Compare Fractions: Find the Missing Symbol Between 2/8 and 3/4

Q: Why can't I just compare 2 and 3 since 2 is smaller?

You can't compare numerators alone because the denominators are different! $ \frac{2}{8} $ and $ \frac{3}{4} $ have different-sized pieces, so you need common denominators to make a fair comparison.

Q: How do I find the common denominator quickly?

Look for the least common multiple (LCM) of the denominators. Since 8 is already a multiple of 4, the LCM is 8. This makes converting easier!

Q: What if both fractions need to be converted?

Convert both fractions to the common denominator. For example, to compare $ \frac{1}{3} $ and $ \frac{2}{5} $, convert both to fifteenths: $ \frac{5}{15} $ and $ \frac{6}{15} $.

Q: Can I convert to decimals instead?

Yes! $ \frac{2}{8} = 0.25 $ and $ \frac{3}{4} = 0.75 $. Since 0.25

Q: What if the fractions are equal after converting?

If the numerators are the same after converting to common denominators, then the fractions are equal and you'd use the = symbol instead.

Fraction Comparison with Common Denominators

Fill in the missing symbol:

$\frac{2}{8}☐\frac{3}{4}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 First, let's choose the correct math sign.

00:09 We're going to divide the fraction by 2. This will help us find a common denominator.

00:14 Remember, divide both the top and bottom numbers.

00:18 Great! Now, both fractions have the same denominator.

00:24 If denominators match, the fraction with the bigger top number is larger.

00:31 And that's how we solve this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Fill in the missing symbol:

$\frac{2}{8}☐\frac{3}{4}$

Step-by-step solution

To solve this problem, let's follow these steps:

Step 1: Identify a common denominator. Since 8 is a multiple of 4, the least common denominator is 8.
Step 2: Convert $\frac{3}{4}$ into eighths. Multiply numerator and denominator by 2 to get $\frac{6}{8}$ .
Step 3: Compare $\frac{2}{8}$ and $\frac{6}{8}$ . Because 2 is less than 6, we can conclude that $\frac{2}{8}$ is less than $\frac{6}{8}$ .

Therefore, the missing symbol is $<$ .

Final Answer

$<$

Key Points to Remember

Essential concepts to master this topic

Rule: Convert fractions to same denominator before comparing values
Technique: Convert $\frac{3}{4}$ to $\frac{6}{8}$ by multiplying by 2
Check: Compare numerators: 2 < 6, so $\frac{2}{8} < \frac{6}{8}$ ✓

Common Mistakes

Avoid these frequent errors

Comparing numerators and denominators separately without converting
Don't compare 2 vs 3 and 8 vs 4 separately = wrong conclusion! This ignores how denominators affect fraction size. Always convert to common denominators first, then compare only the numerators.

Practice Quiz

Test your knowledge with interactive questions

Fill in the missing sign:

$\frac{5}{9}☐\frac{3}{9}$

FAQ

Everything you need to know about this question

Why can't I just compare 2 and 3 since 2 is smaller?

You can't compare numerators alone because the denominators are different! $\frac{2}{8}$ and $\frac{3}{4}$ have different-sized pieces, so you need common denominators to make a fair comparison.

How do I find the common denominator quickly?

Look for the least common multiple (LCM) of the denominators. Since 8 is already a multiple of 4, the LCM is 8. This makes converting easier!

What if both fractions need to be converted?

Convert both fractions to the common denominator. For example, to compare $\frac{1}{3}$ and $\frac{2}{5}$ , convert both to fifteenths: $\frac{5}{15}$ and $\frac{6}{15}$ .

Can I convert to decimals instead?

Yes! $\frac{2}{8} = 0.25$ and $\frac{3}{4} = 0.75$ . Since 0.25 < 0.75, we get the same answer. Use whichever method feels easier!

What if the fractions are equal after converting?

If the numerators are the same after converting to common denominators, then the fractions are equal and you'd use the = symbol instead.

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