Compare Fractions: Determine the Correct Symbol Between 1/9 and 3/27

Q: How do I know when two fractions are equal?

Two fractions are equal when they simplify to the same fraction. Always reduce both fractions to lowest terms first, then compare the results.

Q: What's the fastest way to simplify a fraction?

Find the GCD (Greatest Common Divisor) of the numerator and denominator, then divide both by that number. For $ \frac{3}{27} $, GCD(3,27) = 3, so divide: $ \frac{3÷3}{27÷3} = \frac{1}{9} $

Comparing Fractions 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

00:04 We are looking for the right math operation sign.

00:08 We need to change the fraction to three to make denominators the same.

00:17 Now, both fractions share a common denominator.

00:21 Guess what? The fractions are actually equal!

00:25 And that's how we solve this math problem!

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 determine the missing sign between $\frac{1}{9}$ and $\frac{3}{27}$ , we will first simplify the fraction $\frac{3}{27}$ .

Step 1: Simplify $\frac{3}{27}$ .
The greatest common divisor (GCD) of 3 and 27 is 3. So, we divide both the numerator and the denominator by 3:

$\frac{3 \div 3}{27 \div 3} = \frac{1}{9}$

Step 2: Compare $\frac{1}{9}$ and the simplified version of $\frac{3}{27}$ , which is $\frac{1}{9}$ .

Since both fractions are equal, we fill in the missing sign with an equals sign.

Therefore, the correct answer is $=$ .

Final Answer

$=$

Key Points to Remember

Essential concepts to master this topic

Simplification Rule: Always reduce fractions to lowest terms before comparing
GCD Method: Find GCD(3,27) = 3, so $\frac{3}{27} = \frac{1}{9}$
Verify: Check that $\frac{1}{9} = \frac{1}{9}$ confirms equal fractions ✓

Common Mistakes

Avoid these frequent errors

Comparing fractions without simplifying first
Don't compare $\frac{1}{9}$ and $\frac{3}{27}$ directly without simplifying = wrong conclusion that they're different! The different numbers hide that they're actually equal. Always simplify 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 when two fractions are equal?

Two fractions are equal when they simplify to the same fraction. Always reduce both fractions to lowest terms first, then compare the results.

What's the fastest way to simplify a fraction?

Find the GCD (Greatest Common Divisor) of the numerator and denominator, then divide both by that number. For $\frac{3}{27}$ , GCD(3,27) = 3, so divide: $\frac{3÷3}{27÷3} = \frac{1}{9}$

Can I cross-multiply to compare these fractions?

Yes! Cross-multiply: 1×27 = 27 and 9×3 = 27. Since both products equal 27, the fractions are equal. But simplifying first is usually faster and clearer.

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

Then you compare the simplified fractions directly. If they have the same denominator, compare numerators. If different denominators, find a common denominator first.

How do I find the GCD quickly?

List the factors of each number and find the largest one they share. For 3 and 27: factors of 3 are {1,3}, factors of 27 are {1,3,9,27}. The largest shared factor is 3.

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