Compare Fractions 1/2 and 1/4: Lunch Portion Problem

Q: Why is 1/2 bigger than 1/4 if 4 is bigger than 2?

Think of it like pizza slices! If you cut a pizza into 2 pieces, each slice is huge. If you cut the same pizza into 4 pieces, each slice is much smaller. So $ \frac{1}{2} $ (1 out of 2 big pieces) is more than $ \frac{1}{4} $ (1 out of 4 small pieces).

Q: How can I visualize this to make sure I understand?

Draw two identical circles. Divide the first into 2 equal parts and shade 1 part. Divide the second into 4 equal parts and shade 1 part. You'll clearly see the shaded part of the first circle is bigger!

Q: What if the fractions had different numerators?

When numerators are different, you need a common denominator to compare. For example, to compare $ \frac{2}{3} $ and $ \frac{3}{4} $, convert both to twelfths: $ \frac{8}{12} $ vs $ \frac{9}{12} $.

Q: Can I use cross multiplication to compare fractions?

Yes! For $ \frac{1}{2} $ vs $ \frac{1}{4} $: multiply 1×4 = 4 and 1×2 = 2. Since 4 > 2, we know $ \frac{1}{2} > \frac{1}{4} $. This works for any fraction comparison!

Q: What's the easiest way to remember this rule?

Remember: "Same top, smaller bottom = bigger fraction!" The denominator tells you how many pieces the whole is divided into. Fewer pieces = bigger pieces!

Fraction Comparison with Same Numerators

Andy eats $\frac{1}{2}$ of his lunch, while Daniel eats $\frac{1}{4}$ of his.

Who eats more?

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Step-by-step written solution

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Understand the problem

Andy eats $\frac{1}{2}$ of his lunch, while Daniel eats $\frac{1}{4}$ of his.

Who eats more?

Step-by-step solution

To solve this problem, we need to compare the fractions $\frac{1}{2}$ and $\frac{1}{4}$ . Since both fractions have the same numerator, the fraction with the smaller denominator is the larger fraction, indicating which portion is larger.

Step-by-step, here's how it goes:

Step 1: Consider the fractions $\frac{1}{2}$ (Andy's portion) and $\frac{1}{4}$ (Daniel's portion).
Step 2: Compare these two fractions. Note that $\frac{1}{2}$ has a smaller denominator than $\frac{1}{4}$ . In terms of fractions with the same numerator (1), a smaller denominator means a larger fraction.
Step 3: Therefore, $\frac{1}{2}$ is greater than $\frac{1}{4}$ , meaning Andy eats more than Daniel.

Consequently, the solution to the problem is that Andy eats more.

Final Answer

Andy

Key Points to Remember

Essential concepts to master this topic

Rule: With same numerators, smaller denominator means larger fraction
Technique: Compare 1/2 and 1/4: since 2 < 4, then 1/2 > 1/4
Check: Convert to decimals: 1/2 = 0.5 and 1/4 = 0.25, so 0.5 > 0.25 ✓

Common Mistakes

Avoid these frequent errors

Thinking larger denominators mean larger fractions
Don't assume 1/4 > 1/2 because 4 > 2 = completely backwards thinking! Denominators show how many pieces the whole is divided into - more pieces means smaller pieces. Always remember: with same numerators, smaller denominator equals larger fraction.

Practice Quiz

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FAQ

Everything you need to know about this question

Why is 1/2 bigger than 1/4 if 4 is bigger than 2?

Think of it like pizza slices! If you cut a pizza into 2 pieces, each slice is huge. If you cut the same pizza into 4 pieces, each slice is much smaller. So $\frac{1}{2}$ (1 out of 2 big pieces) is more than $\frac{1}{4}$ (1 out of 4 small pieces).

How can I visualize this to make sure I understand?

Draw two identical circles. Divide the first into 2 equal parts and shade 1 part. Divide the second into 4 equal parts and shade 1 part. You'll clearly see the shaded part of the first circle is bigger!

What if the fractions had different numerators?

When numerators are different, you need a common denominator to compare. For example, to compare $\frac{2}{3}$ and $\frac{3}{4}$ , convert both to twelfths: $\frac{8}{12}$ vs $\frac{9}{12}$ .

Can I use cross multiplication to compare fractions?

Yes! For $\frac{1}{2}$ vs $\frac{1}{4}$ : multiply 1×4 = 4 and 1×2 = 2. Since 4 > 2, we know $\frac{1}{2} > \frac{1}{4}$ . This works for any fraction comparison!

What's the easiest way to remember this rule?

Remember: "Same top, smaller bottom = bigger fraction!" The denominator tells you how many pieces the whole is divided into. Fewer pieces = bigger pieces!

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