Solve: -412 ÷ (1/3) Missing Comparison Sign Problem

Division of Negative Numbers with Comparisons

Fill in the missing sign (?):

412:(+13)?0 -412:(+\frac{1}{3})\text{?}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 Complete the appropriate sign
00:03 Let's take only the signs and check what will be the result sign
00:06 Negative divided by positive always equals negative
00:09 Negative is necessarily less than 0
00:12 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Fill in the missing sign (?):

412:(+13)?0 -412:(+\frac{1}{3})\text{?}0

2

Step-by-step solution

Note that we are dividing a negative number by a positive number:

:+= -:+=-

Therefore, the exercise is:

?0 -?0

Since we have a negative number, it must be less than zero.

Therefore, the answer is:

<0 - < 0

3

Final Answer

>

Key Points to Remember

Essential concepts to master this topic
  • Rule: Negative divided by positive always equals negative result
  • Technique: Calculate -412 ÷ (1/3) = -412 × 3 = -1236
  • Check: Any negative number is always less than zero: -1236 < 0 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting that negative ÷ positive = negative
    Don't think -412 ÷ (1/3) gives a positive result = wrong comparison sign! Division sign rules are the same as multiplication: negative ÷ positive always equals negative. Always remember that any negative number is less than zero.

Practice Quiz

Test your knowledge with interactive questions

What will be the sign of the result of the next exercise?

\( (-2)\cdot(-4)= \)

FAQ

Everything you need to know about this question

How do I divide by a fraction like 1/3?

+

When dividing by a fraction, multiply by its reciprocal! So -412 ÷ (1/3) becomes -412 × 3 = -1236.

Why is the answer negative when we're dividing?

+

The sign rules for division are the same as multiplication: negative ÷ positive = negative. Since -412 is negative and 1/3 is positive, the result must be negative.

How do I know which comparison sign to use?

+

After calculating the division result, compare it to zero. Since 1236<0 -1236 < 0 , the answer is less than (<).

What if I get confused about the sign rules?

+

Remember this simple pattern: same signs give positive, different signs give negative. Since we have negative ÷ positive (different signs), the answer is negative.

Can the result ever equal zero in problems like this?

+

Only if the numerator is zero. Since -412 ≠ 0, our result cannot equal zero. Any non-zero number divided by another non-zero number gives a non-zero result.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Signed Numbers (Positive and Negative) 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

More Questions

Click on any question to see the complete solution with step-by-step explanations