Reduce the Fraction 3/9: Step-by-Step Simplification

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

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

Q: Can I simplify by canceling individual digits?

No! You cannot cancel digits within numbers. For example, don't cross out the 3's in 33/39. Instead, find the HCF of the entire numbers 33 and 39, which is 3.

Q: What happens if the HCF is 1?

If the HCF is 1, the fraction is already in simplest form! This means the numerator and denominator have no common factors other than 1.

Fraction Simplification with Common Factors

Reduce the given fraction into its simplest form:

$\frac{3}{9}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Reduce as much as possible

00:03 Divide by the greatest common factor

00:06 Make sure to divide both numerator and denominator

00:09 Calculate the quotients

00:12 And that's 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:

$\frac{3}{9}=$

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:

$\frac{3:3}{9:3}=\frac{1}{3}$

Final Answer

$\frac{1}{3}$

Key Points to Remember

Essential concepts to master this topic

Rule: Find the highest common factor (HCF) of numerator and denominator
Technique: Divide both parts by HCF: $\frac{3÷3}{9÷3} = \frac{1}{3}$
Check: Verify simplified fraction cannot be reduced further: 1 and 3 share no common factors ✓

Common Mistakes

Avoid these frequent errors

Dividing numerator and denominator by different numbers
Don't divide 3 by 2 and 9 by 3 = $\frac{1.5}{3}$ which isn't simplified! This creates an unequal fraction that's not equivalent to the original. Always divide both numerator and denominator by the same HCF.

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 highest common factor of 3 and 9?

List the factors of each number: 3: 1, 3 and 9: 1, 3, 9. The largest number that appears in both lists is 3, so HCF = 3.

What if I can't see the common factor right away?

Try dividing the larger number by the smaller one! Since 9 ÷ 3 = 3 exactly, this tells us that 3 is a common factor. You can also use prime factorization.

How do I know when a fraction is fully simplified?

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

Can I simplify by canceling individual digits?

No! You cannot cancel digits within numbers. For example, don't cross out the 3's in 33/39. Instead, find the HCF of the entire numbers 33 and 39, which is 3.

What happens if the HCF is 1?

If the HCF is 1, the fraction is already in simplest form! This means the numerator and denominator have no common factors other than 1.

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