Compare Operations: Is 360÷360 Equal to 360×1?

Q: Why does any number divided by itself equal 1?

Think of it this way: division asks 'how many groups?' If you have 360 items and divide them into groups of 360, you get exactly 1 group. This works for any non-zero number!

Q: What happens when I multiply any number by 1?

Multiplying by 1 is the multiplicative identity - it leaves the number unchanged! So 360×1 = 360, just like 25×1 = 25 or 0.5×1 = 0.5.

Q: How do I remember which symbol to use when comparing?

Think of the symbol as a 'hungry mouth' that always opens toward the larger number. Since 1

Q: Can I use this same method for other numbers?

Absolutely! Try 50÷50 vs 50×1. You'll get 1

Q: What if the number was 0 instead of 360?

Great question! 0÷0 is undefined in mathematics, so we can't use this comparison method. But 0×1 = 0, which is perfectly valid.

Division vs Multiplication with Identity Elements

Choose the correct sign (?):

$360:360\stackrel{?}{=}360\times1$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Identify the correct mathematical sign

00:04 Any number divided by itself always equals 1

00:12 Any number multiplied by 1 always equals itself

00:24 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Choose the correct sign (?):

$360:360\stackrel{?}{=}360\times1$

Step-by-step solution

To solve this problem, we'll evaluate each expression and then compare the results:

Step 1: Compute $360 \div 360$ which simplifies to $1$ because any non-zero number divided by itself equals $1$ .
Step 2: Compute $360 \times 1$ which simplifies to $360$ because any number multiplied by $1$ remains unchanged.

Now, we'll compare $1$ and $360$ :

- Since $1$ is less than $360$ , the correct sign to use is $\lt$ .

Thus, the correct expression is $360 \div 360 \lt 360 \times 1$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Division Rule: Any non-zero number divided by itself equals 1
Technique: Calculate each side separately: 360÷360 = 1, 360×1 = 360
Check: Compare final values: 1 < 360, so use < symbol ✓

Common Mistakes

Avoid these frequent errors

Assuming division and multiplication with 1 give the same result
Don't think 360÷360 equals 360×1 because both involve 360 and 1 = wrong comparison! Division by itself always gives 1, while multiplication by 1 keeps the original number. Always calculate each expression separately before comparing.

Practice Quiz

Test your knowledge with interactive questions

$$ 2+0= $$

FAQ

Everything you need to know about this question

Why does any number divided by itself equal 1?

Think of it this way: division asks 'how many groups?' If you have 360 items and divide them into groups of 360, you get exactly 1 group. This works for any non-zero number!

What happens when I multiply any number by 1?

Multiplying by 1 is the multiplicative identity - it leaves the number unchanged! So 360×1 = 360, just like 25×1 = 25 or 0.5×1 = 0.5.

How do I remember which symbol to use when comparing?

Think of the symbol as a 'hungry mouth' that always opens toward the larger number. Since 1 < 360, the mouth opens toward 360, giving us the < symbol.

Can I use this same method for other numbers?

Absolutely! Try 50÷50 vs 50×1. You'll get 1 < 50. Or 7÷7 vs 7×1 gives 1 < 7. The pattern always holds for positive numbers.

What if the number was 0 instead of 360?

Great question! 0÷0 is undefined in mathematics, so we can't use this comparison method. But 0×1 = 0, which is perfectly valid.

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