Compare Fractions: Determine the Correct Symbol Between 1/3 and 4/12

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

Two fractions are equal when they represent the same portion of a whole. The easiest way is to simplify both fractions and see if you get the same result!

Q: How do I find the GCD quickly?

List the factors of both numbers and find the largest one they share. For 4 and 12: factors of 4 are 1, 2, 4 and factors of 12 are 1, 2, 3, 4, 6, 12. The GCD is 4!

Q: Can I use cross-multiplication instead?

Yes! Cross-multiply: 1 × 12 = 12 and 3 × 4 = 12. Since both products equal 12, the fractions are equal. This works great as a checking method!

Q: What does it mean to simplify a fraction?

Simplifying means dividing both the numerator and denominator by their greatest common divisor. This gives you the smallest possible numbers that represent the same fraction.

Fraction Comparison with Simplification

Fill in the missing sign:

$\frac{1}{3}☐\frac{4}{12}$

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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 fraction 4 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

00:16 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:

$\frac{1}{3}☐\frac{4}{12}$

Step-by-step solution

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

Step 1: Simplify the fraction $\frac{4}{12}$ .
Step 2: Compare the simplified fraction with $\frac{1}{3}$ .

Now, let's work through each step:
Step 1: Simplifying $\frac{4}{12}$ :
The greatest common divisor (GCD) of 4 and 12 is 4. Simplifying the fraction by dividing both numerator and denominator by their GCD, we get:

$\frac{4}{12} = \frac{4 \div 4}{12 \div 4} = \frac{1}{3}$

Step 2: Compare the simplified fraction with $\frac{1}{3}$ :
Both fractions are equal since $\frac{4}{12} = \frac{1}{3}$ .

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
Technique: Find GCD of 4 and 12, which is 4: $\frac{4}{12} = \frac{1}{3}$
Check: Cross-multiply to verify: 1 × 12 = 12 and 3 × 4 = 12 ✓

Common Mistakes

Avoid these frequent errors

Comparing fractions without simplifying first
Don't compare $\frac{1}{3}$ and $\frac{4}{12}$ directly = wrong comparison! Without simplifying, the different denominators make it hard to see they're equal. Always simplify fractions to lowest terms first.

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 when two fractions are equal?

Two fractions are equal when they represent the same portion of a whole. The easiest way is to simplify both fractions and see if you get the same result!

What if the fractions have different denominators?

Different denominators don't mean the fractions are different! Like $\frac{2}{4}$ and $\frac{1}{2}$ - they look different but equal the same amount when simplified.

How do I find the GCD quickly?

List the factors of both numbers and find the largest one they share. For 4 and 12: factors of 4 are 1, 2, 4 and factors of 12 are 1, 2, 3, 4, 6, 12. The GCD is 4!

Can I use cross-multiplication instead?

Yes! Cross-multiply: 1 × 12 = 12 and 3 × 4 = 12. Since both products equal 12, the fractions are equal. This works great as a checking method!

What does it mean to simplify a fraction?

Simplifying means dividing both the numerator and denominator by their greatest common divisor. This gives you the smallest possible numbers that represent the same fraction.

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