | 0 x 11 | 0 x 12 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
- 0 cars in box 1 + 0 cars in box 2 + 0 cars in box 3 = 0 cars total
- This is the same as 0 x 3 = 0
- Each friend gets 0 pieces
- So 0 x 7 = 0 pieces total
- Each friend gets 0 balloons
- So 0 x 5 = 0 balloons
Try it as a mini adventure
The Great Zero Quest You are a brave explorer who finds a magical treasure map. The map says: "To find the treasure, you must solve the Zero Challenge!" Here's your first clue: "If you have 0 cookies in each of 4 boxes, how many cookies are there in total?" You can solve this by thinking: 0 x 4 = 0 Your second clue: "If you have 0 apples in each of 12 baskets, how many apples are there?" Answer: 0 x 12 = 0 Your final challenge: "If you have 0 toys and 0 friends, how many toys does each friend get?" Answer: 0 x 0 = 0 You have completed the Zero Challenge and found your treasure!Common mistakes
- Mistake: Thinking that 0 ÷ 0 = 0
Why it happens: Children might think that if you have zero of something and divide it by zero, you still have zero.
Correct answer: 0 ÷ 0 is actually undefined (not allowed in maths) because it doesn't make sense to divide nothing by nothing. - Mistake: Believing that 0 x 0 = 1
Why it happens: Sometimes children mix up multiplication with addition and think that 0 + 0 = 0, so 0 x 0 = 1.
Correct answer: 0 x 0 = 0, because zero groups of zero things is still zero things. - Mistake: Thinking that dividing by zero is the same as multiplying by zero
Why it happens: Children may confuse the two operations because both involve the number zero.
Correct answer: Multiplying by zero gives zero, but dividing by zero is not allowed.
Parent and carer guide
How to help your child learn: 1. Use real-life examples: Ask your child to think of situations where they have zero of something. For example, "If you have 0 toys and 3 friends, how many toys does each friend get?" 2. Practice the 0 times table: Write out 0 x 0 to 0 x 12 together. You can use objects like blocks or counters to show zero groups. 3. Explain the difference: Tell your child that multiplying by zero is fine and easy, but dividing by zero is not allowed in maths. Don't worry about the complicated reasons now – just say it's a special rule. 4. Be patient: It's normal for children to get confused about division by zero. Don't worry if they don't understand it right away. They'll learn more about it in school later. 5. Keep it fun: Turn the learning into a game. You can play "Zero Challenge" where you ask questions like "What is 0 x 8?" or "What is 0 x 12?" What to watch for:- Confusion between multiplication and division by zero
- Thinking that 0 ÷ 0 = 0 or 0 ÷ 0 = 1
- Trying to divide by zero in games or puzzles
Practice questions
- What is 0 x 6?
- What is 0 x 11?
- What is 0 x 0?
- What is 0 x 100?
- What is 0 x 1?
- 0
- 0
- 0
- 0
- 0
FAQ
Why is 0 times anything equal to 0?
When you multiply by zero, you're saying you have zero groups of something. No matter how big each group is, if there are no groups, you still have nothing.
Can you divide by zero?
No, you cannot divide by zero in maths. It's not allowed because it doesn't make sense. It's like trying to share 10 sweets between 0 friends.
Is 0 x 0 = 0?
Yes, 0 x 0 = 0. This means you have zero groups of zero things, which is still zero things.
Why do we need to know the 0 times table?
Knowing the 0 times table helps you solve bigger maths problems. It's also important because it helps you understand what happens when you see zero in any multiplication problem.
What happens when you divide by zero?
When you try to divide by zero, mathematicians say it's undefined or not allowed. It's not a number you can get as an answer. It's a special rule that helps keep maths consistent.