Determine the Sign: Multiplying Fractions 1/4 × 1/2

Sign Rules with Positive Fractions

Determine the resulting sign of the following exercise:

1412= \frac{1}{4}\cdot\frac{1}{2}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:07 Let's find out the sign of the result.
00:11 Remember, a positive number times a positive number is always positive.
00:16 Now, multiply the numerators with each other, and the denominators with each other.
00:21 And there you have it! That's how we solve this problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Determine the resulting sign of the following exercise:

1412= \frac{1}{4}\cdot\frac{1}{2}=

2

Step-by-step solution

When there is no minus or plus sign before the numbers, we usually assume that these are positive numbers as shown below:

(+1/4)*(+1/2)=

The dot in the middle represents multiplication:

So the question in other words is - what happens when we multiply two positive numbers together?

We know that two positive integers when multiplied result in a positive integer:

Therefore the answer is "positive".

3

Final Answer

Positive

Key Points to Remember

Essential concepts to master this topic
  • Rule: Positive numbers multiplied together always give positive results
  • Technique: No sign means positive: 14×12=(+14)×(+12) \frac{1}{4} \times \frac{1}{2} = (+\frac{1}{4}) \times (+\frac{1}{2})
  • Check: Two positive signs multiply to give positive: (+) × (+) = (+) ✓

Common Mistakes

Avoid these frequent errors
  • Assuming fractions are automatically negative
    Don't think fractions like 1/4 are negative because they're less than 1 = wrong sign determination! Fractions can be positive or negative just like whole numbers. Always look for actual negative signs (-) to determine if a number is negative.

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 know if a fraction is positive or negative?

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Look for the minus sign (-)! If there's no minus sign in front, the fraction is positive. For example, 14 \frac{1}{4} is positive, but 14 -\frac{1}{4} is negative.

What happens when I multiply two positive fractions?

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The result is always positive! Just like with whole numbers: positive × positive = positive. The size doesn't matter - even tiny fractions follow this rule.

Does the size of the fraction affect the sign?

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No! Whether a fraction is 11000 \frac{1}{1000} or 9991000 \frac{999}{1000} , if there's no negative sign, it's positive. Size and sign are completely different things.

What if one fraction was negative instead?

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Then you'd get a negative result! Remember: positive × negative = negative. For example, 14×(12) \frac{1}{4} \times (-\frac{1}{2}) would be negative.

How can I remember the sign rules?

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  • Same signs: positive × positive = positive, negative × negative = positive
  • Different signs: positive × negative = negative, negative × positive = negative

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