Compare Fractions: Determine the Symbol Between 2/9 and 3/14

Q: Why can't I just compare the numerators 2 and 3?

Because fractions represent parts of different wholes! Comparing $ \frac{2}{9} $ and $ \frac{3}{14} $ is like comparing 2 pieces of a 9-slice pizza to 3 pieces of a 14-slice pizza - you need equal slice sizes to compare fairly.

Q: How do I find the LCD of 9 and 14 quickly?

Since 9 and 14 share no common factors (they're relatively prime), multiply them directly: 9 × 14 = 126. For numbers that do share factors, use prime factorization or list multiples.

Q: Is there a faster way than finding the LCD?

Yes! You can cross-multiply: Compare $ 2 × 14 $ with $ 3 × 9 $. Since 28 > 27, we know $ \frac{2}{9} > \frac{3}{14} $.

Q: What if I get the same numerator after converting?

Then the fractions are equal! Use the equals sign (=). This happens when the original fractions represent the same portion, just written differently.

Q: Can I convert to decimals instead?

Absolutely! $ \frac{2}{9} ≈ 0.222... $ and $ \frac{3}{14} ≈ 0.214... $. Since 0.222 > 0.214, we confirm $ \frac{2}{9} > \frac{3}{14} $.

Fraction Comparison with Different Denominators

Fill in the missing sign:

$\frac{2}{9}☐\frac{3}{14}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Choose the appropriate sign

00:03 We want to find a common denominator

00:06 So we'll multiply each fraction by the denominator of the second fraction

00:09 Remember to multiply both numerator and denominator

00:19 Now let's use the same method for the second fraction

00:24 Remember to multiply by the denominator of the second fraction

00:27 Remember to multiply both numerator and denominator

00:31 Now we have a common denominator between the fractions

00:37 When denominators are equal, the larger the numerator, the larger the fraction

00:45 And that's 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:

$\frac{2}{9}☐\frac{3}{14}$

Step-by-step solution

To solve this problem, we'll compare the fractions $\frac{2}{9}$ and $\frac{3}{14}$ by finding a common denominator:

Step 1: Find the common denominator. The denominators are $9$ and $14$ . The least common multiple of $9$ and $14$ is $126$ .
Step 2: Convert each fraction to an equivalent fraction with a denominator of $126$ .
For $\frac{2}{9}$ : $\frac{2}{9} = \frac{2 \times 14}{9 \times 14} = \frac{28}{126}$ .
For $\frac{3}{14}$ : $\frac{3}{14} = \frac{3 \times 9}{14 \times 9} = \frac{27}{126}$ .
Step 3: Compare the numerators of the equivalent fractions. $28 > 27$ , so $\frac{28}{126} > \frac{27}{126}$ .

Therefore, the fraction $\frac{2}{9}$ is greater than $\frac{3}{14}$ , and the correct inequality sign is $>$ .

Hence, the answer is $\frac{2}{9} > \frac{3}{14}$ .

Final Answer

$>$

Key Points to Remember

Essential concepts to master this topic

Common Denominator Rule: Find LCD to compare fractions accurately
LCD Technique: LCM of 9 and 14 equals 126
Verification: Check numerators: 28 > 27, so $\frac{2}{9} > \frac{3}{14}$ ✓

Common Mistakes

Avoid these frequent errors

Comparing numerators and denominators separately
Don't compare 2 vs 3 and 9 vs 14 separately = wrong conclusion! This ignores how fractions actually work as ratios. Always convert to equivalent fractions with the same denominator first, then compare 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 the numerators 2 and 3?

Because fractions represent parts of different wholes! Comparing $\frac{2}{9}$ and $\frac{3}{14}$ is like comparing 2 pieces of a 9-slice pizza to 3 pieces of a 14-slice pizza - you need equal slice sizes to compare fairly.

How do I find the LCD of 9 and 14 quickly?

Since 9 and 14 share no common factors (they're relatively prime), multiply them directly: 9 × 14 = 126. For numbers that do share factors, use prime factorization or list multiples.

Is there a faster way than finding the LCD?

Yes! You can cross-multiply: Compare $2 × 14$ with $3 × 9$ . Since 28 > 27, we know $\frac{2}{9} > \frac{3}{14}$ .

What if I get the same numerator after converting?

Then the fractions are equal! Use the equals sign (=). This happens when the original fractions represent the same portion, just written differently.

Can I convert to decimals instead?

Absolutely! $\frac{2}{9} ≈ 0.222...$ and $\frac{3}{14} ≈ 0.214...$ . Since 0.222 > 0.214, we confirm $\frac{2}{9} > \frac{3}{14}$ .

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