Simplify the Fraction 90/27: Step-by-Step Reduction

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

A fraction is fully simplified when the GCF of the numerator and denominator is 1. This means they share no common factors except 1.

Q: Can I convert this to a mixed number instead?

Yes! $ \frac{10}{3} = 3\frac{1}{3} $ because 10 ÷ 3 = 3 remainder 1. Both forms are correct, but improper fractions are often preferred in algebra.

Q: What if the numbers are really big?

Use the same method! You can also try prime factorization: break both numbers into prime factors, then multiply the common ones to find the GCF.

Fraction Simplification with Greatest Common Factor

Simplify the following fraction:

$\frac{90}{27}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Reduce the fraction by 9

00:03 Divide the fraction by the given factor

00:07 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 following fraction:

$\frac{90}{27}=$

Step-by-step solution

Let's simplify as follows, divide both the numerator and denominator by 9:

$\frac{90:9}{27:9}=\frac{10}{3}$

Final Answer

$\frac{10}{3}$

Key Points to Remember

Essential concepts to master this topic

Rule: Find the greatest common factor of numerator and denominator
Technique: Divide both 90 and 27 by GCF: 90÷9 = 10, 27÷9 = 3
Check: Verify $\frac{10}{3}$ cannot be reduced further: GCF(10,3) = 1 ✓

Common Mistakes

Avoid these frequent errors

Dividing by a common factor that isn't the greatest
Don't divide 90/27 by 3 to get 30/9, then stop = incomplete simplification! This leaves the fraction unreduced. Always find the greatest common factor (9) and divide both parts by it in one step.

Practice Quiz

Test your knowledge with interactive questions

Simplify the following fraction by a factor of 4:

$\frac{4}{8}=$

FAQ

Everything you need to know about this question

How do I find the greatest common factor of 90 and 27?

List the factors of each number: 90 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90 and 27 = 1, 3, 9, 27. The greatest common factor is the largest number that appears in both lists: 9.

What if I divide by a smaller common factor first?

You can still get the right answer, but it takes more steps! For example, $\frac{90}{27} \div 3 = \frac{30}{9} \div 3 = \frac{10}{3}$ . It's faster to use the GCF directly.

How do I know when a fraction is fully simplified?

A fraction is fully simplified when the GCF of the numerator and denominator is 1. This means they share no common factors except 1.

Can I convert this to a mixed number instead?

Yes! $\frac{10}{3} = 3\frac{1}{3}$ because 10 ÷ 3 = 3 remainder 1. Both forms are correct, but improper fractions are often preferred in algebra.

What if the numbers are really big?

Use the same method! You can also try prime factorization: break both numbers into prime factors, then multiply the common ones to find the GCF.

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