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

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

List the factors of both numbers and find the largest number that appears in both lists. For example, factors of 4 are {1, 2, 4} and factors of 16 are {1, 2, 4, 8, 16}, so GCD = 4.

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

Yes! Cross-multiply: $ 2 \times 16 = 32 $ and $ 8 \times 4 = 32 $. Since both products equal 32, the fractions are equal.

Q: Why is simplifying fractions important?

Simplifying shows the true value of a fraction in its clearest form. $ \frac{2}{8} $ and $ \frac{4}{16} $ both equal $ \frac{1}{4} $, making the comparison obvious!

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

Use the division method: keep dividing both numerator and denominator by small numbers (2, 3, 5...) until you can't divide evenly anymore. You'll reach the simplified form step by step.

Fraction Comparison with Equivalent Simplification

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

00:00 Choose the appropriate sign

00:03 We want to reduce the fraction by 2 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

00:16 We can see that the fractions are equal

00:19 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:

$\frac{2}{8}☐\frac{4}{16}$

Step-by-step solution

We will compare the fractions $\frac{2}{8}$ and $\frac{4}{16}$ by simplifying them to their lowest terms.

Step 1: Simplify $\frac{2}{8}$ :
The greatest common divisor (GCD) of 2 and 8 is 2.
Dividing the numerator and the denominator by 2 gives us:
$\frac{2}{8} = \frac{2 \div 2}{8 \div 2} = \frac{1}{4}$

Step 2: Simplify $\frac{4}{16}$ :
The greatest common divisor (GCD) of 4 and 16 is 4.
Dividing the numerator and the denominator by 4 gives us:
$\frac{4}{16} = \frac{4 \div 4}{16 \div 4} = \frac{1}{4}$

Step 3: Compare the simplified fractions:
Both $\frac{1}{4}$ and $\frac{1}{4}$ are equal.

Therefore, the correct comparison sign to fill in the blank is $=$ .

Final Answer

$=$

Key Points to Remember

Essential concepts to master this topic

Rule: Always simplify fractions to lowest terms before comparing them
Technique: Find GCD of numerator and denominator: GCD(4,16) = 4
Check: Both fractions simplify to the same form = they're equal ✓

Common Mistakes

Avoid these frequent errors

Comparing fractions without simplifying first
Don't just look at 2/8 vs 4/16 and think they're different because the numbers look different = wrong comparison! The fractions might be equivalent even with different numbers. Always simplify both fractions to lowest terms first, then compare.

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) quickly?

List the factors of both numbers and find the largest number that appears in both lists. For example, factors of 4 are {1, 2, 4} and factors of 16 are {1, 2, 4, 8, 16}, so GCD = 4.

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

Then you compare the simplified fractions! Convert them to the same denominator if needed, then compare numerators. The fraction with the larger numerator is greater.

Can I cross-multiply to compare these fractions?

Yes! Cross-multiply: $2 \times 16 = 32$ and $8 \times 4 = 32$ . Since both products equal 32, the fractions are equal.

Why is simplifying fractions important?

Simplifying shows the true value of a fraction in its clearest form. $\frac{2}{8}$ and $\frac{4}{16}$ both equal $\frac{1}{4}$ , making the comparison obvious!

What if I can't find the GCD easily?

Use the division method: keep dividing both numerator and denominator by small numbers (2, 3, 5...) until you can't divide evenly anymore. You'll reach the simplified form step by step.

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