Fraction Comparison: Find the Missing Symbol Between 2/8 and 7/8

Q: What if the denominators were different?

When denominators are different, you need to find a common denominator first. For example, to compare $ \frac{1}{3} $ and $ \frac{2}{5} $, convert to $ \frac{5}{15} $ and $ \frac{6}{15} $, then compare numerators.

Q: Why can I just look at the numerators?

Think of it like pizza slices! Both fractions represent pieces from pizzas cut into 8 equal slices. Since the slice sizes are identical, 2 slices will always be less than 7 slices.

Q: What does the < symbol mean exactly?

The . The smaller side (left) points to the smaller number. So \( \frac{2}{8} reads as "two-eighths is less than seven-eighths."

Q: How do I remember which way the symbol points?

Remember: the symbol always "eats" the bigger number! Think of it like a hungry mouth - it opens wide toward the larger fraction and closes to a point toward the smaller one.

Q: Can two fractions with the same denominator ever be equal?

Yes! If the numerators are also the same, then the fractions are equal. For example, $ \frac{5}{8} = \frac{5}{8} $ because both the numerator (5) and denominator (8) match perfectly.

Q: What if I simplified the fractions first?

You could simplify $ \frac{2}{8} = \frac{1}{4} $, but then you'd need a common denominator again! It's much easier to compare when denominators already match.

Fraction Comparison with Same Denominators

Fill in the missing sign:

$\frac{2}{8}☐\frac{7}{8}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Choose the correct sign

00:03 The denominator is equal

00:09 When the denominator is equal, the larger numerator is the larger fraction

00:13 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Fill in the missing sign:

$\frac{2}{8}☐\frac{7}{8}$

Step-by-step solution

To solve the problem, we will compare two fractions: $\frac{2}{8}$ and $\frac{7}{8}$ .

Both fractions have the same denominator (8), which allows us to directly compare the numerators. Therefore, we need only consider the values of the numerators to understand the relationship between the two fractions.

Step 1: Identify the numerators. For $\frac{2}{8}$ , the numerator is 2. For $\frac{7}{8}$ , the numerator is 7.
Step 2: Compare the numerators. We observe that $2 < 7$ .

Since 2 is less than 7, it follows that $\frac{2}{8}$ is less than $\frac{7}{8}$ .

Therefore, the correct sign to place between $\frac{2}{8}$ and $\frac{7}{8}$ is $<$ .

The solution to the problem is $<$ .

Final Answer

$<$

Key Points to Remember

Essential concepts to master this topic

Rule: When denominators are equal, compare numerators directly
Technique: Since 8 = 8, compare 2 vs 7: 2 < 7
Check: Verify $\frac{2}{8} < \frac{7}{8}$ makes sense: 2 pieces < 7 pieces ✓

Common Mistakes

Avoid these frequent errors

Converting to decimals unnecessarily
Don't convert $\frac{2}{8}$ and $\frac{7}{8}$ to decimals when denominators match = extra work and potential errors! This wastes time and creates opportunities for calculation mistakes. Always compare numerators directly when denominators are the same.

Practice Quiz

Test your knowledge with interactive questions

Fill in the missing sign:

$\frac{5}{25}☐\frac{1}{5}$

FAQ

Everything you need to know about this question

What if the denominators were different?

When denominators are different, you need to find a common denominator first. For example, to compare $\frac{1}{3}$ and $\frac{2}{5}$ , convert to $\frac{5}{15}$ and $\frac{6}{15}$ , then compare numerators.

Why can I just look at the numerators?

Think of it like pizza slices! Both fractions represent pieces from pizzas cut into 8 equal slices. Since the slice sizes are identical, 2 slices will always be less than 7 slices.

What does the < symbol mean exactly?

The < symbol means "less than". The smaller side (left) points to the smaller number. So $\frac{2}{8} < \frac{7}{8}$ reads as "two-eighths is less than seven-eighths."

How do I remember which way the symbol points?

Remember: the symbol always "eats" the bigger number! Think of it like a hungry mouth - it opens wide toward the larger fraction and closes to a point toward the smaller one.

Can two fractions with the same denominator ever be equal?

Yes! If the numerators are also the same, then the fractions are equal. For example, $\frac{5}{8} = \frac{5}{8}$ because both the numerator (5) and denominator (8) match perfectly.

What if I simplified the fractions first?

You could simplify $\frac{2}{8} = \frac{1}{4}$ , but then you'd need a common denominator again! It's much easier to compare when denominators already match.

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