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

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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

Solve the following exercise:

\( (+6)\cdot(+9)= \)

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?

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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?

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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?

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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.

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