Compare Fractions: Determine the Relation Between 2/3 and 8/12

Q: How do I know which fraction to simplify?

Always simplify both fractions to be safe! In this case, $ \frac{2}{3} $ is already simplified, but $ \frac{8}{12} $ can be reduced by dividing by 4.

Q: What if I can't find the GCD easily?

Try dividing by small numbers like 2, 3, or 4 first. For $ \frac{8}{12} $, both 8 and 12 are divisible by 4, so 4 is the GCD.

Q: Can I cross-multiply to compare fractions?

Yes! Cross-multiply: 2 × 12 = 24 and 3 × 8 = 24. Since both products equal 24, the fractions are equal!

Q: What does it mean when fractions are equivalent?

Equivalent fractions represent the same amount but written differently. Like $ \frac{2}{3} $ and $ \frac{8}{12} $ - they're both the same piece of the whole!

Q: Do I always need to simplify fractions?

For comparing fractions, yes! Simplifying helps you see if they're equal. It's like cleaning your room - everything becomes clearer and easier to work with.

Fraction Comparison with Equivalent Forms

Fill in the missing sign:

$\frac{2}{3}☐\frac{8}{12}$

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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 reduce fraction 4 to get a common denominator

00:09 Remember to divide both numerator and denominator

00:12 Now we have a common denominator between the fractions

00:15 We can see that the fractions are equal

00:18 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:

$\frac{2}{3}☐\frac{8}{12}$

Step-by-step solution

To solve this problem, we'll compare the two fractions $\frac{2}{3}$ and $\frac{8}{12}$ to determine the suitable mathematical sign between them.

Step 1: Simplify the fraction $\frac{8}{12}$ .

The greatest common divisor of 8 and 12 is 4.
Divide the numerator and the denominator of $\frac{8}{12}$ by 4:
$\frac{8 \div 4}{12 \div 4} = \frac{2}{3}$ .

Step 2: Now we compare the fractions $\frac{2}{3}$ and the simplified $\frac{8}{12} = \frac{2}{3}$ .

Since both fractions $\frac{2}{3}$ and $\frac{2}{3}$ are identical, they are equal.

Therefore, the missing sign to make the statement true is $=$ , since both fractions are equivalent.

This corresponds to choice id="3".

Therefore, the solution to the problem is $=$ .

Final Answer

$=$

Key Points to Remember

Essential concepts to master this topic

Rule: Fractions are equal when simplified to identical forms
Technique: Simplify $\frac{8}{12}$ by dividing by GCD of 4 = $\frac{2}{3}$
Check: Both fractions equal $\frac{2}{3}$ so $\frac{2}{3} = \frac{8}{12}$ ✓

Common Mistakes

Avoid these frequent errors

Comparing fractions without simplifying first
Don't just compare 2 with 8 and 3 with 12 directly = wrong conclusion! This ignores that fractions can look different but be equal. Always simplify both fractions to lowest terms before comparing.

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

How do I know which fraction to simplify?

Always simplify both fractions to be safe! In this case, $\frac{2}{3}$ is already simplified, but $\frac{8}{12}$ can be reduced by dividing by 4.

What if I can't find the GCD easily?

Try dividing by small numbers like 2, 3, or 4 first. For $\frac{8}{12}$ , both 8 and 12 are divisible by 4, so 4 is the GCD.

Can I cross-multiply to compare fractions?

Yes! Cross-multiply: 2 × 12 = 24 and 3 × 8 = 24. Since both products equal 24, the fractions are equal!

What does it mean when fractions are equivalent?

Equivalent fractions represent the same amount but written differently. Like $\frac{2}{3}$ and $\frac{8}{12}$ - they're both the same piece of the whole!

Do I always need to simplify fractions?

For comparing fractions, yes! Simplifying helps you see if they're equal. It's like cleaning your room - everything becomes clearer and easier to work with.

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