Compare Fractions: Find the Missing Sign Between 2/3 and 6/4

Q: Why can't I just compare the numerators 2 and 6?

Because fractions have both numerators and denominators! The fraction $ \frac{2}{3} $ means 2 out of 3 parts, while $ \frac{6}{4} $ means 6 out of 4 parts. You must consider both numbers together.

Q: What exactly is cross-multiplication doing?

Cross-multiplication creates equivalent fractions with the same denominator so you can compare them fairly. When you calculate 2×4=8 and 3×6=18, you're really comparing $ \frac{8}{12} $ vs $ \frac{18}{12} $.

Q: Can I convert to decimals instead?

Absolutely! Converting gives you $ \frac{2}{3} \approx 0.67 $ and $ \frac{6}{4} = 1.5 $. Since 0.67 \( \frac{2}{3} . Both methods work!

Q: What if the cross products are equal?

If your cross products are equal, then the fractions are equal too! For example, if 2×4 = 3×6 was true (it's not in this case), then $ \frac{2}{3} = \frac{6}{4} $.

Q: Do I always multiply diagonally?

Yes! Always multiply the numerator of the first fraction by the denominator of the second, and the denominator of the first by the numerator of the second. Think of drawing an X between the fractions.

Fraction Comparison with Cross-Multiplication Method

Fill in the missing sign:

$\frac{2}{3}☐\frac{6}{4}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's find the correct sign.

00:07 We need a common denominator for our fractions.

00:11 So, we'll multiply each fraction by the other's denominator.

00:16 Remember, multiply both the top, and bottom numbers.

00:26 Let's apply this method to the second fraction.

00:31 Multiply by the second fraction's denominator.

00:35 Again, multiply both numerator, and denominator.

00:41 Now our fractions share a common denominator.

00:45 With equal denominators, the larger the numerator, the bigger the fraction.

00:55 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:

$\frac{2}{3}☐\frac{6}{4}$

Step-by-step solution

To solve this problem, we will use cross-multiplication to compare the two fractions $\frac{2}{3}$ and $\frac{6}{4}$ .

Step 1: Calculate the cross products. Multiply the numerator of the first fraction by the denominator of the second fraction, and the denominator of the first fraction by the numerator of the second fraction.
Step 2: Compare the two products to determine which fraction is larger.

Now, let's work through the steps:

Step 1: Cross-multiply the two fractions:
$\text{First Product} = 2 \times 4 = 8$
$\text{Second Product} = 3 \times 6 = 18$

Step 2: Compare the resulting products:
Since $8 < 18$ , it follows that $\frac{2}{3} < \frac{6}{4}$ .

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

Final Answer

$<$

Key Points to Remember

Essential concepts to master this topic

Rule: Cross-multiply to compare fractions without finding common denominators
Technique: Multiply 2×4=8 and 3×6=18, then compare products
Check: Convert to decimals: 2/3≈0.67 and 6/4=1.5, so 0.67<1.5 ✓

Common Mistakes

Avoid these frequent errors

Comparing numerators and denominators separately
Don't just compare 2<6 and say 2/3<6/4 = wrong answer! This ignores the denominators completely. Always cross-multiply: 2×4=8 vs 3×6=18, then compare the products.

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 the numerators 2 and 6?

Because fractions have both numerators and denominators! The fraction $\frac{2}{3}$ means 2 out of 3 parts, while $\frac{6}{4}$ means 6 out of 4 parts. You must consider both numbers together.

What exactly is cross-multiplication doing?

Cross-multiplication creates equivalent fractions with the same denominator so you can compare them fairly. When you calculate 2×4=8 and 3×6=18, you're really comparing $\frac{8}{12}$ vs $\frac{18}{12}$ .

Can I convert to decimals instead?

Absolutely! Converting gives you $\frac{2}{3} \approx 0.67$ and $\frac{6}{4} = 1.5$ . Since 0.67 < 1.5, we know $\frac{2}{3} < \frac{6}{4}$ . Both methods work!

What if the cross products are equal?

If your cross products are equal, then the fractions are equal too! For example, if 2×4 = 3×6 was true (it's not in this case), then $\frac{2}{3} = \frac{6}{4}$ .

Do I always multiply diagonally?

Yes! Always multiply the numerator of the first fraction by the denominator of the second, and the denominator of the first by the numerator of the second. Think of drawing an X between the fractions.

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