Compare Fractions: Finding the Correct Symbol Between 1/3 and 2/3

Q: Why can I just compare the top numbers when the bottom numbers are the same?

When denominators are the same, you're comparing pieces of the same size. Think of pizza slices: $ \frac{1}{3} $ is 1 slice and $ \frac{2}{3} $ is 2 slices of the same pizza!

Q: What if the denominators were different?

If denominators are different, you'd need to find a common denominator first. For example, to compare $ \frac{1}{2} $ and $ \frac{2}{3} $, convert to $ \frac{3}{6} $ and $ \frac{4}{6} $.

Q: How can I remember which symbol means 'less than'?

The less than symbol ( opens toward the larger number. Think of it like a hungry alligator that always wants to eat the bigger number!

Q: Can I use a number line to check my answer?

Absolutely! On a number line, $ \frac{1}{3} $ comes before $ \frac{2}{3} $, so \( \frac{1}{3} is correct.

Q: What does the ☐ symbol mean in the problem?

The ☐ (empty box) is a placeholder where you need to fill in the correct comparison symbol: (greater than), or = (equal to).

Fraction Comparison with Same Denominators

Fill in the missing sign:

$\frac{1}{3}☐\frac{2}{3}$

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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

00:06 When the denominator is equal, the larger numerator is the larger fraction

00:09 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:

$\frac{1}{3}☐\frac{2}{3}$

Step-by-step solution

To find the correct comparison sign for the fractions $\frac{1}{3}$ and $\frac{2}{3}$ , follow these logical steps:

Step 1: Look at the fractions $\frac{1}{3}$ and $\frac{2}{3}$ . Both fractions have the same denominator, which is 3.
Step 2: Identify the numerators of the fractions. The numerator of $\frac{1}{3}$ is 1, and the numerator of $\frac{2}{3}$ is 2.
Step 3: Compare these numerators. Since 1 is less than 2, we deduce that $\frac{1}{3} \lt \frac{2}{3}$ .

Therefore, the missing sign to correctly complete the expression $\frac{1}{3} ☒ \frac{2}{3}$ is $\lt$ . Thus, the solution to the problem is $\frac{1}{3} \lt \frac{2}{3}$ .

Final Answer

$<$

Key Points to Remember

Essential concepts to master this topic

Rule: Same denominators mean compare numerators directly only
Technique: Since 1 < 2, then $\frac{1}{3} < \frac{2}{3}$
Check: Visualize: 1 piece vs 2 pieces of same-sized thirds ✓

Common Mistakes

Avoid these frequent errors

Comparing denominators instead of numerators
Don't compare the 3's in both fractions = meaningless comparison! The denominators tell us the size of each piece, but the numerators tell us how many pieces we have. Always compare numerators when denominators are the same.

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 top numbers when the bottom numbers are the same?

When denominators are the same, you're comparing pieces of the same size. Think of pizza slices: $\frac{1}{3}$ is 1 slice and $\frac{2}{3}$ is 2 slices of the same pizza!

What if the denominators were different?

If denominators are different, you'd need to find a common denominator first. For example, to compare $\frac{1}{2}$ and $\frac{2}{3}$ , convert to $\frac{3}{6}$ and $\frac{4}{6}$ .

How can I remember which symbol means 'less than'?

The less than symbol (<) opens toward the larger number. Think of it like a hungry alligator that always wants to eat the bigger number!

Can I use a number line to check my answer?

Absolutely! On a number line, $\frac{1}{3}$ comes before $\frac{2}{3}$ , so $\frac{1}{3} < \frac{2}{3}$ is correct.

What does the ☐ symbol mean in the problem?

The ☐ (empty box) is a placeholder where you need to fill in the correct comparison symbol: < (less than), > (greater than), or = (equal to).

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