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

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

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

Q: How can I visualize this on a number line?

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!

Q: What's the easiest way to compare negative fractions?

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

Q: Do I always flip the inequality sign with negative numbers?

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).

Q: Can I use cross multiplication to compare these fractions?

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

Negative Fraction Comparison with Number Line

Fill in the corresponding sign

$-\frac{1}{2}?-\frac{1}{4}$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Fill in the corresponding sign

$-\frac{1}{2}?-\frac{1}{4}$

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:

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

$-\frac{1}{2} < -\frac{1}{4}$

Final Answer

$<$

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

Test your knowledge with interactive questions

$$ 5 < -5 $$

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?

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

How can I visualize this on a number line?

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?

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

Do I always flip the inequality sign with negative numbers?

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?

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

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Signed Numbers (Positive and Negative) questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime