Simplify the Fraction 8/24: Step-by-Step Reduction

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

Start by dividing both numbers by small common factors like 2, 3, or 4. Keep going until you can't divide anymore. The result will be in simplest form!

Q: How do I know when a fraction is fully simplified?

A fraction is in simplest form when the numerator and denominator share no common factors except 1. For $ \frac{1}{3} $, since 1 and 3 only share the factor 1, it's fully simplified.

Q: Can I use this method for any fraction?

Absolutely! This GCF method works for any fraction, no matter how large the numbers. Just find the greatest common factor and divide both top and bottom by it.

Q: What if the GCF is 1?

If the GCF is 1, then your fraction is already in simplest form! For example, $ \frac{3}{7} $ cannot be simplified because 3 and 7 share no common factors except 1.

Fraction Simplification with Greatest Common Factor

Simplify the given fraction to its simplest form:

$\frac{8}{24}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Reduce the fraction as much as possible

00:03 Divide the fraction by the greatest common factor

00:06 Make sure to divide both numerator and denominator

00:10 Calculate the quotients

00:14 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

Simplify the given fraction to its simplest form:

$\frac{8}{24}=$

Step-by-step solution

We must identify the highest common factor (HCF): The largest number that both the numerator and the denominator can be divided by.

In this case, the number is 8, therefore:

$\frac{8:8}{24:8}=\frac{1}{3}$

Final Answer

$\frac{1}{3}$

Key Points to Remember

Essential concepts to master this topic

Rule: Find the greatest common factor of numerator and denominator
Technique: Divide both 8 and 24 by their GCF of 8
Check: Verify $\frac{1}{3}$ cannot be reduced further ✓

Common Mistakes

Avoid these frequent errors

Dividing by a smaller common factor instead of the greatest
Don't divide 8/24 by 2 to get 4/12, then by 2 again = extra steps and potential errors! This makes the process longer and increases chances of mistakes. Always find the greatest common factor first and divide both parts by it in one step.

Practice Quiz

Test your knowledge with interactive questions

Without calculating, determine whether the quotient in the division exercise is less than 1 or not:

$$ 5:6= $$

FAQ

Everything you need to know about this question

How do I find the greatest common factor quickly?

List the factors of both numbers! For 8: {1, 2, 4, 8} and for 24: {1, 2, 3, 4, 6, 8, 12, 24}. The largest number that appears in both lists is your GCF.

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

Start by dividing both numbers by small common factors like 2, 3, or 4. Keep going until you can't divide anymore. The result will be in simplest form!

How do I know when a fraction is fully simplified?

A fraction is in simplest form when the numerator and denominator share no common factors except 1. For $\frac{1}{3}$ , since 1 and 3 only share the factor 1, it's fully simplified.

Can I use this method for any fraction?

Absolutely! This GCF method works for any fraction, no matter how large the numbers. Just find the greatest common factor and divide both top and bottom by it.

What if the GCF is 1?

If the GCF is 1, then your fraction is already in simplest form! For example, $\frac{3}{7}$ cannot be simplified because 3 and 7 share no common factors except 1.

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