Find the Missing Symbol in Operation Sequence: +314:-209:-5⅓?0

Sign Analysis with Sequential Operations

Fill in the missing symbol (?):

+314:209:513?0 +314:-209:-5\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
00:04 Let's take only the signs and check what will be the result sign
00:12 Positive divided by negative always equals negative
00:20 Negative divided by negative always equals positive
00:23 Positive is necessarily greater than 0
00:26 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 symbol (?):

+314:209:513?0 +314:-209:-5\frac{1}{3}\text{?}0

2

Step-by-step solution

Note that in the first step we are dividing a positive number by a negative number:

+:= +:-=-

Therefore, we the exercise is:

:?0 -:-?0

Now we are dividing a negative number by a negative number, that is:

:=+ -:-=+

Therefore, the final exercise will look like this:

+?0 +?0

Since we have a positive number, it is greater than zero.

Therefore, the answer is:

+>0 + > 0

3

Final Answer

<

Key Points to Remember

Essential concepts to master this topic
  • Division Rules: Positive ÷ Negative = Negative, Negative ÷ Negative = Positive
  • Technique: Track signs step by step: +314÷(-209) = negative result
  • Check: Final positive result must be greater than zero ✓

Common Mistakes

Avoid these frequent errors
  • Ignoring negative signs in division
    Don't assume all divisions give positive results = wrong comparison with zero! Negative divided by negative gives positive, but positive divided by negative gives negative. Always apply division sign rules at each step to track the final sign correctly.

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

Why do I need to worry about signs when dividing?

+

Signs determine the final result! When dividing numbers with different signs, you get negative results. When dividing numbers with the same signs, you get positive results. This affects whether your answer is greater or less than zero.

How do I remember the division sign rules?

+

Use this simple pattern: Same signs = Positive result, Different signs = Negative result. So (+)÷(-) = negative, while (-)÷(-) = positive!

Do I need to calculate the exact numbers?

+

No! You only need to track the signs through each operation. Since we're comparing to zero, knowing whether the result is positive or negative is enough to determine <, >, or =.

What if the final result equals zero exactly?

+

That would only happen if the numerator in your final division equals zero. In this problem, we have a positive number after all operations, so the result is greater than zero.

Can I work backwards from the comparison symbols?

+

Not recommended! It's better to work step by step through the operations, tracking signs carefully. This builds understanding and prevents errors in more complex problems.

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