Compare Negative Fractions: Finding the Relation Between -1/2 and -1/4

Negative Fraction Comparison with Number Line

Fill in the corresponding sign

12?14 -\frac{1}{2}?-\frac{1}{4}

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1

Understand the problem

Fill in the corresponding sign

12?14 -\frac{1}{2}?-\frac{1}{4}

2

Step-by-step solution

Let's place the numbers on the number line.

We will use whole numbers as reference points.

That is, both fractions are located between the numbers 0 and 1:

-1-1-1000

Since negative one-quarter is closer to zero, it is greater, therefore:

12<14 -\frac{1}{2} < -\frac{1}{4}

3

Final Answer

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Key Points to Remember

Essential concepts to master this topic
  • Rule: For negative fractions, closer to zero means greater value
  • Technique: Use number line: -1/2 is farther from zero than -1/4
  • Check: Convert to decimals: -0.5 < -0.25 confirms our answer ✓

Common Mistakes

Avoid these frequent errors
  • Applying positive fraction rules to negative fractions
    Don't compare 1/2 > 1/4 and conclude -1/2 > -1/4 = wrong sign! Negative numbers flip the inequality direction. Always remember: for negatives, the fraction closer to zero is actually larger.

Practice Quiz

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All negative numbers appear on the number line to the left of the number 0.

FAQ

Everything you need to know about this question

Why is -1/4 greater than -1/2 when 1/2 is bigger than 1/4?

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Great question! When numbers become negative, they flip positions on the number line. Think of it like debt: owing 0.25isbetterthanowing0.25 is better than owing 0.50!

How can I visualize this on a number line?

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Draw a number line with 0 in the middle. -1/2 = -0.5 goes further left, while -1/4 = -0.25 stays closer to zero. Closer to zero means greater value!

What's the easiest way to compare negative fractions?

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Convert to decimals first! 12=0.5 -\frac{1}{2} = -0.5 and 14=0.25 -\frac{1}{4} = -0.25 . Then remember: -0.25 is closer to zero, so it's larger.

Do I always flip the inequality sign with negative numbers?

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No! You only flip when multiplying or dividing by a negative number. When just comparing negative values, use the number line to see which is further right (closer to zero).

Can I use cross multiplication to compare these fractions?

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Not directly! First compare the positive versions: 12 \frac{1}{2} vs 14 \frac{1}{4} . Since 12>14 \frac{1}{2} > \frac{1}{4} , then 12<14 -\frac{1}{2} < -\frac{1}{4} .

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