Solve: 100×0×3?0:30 - Determining the Correct Comparison Operator

Q: Why does any number times zero equal zero?

Think of multiplication as repeated addition. If you add zero to itself 100 times, you still get zero! This is the zero property of multiplication - it's a fundamental math rule.

Q: What does 0:30 mean in this problem?

The notation 0:30 represents zero divided by thirty, which equals $ \frac{0}{30} = 0 $. Any zero divided by a non-zero number always equals zero.

Q: Do I need to calculate 100 × 3 first?

No! Since there's a zero in the multiplication chain, you can immediately say the result is zero. The zero property makes calculation much faster.

Q: How do I compare 0 and 0:30?

Both expressions equal zero: $ 100 \times 0 \times 3 = 0 $ and $ 0:30 = 0 $. Since 0 = 0, the correct comparison sign is equals (=).

Q: What if the zero wasn't there?

Without zero, you'd calculate $ 100 \times 3 = 300 $ and compare it to 30. But the zero changes everything - it makes the whole left side equal zero!

Multiplication with Zero Properties

Choose the correct sign (?):

$100\times0\times3?0:30$

❤️ 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 Any number multiplied by 0 always equals 0

00:11 Whenever 0 is a factor, the product is 0

00:24 0 divided by any number always equals 0

00:31 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 (?):

$100\times0\times3?0:30$

Step-by-step solution

In this problem, we need to determine the correct sign that fits between the expressions on either side, specifically involving multiplication and comparison. We will follow these steps:

Step 1: Calculate the left-hand side of the expression, $100 \times 0 \times 3$ .
Step 2: Use the multiplication property of zero.
Step 3: Compare the result from Step 1 to the number 30.

Step 1: Let's calculate $100 \times 0$ . According to arithmetic rules, any number multiplied by zero is zero. Thus, $100 \times 0 = 0$ .

Step 2: Now let's proceed with $0 \times 3$ . Again, multiplying zero by any number yields zero. So, $0 \times 3 = 0$ .

Step 3: Now we compare the result $0$ to $30$ . Since zero is less than thirty, we check whether the expressions are equal or not.

Since $0 = 0$ , the correct sign between the expressions is $=$ . Therefore, the solution to the problem is: $=$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Zero Rule: Any number multiplied by zero equals zero
Technique: Calculate $100 \times 0 \times 3 = 0$ step by step
Check: Compare final results: 0 and 0:30 both equal 0 ✓

Common Mistakes

Avoid these frequent errors

Ignoring zero in multiplication chains
Don't calculate 100 × 3 = 300 first and ignore the zero = wrong answer of 300! When zero appears anywhere in multiplication, the entire result becomes zero. Always apply the zero property immediately when you see it.

Practice Quiz

Test your knowledge with interactive questions

$1\times1000=$

FAQ

Everything you need to know about this question

Why does any number times zero equal zero?

Think of multiplication as repeated addition. If you add zero to itself 100 times, you still get zero! This is the zero property of multiplication - it's a fundamental math rule.

What does 0:30 mean in this problem?

The notation 0:30 represents zero divided by thirty, which equals $\frac{0}{30} = 0$ . Any zero divided by a non-zero number always equals zero.

Do I need to calculate 100 × 3 first?

No! Since there's a zero in the multiplication chain, you can immediately say the result is zero. The zero property makes calculation much faster.

How do I compare 0 and 0:30?

Both expressions equal zero: $100 \times 0 \times 3 = 0$ and $0:30 = 0$ . Since 0 = 0, the correct comparison sign is equals (=).

What if the zero wasn't there?

Without zero, you'd calculate $100 \times 3 = 300$ and compare it to 30. But the zero changes everything - it makes the whole left side equal zero!

🌟 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