Simplify the Fraction 6/24: Step-by-Step Reduction Guide

Q: How do I find the greatest common factor quickly?

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

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

Start by dividing by small numbers like 2 or 3! For $ \frac{6}{24} $, divide both by 2 to get $ \frac{3}{12} $, then by 3 to get $ \frac{1}{4} $.

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

A fraction is fully simplified when the numerator and denominator have no common factors except 1. For $ \frac{1}{4} $, since 1 and 4 share no common factors, it's done!

Q: Can I use division to simplify fractions?

Yes! Dividing both parts by their GCF is exactly what simplifying means. Think of it as reducing the fraction to its smallest equivalent form.

Q: What happens if I divide by the wrong number?

If you divide by a number that's not a common factor, you'll get decimals or change the fraction's value. Always make sure your chosen number divides both the numerator and denominator evenly!

Fraction Reduction with Greatest Common Factor

Simplify the following fraction:

$\frac{6}{24}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Reduce the fraction to denominator 4

00:03 We'll reduce the fraction with the appropriate divisor so the denominator equals 4

00:06 Make sure to divide both numerator and denominator

00:09 Calculate the quotients

00:12 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 following fraction:

$\frac{6}{24}$

Step-by-step solution

Let's look at the denominator of the fraction. We'll try to find a number that, when divided by 24, gives us a result of 4:

$\frac{6:6}{24:6}=\frac{1}{4}$

Final Answer

$\frac{1}{4}$

Key Points to Remember

Essential concepts to master this topic

Rule: Find the greatest common factor of numerator and denominator
Technique: Divide both 6 and 24 by their GCF of 6
Check: Verify $\frac{1}{4}$ cannot be reduced further ✓

Common Mistakes

Avoid these frequent errors

Dividing by different numbers for numerator and denominator
Don't divide 6 by 2 and 24 by 8 = $\frac{3}{3}$ which is wrong! This changes the fraction's value completely. Always divide both numerator and denominator by the same number.

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 each number: 6 has factors 1, 2, 3, 6 and 24 has factors 1, 2, 3, 4, 6, 8, 12, 24. The largest number that appears in both lists is your GCF!

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

Start by dividing by small numbers like 2 or 3! For $\frac{6}{24}$ , divide both by 2 to get $\frac{3}{12}$ , then by 3 to get $\frac{1}{4}$ .

How do I know when a fraction is fully simplified?

A fraction is fully simplified when the numerator and denominator have no common factors except 1. For $\frac{1}{4}$ , since 1 and 4 share no common factors, it's done!

Can I use division to simplify fractions?

Yes! Dividing both parts by their GCF is exactly what simplifying means. Think of it as reducing the fraction to its smallest equivalent form.

What happens if I divide by the wrong number?

If you divide by a number that's not a common factor, you'll get decimals or change the fraction's value. Always make sure your chosen number divides both the numerator and denominator evenly!

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