Fraction Symbol Problem: Finding the Relationship Between 1/9 and 3/27

Q: How do I know when a fraction is fully simplified?

A fraction is fully simplified when the numerator and denominator share no common factors other than 1. For example, $ \frac{3}{27} $ can be simplified because both 3 and 27 are divisible by 3.

Q: What if the fractions look completely different?

Don't panic! Fractions that look different can be equal. Always simplify both fractions first - you might be surprised! $ \frac{4}{12} $ and $ \frac{1}{3} $ are the same value.

Q: What's the easiest way to find the greatest common factor?

Start with the smaller number and work backwards. For $ \frac{3}{27} $, check if 3 divides into 27: 27 ÷ 3 = 9. Since it divides evenly, 3 is your GCF!

Q: Do I always need to simplify fractions?

For comparing fractions, yes! It makes the comparison much clearer. Plus, simplified fractions are easier to work with in future problems. It's a great habit to develop!

Fraction Comparison with Simplification

Fill in the missing sign:

$\frac{1}{9}☐\frac{3}{27}$

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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 3 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:

$\frac{1}{9}☐\frac{3}{27}$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Simplify each fraction.
Step 2: Compare the simplified fractions.

Now, let's work through each step:
Step 1: Simplify the fractions.
- The fraction $\frac{1}{9}$ is already in its simplest form.
- The fraction $\frac{3}{27}$ can be simplified by dividing both the numerator and the denominator by 3, resulting in $\frac{1}{9}$ .

Step 2: Compare the simplified fractions.
Both simplified fractions are $\frac{1}{9}$ and $\frac{1}{9}$ , which are equal.

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

Final Answer

$=$

Key Points to Remember

Essential concepts to master this topic

Rule: Simplify fractions to lowest terms before comparing values
Technique: Divide 3÷3 and 27÷3 to get $\frac{1}{9}$
Check: Both fractions equal $\frac{1}{9}$ , so they're equal ✓

Common Mistakes

Avoid these frequent errors

Comparing fractions without simplifying first
Don't compare $\frac{1}{9}$ and $\frac{3}{27}$ directly = wrong comparison! Different numbers make it look unequal when they're actually the same. Always simplify both fractions to lowest terms first.

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 when a fraction is fully simplified?

A fraction is fully simplified when the numerator and denominator share no common factors other than 1. For example, $\frac{3}{27}$ can be simplified because both 3 and 27 are divisible by 3.

What if the fractions look completely different?

Don't panic! Fractions that look different can be equal. Always simplify both fractions first - you might be surprised! $\frac{4}{12}$ and $\frac{1}{3}$ are the same value.

Can I cross-multiply to compare these fractions?

Yes! Cross-multiplication works great for comparing fractions. For $\frac{1}{9}$ and $\frac{3}{27}$ , multiply: 1×27 = 27 and 9×3 = 27. Same products mean equal fractions!

What's the easiest way to find the greatest common factor?

Start with the smaller number and work backwards. For $\frac{3}{27}$ , check if 3 divides into 27: 27 ÷ 3 = 9. Since it divides evenly, 3 is your GCF!

Do I always need to simplify fractions?

For comparing fractions, yes! It makes the comparison much clearer. Plus, simplified fractions are easier to work with in future problems. It's a great habit to develop!

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