Compare Fractions: Determine if 2/7 >, <, or = 6/21

Q: How do I find the greatest common divisor (GCD)?

List the factors of both numbers and find the largest one they share. For 6 and 21: factors of 6 are 1, 2, 3, 6 and factors of 21 are 1, 3, 7, 21. The largest common factor is 3.

Q: Why do I need to simplify fractions before comparing?

Simplifying reveals the true value of each fraction! $ \frac{6}{21} $ looks different from $ \frac{2}{7} $, but they're actually the same number when simplified.

Q: What if the fractions don't simplify to the same thing?

Then you can compare them directly! If they have the same denominator after simplifying, compare numerators. If denominators differ, find a common denominator or convert to decimals.

Q: Can I just cross-multiply to compare fractions?

Yes! Cross-multiplication works too. For $ \frac{2}{7} $ and $ \frac{6}{21} $: 2×21 = 42 and 7×6 = 42. Since they're equal, the fractions are equivalent.

Q: Is there a faster way to see if fractions are equal?

Look for multiplication patterns! Notice that 6 = 2×3 and 21 = 7×3. Since both numerator and denominator are multiplied by the same number (3), the fractions are equivalent.

Fraction Comparison with Equivalent Forms

Fill in the missing sign:

$\frac{2}{7}☐\frac{6}{21}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Let's begin looking for the correct sign. Ready?

00:10 We want to simplify the fraction by dividing by 3. This helps us find a common denominator.

00:16 Remember, divide both the top number and the bottom number by 3. Good job!

00:23 Now we have the same denominator for both fractions. Isn't that great?

00:27 Look carefully; the fractions are now equal.

00:31 And there you have it! That's how we solve the problem. Well done!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Fill in the missing sign:

$\frac{2}{7}☐\frac{6}{21}$

Step-by-step solution

To solve this problem, let's follow these steps:

Step 1: Simplify the fraction $\frac{6}{21}$ .
Step 2: Compare the fractions $\frac{2}{7}$ and the simplified form of $\frac{6}{21}$ .

Now, let's carry out these steps:

Step 1: Simplify $\frac{6}{21}$ .
To simplify $\frac{6}{21}$ , we find the greatest common divisor (GCD) of 6 and 21, which is 3. Dividing the numerator and the denominator by their GCD, we get:

$\frac{6 \div 3}{21 \div 3} = \frac{2}{7}$ .

Step 2: Now, compare $\frac{2}{7}$ with the simplified form of $\frac{6}{21}$ , which is also $\frac{2}{7}$ . Thus, we have:

$\frac{2}{7} = \frac{2}{7}$ .

Therefore, the missing sign between the fractions $\frac{2}{7}$ and $\frac{6}{21}$ is $=$ .

Final Answer

$=$

Key Points to Remember

Essential concepts to master this topic

Simplification: Find GCD to reduce fractions to lowest terms
Technique: GCD of 6 and 21 is 3, so $\frac{6}{21} = \frac{2}{7}$
Check: Both fractions equal $\frac{2}{7}$ , so they are equivalent ✓

Common Mistakes

Avoid these frequent errors

Comparing fractions without simplifying first
Don't compare $\frac{2}{7}$ and $\frac{6}{21}$ directly without simplifying = confusing different-looking fractions! This makes comparison unnecessarily difficult and leads to wrong conclusions. Always simplify fractions to lowest terms before comparing.

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

How do I find the greatest common divisor (GCD)?

List the factors of both numbers and find the largest one they share. For 6 and 21: factors of 6 are 1, 2, 3, 6 and factors of 21 are 1, 3, 7, 21. The largest common factor is 3.

Why do I need to simplify fractions before comparing?

Simplifying reveals the true value of each fraction! $\frac{6}{21}$ looks different from $\frac{2}{7}$ , but they're actually the same number when simplified.

What if the fractions don't simplify to the same thing?

Then you can compare them directly! If they have the same denominator after simplifying, compare numerators. If denominators differ, find a common denominator or convert to decimals.

Can I just cross-multiply to compare fractions?

Yes! Cross-multiplication works too. For $\frac{2}{7}$ and $\frac{6}{21}$ : 2×21 = 42 and 7×6 = 42. Since they're equal, the fractions are equivalent.

Is there a faster way to see if fractions are equal?

Look for multiplication patterns! Notice that 6 = 2×3 and 21 = 7×3. Since both numerator and denominator are multiplied by the same number (3), the fractions are equivalent.

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