Compare Fractions: Find the Missing Sign Between 2/15 and 1/3

Q: Why can't I just compare 2 with 1 since 2 is bigger?

Because you're only looking at the numerators! $ \frac{2}{15} $ means 2 parts out of 15, while $ \frac{1}{3} $ means 1 part out of 3. Since thirds are much bigger than fifteenths, you need to compare the actual fraction values.

Q: How do I find the common denominator quickly?

Look for the Least Common Multiple (LCM). Since 3 divides into 15 evenly (3 × 5 = 15), the LCM is 15. When one denominator divides the other, the larger one is always the LCM!

Q: What if both fractions need to be converted?

Convert both fractions to have the common denominator. For example, if comparing $ \frac{2}{6} $ and $ \frac{3}{8} $, find LCM of 6 and 8 (which is 24), then convert both: $ \frac{8}{24} $ vs $ \frac{9}{24} $.

Q: Can I use decimals instead of common denominators?

Yes! Convert both fractions to decimals: $ \frac{2}{15} = 0.133... $ and $ \frac{1}{3} = 0.333... $. Since 0.133

Q: How do I remember which sign to use?

Think of it as pointing to the smaller number. The pointy end of \( \frac{2}{15} means the first fraction is smaller.

Fraction Comparison with Common Denominators

Fill in the missing sign:

$\frac{2}{15}☐\frac{1}{3}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 First, let's choose the right sign.

00:07 Next, we'll multiply the fraction by 5, to find a common denominator.

00:13 Remember, multiply both the top and bottom numbers.

00:17 Now we have fractions with the same denominator.

00:23 With equal bottoms, the fraction with the bigger top is larger.

00:33 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 sign:

$\frac{2}{15}☐\frac{1}{3}$

Step-by-step solution

To solve this problem, we'll convert both fractions to have a common denominator and compare:

Step 1: Identify the denominators $(15$ and $3)$ of the fractions $\frac{2}{15}$ and $\frac{1}{3}$ .
Step 2: Find the common denominator. The least common multiple (LCM) of $15$ and $3$ is $15$ .
Step 3: Convert each fraction to have the common denominator $15$ .

For $\frac{2}{15}$ , the fraction is already over $15$ , so it stays $\frac{2}{15}$ .
For $\frac{1}{3}$ , multiply both the numerator and the denominator by $5$ to get an equivalent fraction: $\frac{1 \times 5}{3 \times 5} = \frac{5}{15}$ .

Step 4: Compare the equivalent fractions $\frac{2}{15}$ and $\frac{5}{15}$ .
Step 5: Since $2 \lt 5$ , it follows that $\frac{2}{15} \lt \frac{5}{15}$ .

Therefore, the correct sign to fill in the missing slot is $\lt$ .

Consequently, the completed expression is $\frac{2}{15} \lt \frac{1}{3}$ .

Therefore, the solution to the problem is $\lt$ .

Final Answer

$<$

Key Points to Remember

Essential concepts to master this topic

Rule: Convert fractions to common denominators before comparing values
Technique: Find LCM of denominators: LCM of 15 and 3 is 15
Check: Compare numerators only: 2 < 5, so $\frac{2}{15} < \frac{5}{15}$ ✓

Common Mistakes

Avoid these frequent errors

Comparing numerators and denominators separately
Don't compare 2 vs 1 and 15 vs 3 separately = wrong conclusions! This ignores fraction values completely. Always convert to common denominators first, then compare only the numerators.

Practice Quiz

Test your knowledge with interactive questions

Fill in the missing sign:

$\frac{5}{25}☐\frac{1}{5}$

FAQ

Everything you need to know about this question

Why can't I just compare 2 with 1 since 2 is bigger?

Because you're only looking at the numerators! $\frac{2}{15}$ means 2 parts out of 15, while $\frac{1}{3}$ means 1 part out of 3. Since thirds are much bigger than fifteenths, you need to compare the actual fraction values.

How do I find the common denominator quickly?

Look for the Least Common Multiple (LCM). Since 3 divides into 15 evenly (3 × 5 = 15), the LCM is 15. When one denominator divides the other, the larger one is always the LCM!

What if both fractions need to be converted?

Convert both fractions to have the common denominator. For example, if comparing $\frac{2}{6}$ and $\frac{3}{8}$ , find LCM of 6 and 8 (which is 24), then convert both: $\frac{8}{24}$ vs $\frac{9}{24}$ .

Can I use decimals instead of common denominators?

Yes! Convert both fractions to decimals: $\frac{2}{15} = 0.133...$ and $\frac{1}{3} = 0.333...$ . Since 0.133 < 0.333, we get the same answer. Choose whichever method feels easier!

How do I remember which sign to use?

Think of it as pointing to the smaller number. The pointy end of < points to 2, and the open end faces 5, showing that 2 is smaller. So $\frac{2}{15} < \frac{1}{3}$ means the first fraction is smaller.

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