Brahmagupta and the rules of zero

Quick answer

Brahmagupta was an ancient Indian mathematician who invented the rules for using zero in maths. He showed us how to add, subtract, multiply, and divide with zero, which helps us do more complex maths today.

Learning outcome

By the end of this page, you will understand that zero is a special number that helps us do maths, and that ancient mathematicians like Brahmagupta had to work out the rules for how to use it properly.

• You can explain that zero means "nothing" in maths
• You can show how adding zero to a number doesn’t change it
• You can understand that multiplying by zero always gives zero
• You can describe how Brahmagupta helped make maths more powerful

Why this matters

Zero is one of the most important numbers in maths. Without it, we couldn’t do complex maths or use our number system the way we do today. Brahmagupta's work helped make modern maths possible. You use zero every day when you count, share, or even play games!

How it works

Imagine you have 5 apples. If you add 0 apples, you still have 5 apples. If you take away 0 apples, you still have 5 apples. But what happens when you multiply by 0? You get 0 apples. These are the rules that Brahmagupta helped create.

1. Zero means "nothing"
2. Adding zero to a number doesn’t change it
3. Subtracting zero from a number doesn’t change it
4. Multiplying any number by zero gives zero
5. Dividing zero by any number gives zero

Examples you can see

Let's imagine you're at a party:

• You have 7 cookies. You get 0 more cookies. Now you still have 7 cookies. (7 + 0 = 7)
• You have 10 stickers. You give away 0 stickers. Now you still have 10 stickers. (10 - 0 = 10)
• You have 3 bags, each with 0 marbles. You have 0 marbles in total. (3 × 0 = 0)
• You have 0 cakes and 5 friends. Each friend gets 0 cakes. (0 ÷ 5 = 0)

Here is a table showing how zero works in maths:

Try it as a mini adventure

Imagine you are a detective solving a mystery in an ancient city. You find a strange number system that uses zero. Your mission is to discover how zero works in this ancient maths. You must solve these clues:

1. You have 12 gold coins and find 0 more. How many coins do you have now? Answer: 12
2. You have 8 toy cars and give away 0 cars. How many cars do you have now? Answer: 8
3. You have 0 balloons and 3 friends. How many balloons does each friend get? Answer: 0
4. You have 5 groups of 0 stickers. How many stickers do you have? Answer: 0

Common mistakes

• Mistake: Thinking that 0 divided by 0 equals 0
  Why it happens: Confusing rules for dividing by zero
  Fix: Remember that 0 divided by any number (except 0) equals 0. 0 ÷ 5 = 0, but 0 ÷ 0 is undefined.
• Mistake: Believing that multiplying by zero gives a big number
  Why it happens: Mixing up the rules for addition and multiplication
  Fix: Always remember: any number times 0 = 0
• Mistake: Thinking zero means "nothing" in all situations
  Why it happens: Not understanding that zero is a number like any other
  Fix: Zero is a number that helps us count and measure. It's just special!

Parent and carer guide

Help your child understand zero by using everyday examples:

• When you're cooking, ask them to add 0 teaspoons of salt to a recipe. Show that the recipe doesn't change.
• Use toys or food to demonstrate that 5 + 0 = 5 or 5 - 0 = 5.
• Explain that zero is not just "nothing" – it's a number that helps us do maths better.
• Point out that zero is used in many places: clocks (09:00), temperature (0°C), and even in games like football (0 goals).
• Encourage them to ask questions about why zero is important – it's a great way to build curiosity!

Practice questions

1. What is 7 + 0? Answer: 7
2. What is 10 - 0? Answer: 10
3. What is 0 × 8? Answer: 0
4. What is 0 ÷ 6? Answer: 0
5. What is 15 + 0? Answer: 15
6. What is 0 × 12? Answer: 0
7. What is 0 ÷ 3? Answer: 0
8. What is 9 - 0? Answer: 9
9. What is 0 × 0? Answer: 0
10. What is 11 + 0? Answer: 11

FAQ

Who was Brahmagupta?

Brahmagupta was an ancient Indian mathematician who lived around 598–668 AD. He was one of the first to write about zero and how to use it in maths.

Why is zero important in maths?

Zero helps us count and measure properly. Without it, we couldn’t have the number system we use today. It also helps us do more complex maths, like algebra and calculus.

Can you divide by zero?

Not really. We can't divide any number by zero because it doesn’t make sense. But we can divide zero by any number (except zero), and that always equals zero.

How did people use zero before Brahmagupta?

People used to use spaces or dots to show "nothing," but Brahmagupta was the first to treat zero like a real number with its own rules.

What other numbers did Brahmagupta work with?

Brahmagupta also worked with negative numbers, algebra, and geometry. He was one of the greatest mathematicians of his time!