Solve the Fraction Division: 432/864 Simplification Challenge

Q: What if I can't see the GCF right away?

Start by finding any common factors you can see, then keep going. For example: divide both by 2, then by 2 again, until you can't divide anymore. The result will be the same!

Q: Can I simplify fractions by canceling digits?

Never cancel individual digits! For example, don't cross out the 4's in $ \frac{432}{864} $. You must divide the entire numerator and denominator by the same number.

Q: What if my answer doesn't match any of the choices?

Double-check your GCF calculation! Make sure you divided both the numerator and denominator by the same number. A common error is using the wrong GCF.

Fraction Simplification with Greatest Common Factor

Simplify the following fraction:

$\frac{432}{864}=$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Simplify the following fraction:

$\frac{432}{864}=$

Step-by-step solution

First we will divide the numerator and denominator by the highest number that both are divisible by.

In this case, the number is 432.

Then we will divide the fraction as follows:

$\frac{432:432}{864:432}=\frac{1}{2}$

Final Answer

$\frac{1}{2}$

Key Points to Remember

Essential concepts to master this topic

Rule: Find the greatest common factor (GCF) of numerator and denominator
Technique: Divide both parts by GCF: 432÷432 = 1, 864÷432 = 2
Check: Verify GCF is correct: 1×432 = 432, 2×432 = 864 ✓

Common Mistakes

Avoid these frequent errors

Dividing by any common factor instead of the greatest one
Don't divide by small factors like 2 or 4 first = extra steps and possible errors! This makes the problem longer and increases chances of mistakes. Always find the GCF (greatest common factor) first to simplify in one step.

Practice Quiz

Test your knowledge with interactive questions

Write the fraction shown in the diagram as a number:

FAQ

Everything you need to know about this question

How do I find the greatest common factor quickly?

Look for patterns! Since 432 appears in both numbers, check if one divides the other. Here, 864 ÷ 432 = 2, so 432 is the GCF!

What if I can't see the GCF right away?

Start by finding any common factors you can see, then keep going. For example: divide both by 2, then by 2 again, until you can't divide anymore. The result will be the same!

Can I simplify fractions by canceling digits?

Never cancel individual digits! For example, don't cross out the 4's in $\frac{432}{864}$ . You must divide the entire numerator and denominator by the same number.

How do I know when my fraction is fully simplified?

A fraction is fully simplified when the numerator and denominator have no common factors except 1. Since 1 and 2 share no common factors, $\frac{1}{2}$ is fully simplified!

What if my answer doesn't match any of the choices?

Double-check your GCF calculation! Make sure you divided both the numerator and denominator by the same number. A common error is using the wrong GCF.

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