Solve the Expression: Finding the Correct Sign in 0:4?4+0

Q: What does the colon (:) symbol mean in math?

The colon (:) is another way to write division! So $ 0:4 $ means the same thing as $ 0 ÷ 4 $ or $ \frac{0}{4} $.

Q: Why does 0 divided by any number equal 0?

Think of division as "how many groups?" If you have 0 items to divide into 4 groups, each group gets 0 items. So $ \frac{0}{4} = 0 $.

Q: Does adding zero change a number?

No! Adding zero to any number leaves it unchanged. This is called the additive identity property. So $ 4 + 0 = 4 $.

Q: How do I know which inequality sign to use?

Compare the two values like you would on a number line. Since 0 is to the left of 4 on the number line, we write \( 0 .

Q: What if both sides were equal?

If both sides gave the same result, you'd use the equals sign (=). But here, $ 0 ≠ 4 $, so we need either .

Comparing Expressions with Division and Addition

Choose the correct sign (?):

$0:4?4+0$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Identify the correct mathematical sign

00:04 0 divided by any number always equals 0

00:10 Any number plus 0 always equals the number itself

00:22 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 (?):

$0:4?4+0$

Step-by-step solution

To solve this problem, we will evaluate each part of the expression separately.

Firstly, evaluate $0:4$ which is interpreted as $\frac{0}{4}$ . Since dividing zero by any non-zero number results in zero, we get $\frac{0}{4} = 0$ .
Next, evaluate $4+0$ . According to the property of addition, adding zero to any number does not change the number, thus $4+0 = 4$ .

Now, we need to compare the two results: $0$ and $4$ .

Since $0$ is less than $4$ , the correct inequality sign to use between them is $<$ .

Thus, the correct sign for the expression $0:4?4+0$ is $<$ .

Therefore, the solution to the problem is $0:4 < 4+0$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Division Rule: Any number divided by zero is undefined; zero divided by any non-zero number equals zero
Technique: Evaluate each side separately: $0:4 = 0$ and $4+0 = 4$
Check: Compare final values: $0 < 4$ makes sense since zero is less than four ✓

Common Mistakes

Avoid these frequent errors

Misinterpreting the division notation
Don't treat 0:4 as multiplication or another operation = wrong calculation! The colon (:) represents division, so 0:4 means 0÷4. Always recognize that : means division and evaluate accordingly.

Practice Quiz

Test your knowledge with interactive questions

$1\times1000=$

FAQ

Everything you need to know about this question

What does the colon (:) symbol mean in math?

The colon (:) is another way to write division! So $0:4$ means the same thing as $0 ÷ 4$ or $\frac{0}{4}$ .

Why does 0 divided by any number equal 0?

Think of division as "how many groups?" If you have 0 items to divide into 4 groups, each group gets 0 items. So $\frac{0}{4} = 0$ .

Does adding zero change a number?

No! Adding zero to any number leaves it unchanged. This is called the additive identity property. So $4 + 0 = 4$ .

How do I know which inequality sign to use?

Compare the two values like you would on a number line. Since 0 is to the left of 4 on the number line, we write $0 < 4$ .

What if both sides were equal?

If both sides gave the same result, you'd use the equals sign (=). But here, $0 ≠ 4$ , so we need either < or >.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Order of operations for beginners questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime