division
Dividing by itself
Show why a number divided by itself equals 1, except for the special case of zero.
Quick answer
Any number divided by itself equals 1, except for zero, which cannot be divided by itself.Learning outcome
By the end of this page, you will understand why any number (except zero) divided by itself always equals 1. Success signs:- You can explain why 6 ÷ 6 = 1
- You can show that 100 ÷ 100 = 1 using objects or drawings
- You can say why 0 ÷ 0 is not possible
- You can solve simple division problems where the number is divided by itself
Why this matters
This maths rule helps you understand how numbers work and makes solving bigger problems easier. When you know that a number divided by itself equals 1, you can use this fact to check your answers, simplify fractions, and solve puzzles. It's also a useful trick in games, cooking, and everyday life when you need to share things equally.How it works
Division is about sharing equally. When you divide a number by itself, you are asking: "How many groups of this number can I make from this number?" The answer is always 1 group, because you're taking all of it to make one group. Let's think of it like sharing pizza:- If you have 4 slices and you want to share them equally among 4 people, each person gets 1 slice.
- If you have 8 slices and you want to share them equally among 8 people, each person gets 1 slice.
- So 4 ÷ 4 = 1 and 8 ÷ 8 = 1
Examples you can see
Here are some examples of dividing by itself:| Division | What it means | Answer |
|---|---|---|
| 5 ÷ 5 | 5 things shared equally among 5 people | 1 |
| 3 ÷ 3 | 3 things shared equally among 3 people | 1 |
| 12 ÷ 12 | 12 things shared equally among 12 people | 1 |
| 1000 ÷ 1000 | 1000 things shared equally among 1000 people | 1 |
Try it as a mini adventure
Adventure: The Magic Sharing Box You are a treasure hunter and you find a magical box that can share anything equally. The box has a special rule: it can only share items equally with the same number of people as items. You find 5 golden coins and a friend says, "Let's share them equally!" How many coins does each person get? Answer: 5 ÷ 5 = 1 coin each You find 8 blue gems and invite 8 friends to share them. How many gems does each friend get? Answer: 8 ÷ 8 = 1 gem each You find 15 red stones and invite 15 people to share them. How many stones does each person get? Answer: 15 ÷ 15 = 1 stone each Now, what happens if you find 0 coins and try to share them? That's tricky! The magic box can't share nothing with anyone.Common mistakes
- Mistake: Thinking 0 ÷ 0 = 0
Why it happens: Children might think that if you have nothing and try to share nothing, it should equal nothing.
Correct answer: 0 ÷ 0 is not possible because you can't share nothing with nothing. It's like asking how many times zero fits into zero – there's no answer. - Mistake: Thinking 1 ÷ 1 = 0
Why it happens: Children might confuse division with subtraction, thinking 1 - 1 = 0.
Correct answer: 1 ÷ 1 = 1 because one thing shared among one person gives one thing to that person. - Mistake: Thinking 10 ÷ 10 = 10
Why it happens: Children might think they're just keeping the number and not dividing it.
Correct answer: 10 ÷ 10 = 1 because you're sharing 10 things among 10 people, so each person gets 1 thing.
Parent and carer guide
Help your child understand this concept by using real-life examples:
- Use everyday items like apples, cookies, or toys to show sharing equally.
- Ask questions like: "If you have 6 crayons and you want to share them equally among 6 friends, how many crayons does each friend get?"
- Point out that this is the same as asking "How many groups of 6 can you make from 6?"
- Use physical objects to show that 6 ÷ 6 = 1 by placing 6 objects in a line and then grouping them into 6 equal groups.
- Remember that zero is special – explain that you can't share nothing with nothing, so 0 ÷ 0 is not possible.
- Encourage your child to try different numbers: 3 ÷ 3, 7 ÷ 7, 12 ÷ 12, etc.
- Keep it fun! Try the magic box adventure together.
Don't worry if your child gets confused at first – this is a new concept. Be patient and keep practicing with simple examples.
Practice questions
- What is 4 ÷ 4?
- What is 9 ÷ 9?
- What is 15 ÷ 15?
- What is 20 ÷ 20?
- What is 100 ÷ 100?
- What is 1 ÷ 1?
- What is 25 ÷ 25?
- What is 8 ÷ 8?
- What is 30 ÷ 30?
- What is 12 ÷ 12?
- 1
- 1
- 1
- 1
- 1
- 1
- 1
- 1
- 1
- 1
FAQ
Why does any number divided by itself equal 1?
When you divide a number by itself, you are sharing that number equally among that same number of people or groups. So each person or group gets exactly 1 part.
What happens when you divide 0 by 0?
0 ÷ 0 is not possible because it doesn't make sense. You can't share nothing with nothing. There's no answer to this question.
Does this rule work with fractions?
Yes! For example, ½ ÷ ½ = 1. This means half of something shared equally among half of something else gives you 1 whole.
Can I use this rule to solve bigger problems?
Yes! If you know that 12 ÷ 12 = 1, you can use this to simplify fractions or check your work in bigger division problems.
Is this rule true for all numbers?
Yes, it works for all numbers except zero. Zero divided by zero is not possible, so it's a special case.