Compare Fractions: Determine the Correct Sign Between 1/12 and 2/24

Q: How do I know which fraction to simplify?

You can simplify either fraction or both! In this case, $ \frac{2}{24} $ has larger numbers, so it's easier to simplify by dividing both numerator and denominator by their GCD of 2.

Q: Can I use cross-multiplication to compare these fractions?

Yes! Cross-multiply: $ 1 \times 24 = 24 $ and $ 12 \times 2 = 24 $. Since both products equal 24, the fractions are equal!

Q: What does it mean when fractions are equal?

Equal fractions represent the same amount or same portion of a whole. Even though $ \frac{1}{12} $ and $ \frac{2}{24} $ look different, they're just different ways of writing the same value!

Q: How can I double-check my answer?

Convert both fractions to decimals! $ \frac{1}{12} = 0.0833... $ and $ \frac{2}{24} = 0.0833... $. If the decimals are identical, the fractions are definitely equal!

Fraction Comparison with Equivalent Fractions

Fill in the missing sign:

$\frac{1}{12}☐\frac{2}{24}$

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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

00:13 Now we have a common denominator between the fractions

00:17 We can see that the fractions are equal

00:20 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:

$\frac{1}{12}☐\frac{2}{24}$

Step-by-step solution

To solve this problem, let's carefully follow these steps:

Step 1: Simplify the fraction $\frac{2}{24}$ .
Step 2: Compare the simplified fraction with $\frac{1}{12}$ .

Step 1: We start by simplifying $\frac{2}{24}$ .
We find the greatest common divisor of 2 and 24, which is 2. Thus, we divide both the numerator and denominator by 2:

$\frac{2 \div 2}{24 \div 2} = \frac{1}{12}$

Step 2: Now that we have simplified $\frac{2}{24}$ to $\frac{1}{12}$ , we can compare it with the original fraction $\frac{1}{12}$ .

Both fractions are now $\frac{1}{12}$ . Therefore, they are equal.

This means the correct sign to insert is the equality sign $(=)$ .

Hence, the solution to the problem is $\boxed{=}$ .

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 of 2 and 24: $\frac{2}{24} = \frac{1}{12}$
Verification: Check equality by cross-multiplication: 1×24 = 2×12 = 24 ✓

Common Mistakes

Avoid these frequent errors

Comparing fractions without simplifying first
Don't compare $\frac{1}{12}$ and $\frac{2}{24}$ directly = wrong conclusion! Different denominators make comparison confusing. Always simplify one or both fractions first to reveal their true relationship.

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 know which fraction to simplify?

You can simplify either fraction or both! In this case, $\frac{2}{24}$ has larger numbers, so it's easier to simplify by dividing both numerator and denominator by their GCD of 2.

What if I can't find the GCD quickly?

Try dividing by small numbers first! Start with 2, then 3, then 5. For $\frac{2}{24}$ , both numbers are even, so divide by 2: 2÷2 = 1 and 24÷2 = 12.

Can I use cross-multiplication to compare these fractions?

Yes! Cross-multiply: $1 \times 24 = 24$ and $12 \times 2 = 24$ . Since both products equal 24, the fractions are equal!

What does it mean when fractions are equal?

Equal fractions represent the same amount or same portion of a whole. Even though $\frac{1}{12}$ and $\frac{2}{24}$ look different, they're just different ways of writing the same value!

How can I double-check my answer?

Convert both fractions to decimals! $\frac{1}{12} = 0.0833...$ and $\frac{2}{24} = 0.0833...$ . If the decimals are identical, the fractions are definitely equal!

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