Simplify the Fraction 6/15: Step-by-Step Reduction

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

Try dividing by small numbers like 2, 3, or 5 first. If both the numerator and denominator divide evenly, that's a common factor. Keep going until you find the largest one!

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

A fraction is in simplest form when the GCF of the numerator and denominator equals 1. This means they share no common factors except 1.

Q: What happens if the numerator and denominator have no common factors?

Then the fraction is already in simplest form! For example, $ \frac{3}{7} $ cannot be simplified because GCF(3,7) = 1.

Fraction Simplification with Greatest Common Factor

Simplify the given fraction to its simplest form:

$\frac{6}{15}=$

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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 by the greatest common factor

00:07 Make sure to divide both numerator and denominator

00:11 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:

$\frac{6}{15}=$

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 3, therefore:

$\frac{6:3}{15:3}=\frac{2}{5}$

Final Answer

$\frac{2}{5}$

Key Points to Remember

Essential concepts to master this topic

Rule: Find the greatest common factor (GCF) of numerator and denominator
Technique: Divide both 6 and 15 by their GCF of 3
Check: Verify $\frac{2}{5}$ cannot be reduced further: GCF(2,5) = 1 ✓

Common Mistakes

Avoid these frequent errors

Dividing by any common factor instead of the greatest one
Don't divide 6/15 by just 2 because both are even = 3/7.5 which isn't simplified! This leaves the fraction partially reduced with decimals or larger numbers. Always find the GCF first, then divide both parts by that largest common factor.

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 6: {1, 2, 3, 6} and for 15: {1, 3, 5, 15}. The largest number that appears in both lists is your GCF. Here it's 3!

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

Try dividing by small numbers like 2, 3, or 5 first. If both the numerator and denominator divide evenly, that's a common factor. Keep going until you find the largest one!

How do I know when a fraction is fully simplified?

A fraction is in simplest form when the GCF of the numerator and denominator equals 1. This means they share no common factors except 1.

Can I simplify step by step instead of all at once?

Yes! You can divide by smaller common factors repeatedly. For example: $\frac{6}{15} = \frac{6÷3}{15÷3} = \frac{2}{5}$ . Just make sure you end up with the same final answer!

What happens if the numerator and denominator have no common factors?

Then the fraction is already in simplest form! For example, $\frac{3}{7}$ cannot be simplified because GCF(3,7) = 1.

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