Compare Fractions: Find the Symbol Between 2/8 ☐ 4/16

Q: Why can't I just compare the numbers directly?

Because fractions represent parts of a whole! Even though 4 > 2, the fraction $ \frac{4}{16} $ might equal $ \frac{2}{8} $. Always simplify to see the true value.

Q: Is there a faster way to compare fractions?

Yes! You can cross-multiply: for $ \frac{a}{b} $ and $ \frac{c}{d} $, compare a×d with b×c. But simplifying first often makes the comparison obvious!

Q: What does it mean when fractions are equivalent?

Equivalent fractions represent the same amount but are written differently. Like $ \frac{1}{2} $, $ \frac{2}{4} $, and $ \frac{3}{6} $ - they all equal half!

Fraction Comparison with Equivalent Forms

Fill in the missing sign:

$\frac{2}{8}☐\frac{4}{16}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 First, choose the correct sign. This will guide our next steps.

00:11 Next, let's reduce the fraction by dividing by 2. This helps us find a common denominator.

00:18 Remember, divide both the top number, the numerator, and the bottom number, the denominator.

00:24 Great! Now both fractions have the same denominator.

00:29 See? The fractions are equal! That means we're on the right track.

00:35 And that's how we solve this 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:

$\frac{2}{8}☐\frac{4}{16}$

Step-by-step solution

We need to compare the fractions $\frac{2}{8}$ and $\frac{4}{16}$ . To do this, we'll simplify each fraction to see if they are equal or if one is greater than the other.

Step 1: Simplify $\frac{2}{8}$
To simplify, find the greatest common divisor (GCD) of 2 and 8, which is 2. Divide the numerator and denominator by this GCD:
$\frac{2}{8} = \frac{2 \div 2}{8 \div 2} = \frac{1}{4}$

Step 2: Simplify $\frac{4}{16}$
Similarly, find the GCD of 4 and 16, which is 4. Divide both the numerator and denominator by this GCD:
$\frac{4}{16} = \frac{4 \div 4}{16 \div 4} = \frac{1}{4}$

Both fractions simplify to $\frac{1}{4}$ . Thus, they are equal.

Conclusion:
Since the simplified forms of both fractions are equal, the correct sign to fill in is $=$ .

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

Final Answer

$=$

Key Points to Remember

Essential concepts to master this topic

Simplification: Reduce fractions to lowest terms before comparing them
Technique: Find GCD: $\frac{2}{8} = \frac{1}{4}$ and $\frac{4}{16} = \frac{1}{4}$
Check: Compare simplified forms: $\frac{1}{4} = \frac{1}{4}$ confirms equality ✓

Common Mistakes

Avoid these frequent errors

Comparing numerators and denominators separately
Don't just compare 2 vs 4 or 8 vs 16 separately = wrong conclusion! This ignores the relationship between numerator and denominator. Always simplify both fractions first to see their true values.

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 numbers directly?

Because fractions represent parts of a whole! Even though 4 > 2, the fraction $\frac{4}{16}$ might equal $\frac{2}{8}$ . Always simplify to see the true value.

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

List the factors of both numbers and find the largest one they share. For example: factors of 4 are 1, 2, 4 and factors of 16 are 1, 2, 4, 8, 16. The GCD is 4.

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

Then they're not equal! Convert both to the same denominator or decimal form to compare. For example: $\frac{1}{4} = 0.25$ and $\frac{1}{3} ≈ 0.33$ , so $\frac{1}{3} > \frac{1}{4}$ .

Is there a faster way to compare fractions?

Yes! You can cross-multiply: for $\frac{a}{b}$ and $\frac{c}{d}$ , compare a×d with b×c. But simplifying first often makes the comparison obvious!

What does it mean when fractions are equivalent?

Equivalent fractions represent the same amount but are written differently. Like $\frac{1}{2}$ , $\frac{2}{4}$ , and $\frac{3}{6}$ - they all equal half!

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