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

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 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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