Solve (3¼) ÷ (⅖): Determining the Sign of Mixed Number Division

Sign Rules with Mixed Number Division

Determine the resulting sign from the following exercise:

(+314):(+25) (+3\frac{1}{4}):(+\frac{2}{5})

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the result sign
00:03 Let's find what sign each number has
00:07 Positive divided by positive is always positive
00:10 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

Determine the resulting sign from the following exercise:

(+314):(+25) (+3\frac{1}{4}):(+\frac{2}{5})

2

Step-by-step solution

We will only look at whether the number is negative or positive.

In other words, the division exercise looks like this:

+:+= +:+=

Since we are dividing a positive number by a positive number, our result must be positive.

3

Final Answer

+

Key Points to Remember

Essential concepts to master this topic
  • Sign Rule: Positive divided by positive always equals positive
  • Technique: Focus on signs first: (+):(+)=(+) (+):(+) = (+)
  • Check: Both numbers are positive, so result must be positive ✓

Common Mistakes

Avoid these frequent errors
  • Calculating the actual division instead of just determining the sign
    Don't solve 314÷25=818 3\frac{1}{4} ÷ \frac{2}{5} = 8\frac{1}{8} when asked only for the sign! This wastes time and risks calculation errors. Always read the question carefully - it only asks for positive or negative, not the numerical answer.

Practice Quiz

Test your knowledge with interactive questions

Solve the following exercise:

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

FAQ

Everything you need to know about this question

Why don't I need to convert the mixed number to an improper fraction?

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Since we only need the sign of the result, not the actual value, we can skip the conversion! Both +314 +3\frac{1}{4} and +25 +\frac{2}{5} are clearly positive.

What if one number was negative instead?

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Then you'd use the rule: positive ÷ negative = negative or negative ÷ positive = negative. Only when both numbers have the same sign is the result positive!

How do I remember the division sign rules?

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Same signs give positive, different signs give negative. Think:

  • (+) ÷ (+) = (+)
  • (-) ÷ (-) = (+)
  • (+) ÷ (-) = (-)
  • (-) ÷ (+) = (-)

Does it matter that these are fractions instead of whole numbers?

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No! Sign rules work the same for all numbers - whole numbers, fractions, decimals, or mixed numbers. The type of number doesn't change the sign rules.

What if the question asked for the actual answer?

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Then you'd convert 314 3\frac{1}{4} to 134 \frac{13}{4} , then multiply by the reciprocal: 134×52=658 \frac{13}{4} \times \frac{5}{2} = \frac{65}{8} or 818 8\frac{1}{8} . But this question only wants the sign!

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