If you’ve been wondering about math, you might have some knowledge about infinity, zero, and division. But did you know that today’s Wonder of the Day combines all of these topics?

In school, you might have learned that math follows certain rules. For example, multiplying two negative numbers always gives a positive result. Dividing any number by itself always equals one. And if you multiply any number by zero, the answer is always zero.

However, today we’re going to talk about a rule that seems to contradict the last one: you can’t divide any number by zero.

Why is that? Like many math concepts, it’s easier to understand through a real-life example. Imagine you and three family members are sharing a pizza for dinner. The pizza has eight slices and there are four of you. How many slices of pizza can each person have?

If you said two, you’re correct! Division is all about dividing numbers into equal groups. Now, what if there were only two people sharing the pizza? Eight slices divided by two means each person gets four slices. And if you were the only one having dinner? Congratulations, you get all eight slices!

Now, imagine dividing eight slices of pizza among zero people. How many slices would each person get? If you’re confused, don’t worry. It’s impossible to divide a pizza among zero people. There’s no way to split those eight slices into zero equal groups. It just doesn’t make sense!

Just like in this example, it’s impossible to divide any number by zero in math. Or at least, there’s currently no known way to do it. Mathematicians are always trying to find answers to challenging math problems, and many have attempted to figure out how to divide by zero. However, none have been successful so far.

Instead, any number divided by zero is undefined. In fact, even zero divided by zero is undefined! This means that we don’t have an answer for this problem yet. After all, how can you divide zero into zero equal groups?

So, what does infinity have to do with this? As you divide a number (the dividend) by smaller and smaller numbers (divisors), the answer (quotient) becomes larger and larger. Take a look at this example:

1 ÷ 1 = 1.

1 ÷ 0.1 = 10.

1 ÷ 0.01 = 100.

1 ÷ 0.000001 = 1,000,000.

In other words, as the divisor gets closer to zero, the quotient approaches infinity. Will mathematicians ever find a way to divide by zero? Maybe! But for now, dividing by zero will always give an undefined answer.

## Give it a try

Keep learning with the help of a friend or family member and the activities below.

- If you want to know more about the concept and history of zero, you can find interesting facts on Kiddle. Are you intrigued by anything about the number zero? Did you know that some countries and cultures in the past were not aware of zero? Feel free to share the most fascinating facts with a friend or family member.
- Are you curious about why zero needed to be invented and who invented it? Although it may seem obvious to us now, the invention of zero was a significant advancement in mathematics. Watch the video from the Science Museum and write a brief summary of what you’ve learned. Share your summary with a friend or family member.
- Undefined numbers and infinity? It’s understandable why dividing by zero can be perplexing. The concept of zero itself can be mystifying. Here are a few practical activities that can help you become more familiar with the idea. Make sure to try these activities with a friend or family member.

### Sources of Wonder

https://www.mathsisfun.com/numbers/dividing-by-zero.html (accessed on 22nd September 2021)

https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:foundation-algebra/x2f8bb11595b61c86:division-zero/v/why-dividing-by-zero-is-undefined (accessed on 22nd September 2021)

http://ee.usc.edu/stochastic-nets/docs/divide-by-zero.pdf (accessed on 22nd September 2021)

https://mathwithbaddrawings.com/2013/05/07/why-cant-you-divide-by-zero/ (accessed on 22nd September 2021)

https://learnersdictionary.com/ (accessed on 22nd September 2021)

## FAQ

**1. Can you divide by zero?**

No, you cannot divide by zero. Division by zero is undefined in mathematics. When you divide a number by zero, you encounter a contradiction. This is because division is essentially the process of finding out how many times one number can fit into another. However, zero cannot be divided into any number to give a meaningful result. It leads to a mathematical error and violates the fundamental rules of arithmetic.

**2. What happens when you divide a number by zero?**

When you divide a number by zero, you encounter a mathematical error. The result is undefined. It is not possible to determine how many times zero can fit into any number because zero cannot be divided into any number without contradicting the basic principles of arithmetic. The operation of dividing by zero leads to an inconsistency, making it an invalid mathematical operation.

**3. Why is dividing by zero not allowed?**

Dividing by zero is not allowed because it leads to contradictions and inconsistencies in mathematics. When you divide a number by zero, you encounter a situation where you are trying to find out how many times zero can fit into a number. However, this is not possible because there is no meaningful answer to this question. It violates the fundamental rules of arithmetic and disrupts the logical structure of mathematics.

**4. What is the concept of division by zero?**

The concept of division by zero refers to the operation of dividing a number by zero. Mathematically, division is the process of finding out how many times one number can fit into another. However, when you divide a number by zero, you encounter a contradiction. Zero cannot be divided into any number without violating the basic principles of arithmetic. Therefore, division by zero is considered undefined and is not allowed in mathematics.

**5. Are there any situations where division by zero is allowed?**

No, there are no situations where division by zero is allowed. Division by zero is undefined and not permissible in mathematics. It leads to contradictions and inconsistencies. In various mathematical applications and calculations, division by zero is considered an error and is not a valid operation. It is important to follow the rules of arithmetic and avoid dividing any number by zero to ensure accurate and meaningful mathematical results.

**6. What are the consequences of dividing by zero?**

The consequences of dividing by zero are mathematical errors and inconsistencies. When you divide a number by zero, the result is undefined. It leads to contradictions and violates the fundamental principles of arithmetic. Division by zero disrupts the logical structure of mathematics and renders the operation invalid. It is essential to avoid dividing any number by zero to ensure accurate and meaningful calculations. Division by zero should be avoided in all mathematical applications to maintain the integrity of the calculations.

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