Reduce the Fraction 9/15 to Its Simplest Form: Step-by-Step Solution

Q: How do I find the greatest common factor of 9 and 15?

List the factors of each number: 9: 1, 3, 9 and 15: 1, 3, 5, 15. The largest number that appears in both lists is 3, so that's your GCF!

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

A fraction is in simplest form when the only common factor of the numerator and denominator is 1. For $ \frac{3}{5} $, since 3 and 5 share no common factors except 1, it's fully reduced!

Q: Can I use prime factorization to find the GCF?

Absolutely! 9 = 3² and 15 = 3 × 5. The common prime factor is 3, so GCF = 3. This method works great for larger numbers!

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 a decimal or mixed number instead of a proper fraction. Always check that your chosen number divides both parts evenly first.

Fraction Simplification with Common Factors

Reduce the given fraction into its simplest form:

$\frac{9}{15}=$

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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

00:12 Calculate the quotients

00:16 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

Reduce the given fraction into its simplest form:

$\frac{9}{15}=$

Step-by-step solution

We need to 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:

$\frac{9:3}{15:3}=\frac{3}{5}$

Final Answer

$\frac{3}{5}$

Key Points to Remember

Essential concepts to master this topic

Rule: Find the greatest common factor of numerator and denominator
Technique: Divide both 9 and 15 by their GCF of 3
Check: Verify $\frac{3}{5}$ cannot be reduced further ✓

Common Mistakes

Avoid these frequent errors

Dividing by any common factor instead of the greatest one
Don't divide 9/15 by just 1 = still 9/15! This leaves the fraction unsimplified. Always find the largest number that divides both parts evenly to get the simplest form 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 of 9 and 15?

List the factors of each number: 9: 1, 3, 9 and 15: 1, 3, 5, 15. The largest number that appears in both lists is 3, so that's your GCF!

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

Try dividing by small numbers first! Start with 2, then 3, then 5. For $\frac{9}{15}$ , both numbers are odd (so not divisible by 2), but both divide evenly by 3.

How do I know when a fraction is fully simplified?

A fraction is in simplest form when the only common factor of the numerator and denominator is 1. For $\frac{3}{5}$ , since 3 and 5 share no common factors except 1, it's fully reduced!

Can I use prime factorization to find the GCF?

Absolutely! 9 = 3² and 15 = 3 × 5. The common prime factor is 3, so GCF = 3. This method works great for larger numbers!

What happens if I divide by the wrong number?

If you divide by a number that's not a common factor, you'll get a decimal or mixed number instead of a proper fraction. Always check that your chosen number divides both parts evenly first.

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