Compare Fractions: Determine the Relation Between 1/2 and 2/4

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

Two fractions are equivalent when they simplify to the same form or represent the same part of a whole. You can also cross-multiply: if $ 1 \times 4 = 2 \times 2 $, they're equal!

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

Find the Greatest Common Divisor (GCD) of the numerator and denominator, then divide both by that number. For $ \frac{2}{4} $, the GCD is 2, so $ \frac{2÷2}{4÷2} = \frac{1}{2} $.

Q: Can I convert to decimals to compare fractions?

Yes! Converting to decimals is a great method. $ \frac{1}{2} = 0.5 $ and $ \frac{2}{4} = 0.5 $, so they're equal. This works especially well with calculator-friendly fractions.

Q: What if the fractions have different denominators?

You have several options: simplify both first, find a common denominator, cross-multiply, or convert to decimals. Choose the method that feels most comfortable to you!

Q: Why does simplifying fractions matter?

Simplifying helps you recognize equivalent fractions easily and makes calculations simpler. It's like cleaning up your work - the math becomes clearer and less prone to errors.

Fraction Equivalence with Simplification

Fill in the missing sign:

$\frac{1}{2}☐\frac{2}{4}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's pick the right math sign. Ready?

00:08 We need to reduce the fraction by 2, so that we have a common denominator.

00:14 Remember, divide both the top number, the numerator, and the bottom number, the denominator.

00:20 Great! Now, both fractions share a common denominator.

00:25 See? The fractions are equal now.

00:27 And that's how we solve this question. Well done!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Fill in the missing sign:

$\frac{1}{2}☐\frac{2}{4}$

Step-by-step solution

To solve the problem, we begin by comparing the fractions $\frac{1}{2}$ and $\frac{2}{4}$ . We will simplify $\frac{2}{4}$ to see if it is equivalent to $\frac{1}{2}$ .

Let's simplify $\frac{2}{4}$ . We do this by finding the greatest common divisor (GCD) of 2 and 4, which is 2. We then divide both the numerator and the denominator by 2:

\frac{2 \div 2}{4 \div 2} = \frac{1}{2}

Now, we see that $\frac{2}{4}$ simplifies to $\frac{1}{2}$ .

Since $\frac{2}{4}$ simplifies to $\frac{1}{2}$ , the two fractions are equivalent.

Therefore, we fill in the missing sign with an equals sign:

$=$

Final Answer

$=$

Key Points to Remember

Essential concepts to master this topic

Rule: Equivalent fractions represent the same value in different forms
Technique: Simplify $\frac{2}{4}$ by dividing both terms by GCD of 2
Check: Both fractions equal 0.5 when converted to decimals ✓

Common Mistakes

Avoid these frequent errors

Comparing fractions without simplifying first
Don't compare $\frac{1}{2}$ and $\frac{2}{4}$ by just looking at the numbers = wrong conclusion! Different numbers don't mean different values. Always simplify fractions to lowest terms before comparing.

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 equivalent?

Two fractions are equivalent when they simplify to the same form or represent the same part of a whole. You can also cross-multiply: if $1 \times 4 = 2 \times 2$ , they're equal!

What's the easiest way to simplify a fraction?

Find the Greatest Common Divisor (GCD) of the numerator and denominator, then divide both by that number. For $\frac{2}{4}$ , the GCD is 2, so $\frac{2÷2}{4÷2} = \frac{1}{2}$ .

Can I convert to decimals to compare fractions?

Yes! Converting to decimals is a great method. $\frac{1}{2} = 0.5$ and $\frac{2}{4} = 0.5$ , so they're equal. This works especially well with calculator-friendly fractions.

What if the fractions have different denominators?

You have several options: simplify both first, find a common denominator, cross-multiply, or convert to decimals. Choose the method that feels most comfortable to you!

Why does simplifying fractions matter?

Simplifying helps you recognize equivalent fractions easily and makes calculations simpler. It's like cleaning up your work - the math becomes clearer and less prone to errors.

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