Compare Fractions: Find the Missing Sign Between 3/10 and 1/10

Q: Why can I just compare the numerators?

When fractions have the same denominator, they represent the same-sized pieces! $ \frac{3}{10} $ means 3 tenths, while $ \frac{1}{10} $ means 1 tenth. Since 3 pieces > 1 piece, the first fraction is larger.

Q: What if the denominators were different?

With different denominators, you'd need to find a common denominator first! For example, to compare $ \frac{1}{2} $ and $ \frac{3}{8} $, convert to $ \frac{4}{8} $ and $ \frac{3}{8} $.

Q: Can I use decimals to check my answer?

Absolutely! Converting to decimals is a great way to verify. $ \frac{3}{10} = 0.3 $ and $ \frac{1}{10} = 0.1 $, so 0.3 > 0.1 confirms our answer.

Q: How do I remember which symbol means 'greater than'?

Think of the symbol as a hungry mouth that always wants to eat the bigger number! The wide opening $ > $ faces the larger number, so $ 3 > 1 $ means 3 is greater than 1.

Q: What if both fractions were equal?

If the numerators were the same (like $ \frac{3}{10} $ and $ \frac{3}{10} $), then you'd use the equals sign (=) because the fractions represent exactly the same amount.

Fraction Comparison with Same Denominators

Fill in the missing sign:

$\frac{3}{10}☐\frac{1}{10}$

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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:

$\frac{3}{10}☐\frac{1}{10}$

Step-by-step solution

To solve this problem, we need to determine which of the two fractions, $\frac{3}{10}$ and $\frac{1}{10}$ , is greater. Since both fractions have the same denominator, the larger fraction will be the one with the larger numerator.

We'll follow these steps:

Step 1: Identify the numerators of the two fractions. For $\frac{3}{10}$ , the numerator is 3. For $\frac{1}{10}$ , the numerator is 1.
Step 2: Compare the numerators. Since 3 is greater than 1, this means that $\frac{3}{10}$ is greater than $\frac{1}{10}$ .

Therefore, the correct mathematical sign to fill in the blank is $>$ .

Thus, the complete inequality is: $\frac{3}{10} > \frac{1}{10}$ .

The correct answer is choice 2: $\frac{3}{10} > \frac{1}{10}$ .

Final Answer

$>$

Key Points to Remember

Essential concepts to master this topic

Same Denominator Rule: Compare numerators directly when denominators are identical
Technique: Since 3 > 1, then $\frac{3}{10} > \frac{1}{10}$
Check: Convert to decimals: 0.3 > 0.1 confirms our answer ✓

Common Mistakes

Avoid these frequent errors

Comparing denominators instead of numerators
Don't look at the denominators when they're the same = wrong comparison! Both fractions have 10 as denominator, so this tells us nothing about size. Always compare the numerators when denominators are identical.

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 I just compare the numerators?

When fractions have the same denominator, they represent the same-sized pieces! $\frac{3}{10}$ means 3 tenths, while $\frac{1}{10}$ means 1 tenth. Since 3 pieces > 1 piece, the first fraction is larger.

What if the denominators were different?

With different denominators, you'd need to find a common denominator first! For example, to compare $\frac{1}{2}$ and $\frac{3}{8}$ , convert to $\frac{4}{8}$ and $\frac{3}{8}$ .

Can I use decimals to check my answer?

Absolutely! Converting to decimals is a great way to verify. $\frac{3}{10} = 0.3$ and $\frac{1}{10} = 0.1$ , so 0.3 > 0.1 confirms our answer.

How do I remember which symbol means 'greater than'?

Think of the symbol as a hungry mouth that always wants to eat the bigger number! The wide opening $>$ faces the larger number, so $3 > 1$ means 3 is greater than 1.

What if both fractions were equal?

If the numerators were the same (like $\frac{3}{10}$ and $\frac{3}{10}$ ), then you'd use the equals sign (=) because the fractions represent exactly the same amount.

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