Simplify the Fraction 6/36: Step-by-Step Reduction Exercise

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

When the numerator and denominator share no common factors except 1. For $ \frac{1}{6} $, the only factor of 1 is 1 itself, so it's fully simplified!

Q: Can I simplify by canceling digits?

No! You can't just cross out the same digits. For example, don't turn $ \frac{16}{64} $ into $ \frac{1}{4} $ by crossing out 6's. Always divide by actual common factors.

Q: What if the GCF is 1?

Then your fraction is already in simplest form! Not all fractions need simplifying. If the GCF is 1, you're done.

Fraction Simplification with Common Factors

Simplify the following fraction to its simplest form:

$\frac{6}{36}=$

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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 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 to its simplest form:

$\frac{6}{36}=$

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 6, therefore:

$\frac{6:6}{36:6}=\frac{1}{6}$

Final Answer

$\frac{1}{6}$

Key Points to Remember

Essential concepts to master this topic

GCF Rule: Find the greatest common factor of numerator and denominator
Technique: Divide both parts by GCF: $\frac{6÷6}{36÷6} = \frac{1}{6}$
Check: Verify 1 and 6 share no common factors except 1 ✓

Common Mistakes

Avoid these frequent errors

Dividing by different numbers
Don't divide 6 by 2 and 36 by 3 = $\frac{3}{12}$ which isn't fully simplified! This happens when you don't find the greatest common factor first. Always find the GCF and 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 (GCF)?

List the factors of both numbers! For 6: {1, 2, 3, 6} and for 36: {1, 2, 3, 4, 6, 9, 12, 18, 36}. The largest number that appears in both lists is your GCF.

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

Try dividing by small numbers first! If both 6 and 36 are even, divide by 2. Keep going until you can't divide anymore. Practice makes this faster!

How do I know when my fraction is fully simplified?

When the numerator and denominator share no common factors except 1. For $\frac{1}{6}$ , the only factor of 1 is 1 itself, so it's fully simplified!

Can I simplify by canceling digits?

No! You can't just cross out the same digits. For example, don't turn $\frac{16}{64}$ into $\frac{1}{4}$ by crossing out 6's. Always divide by actual common factors.

What if the GCF is 1?

Then your fraction is already in simplest form! Not all fractions need simplifying. If the GCF is 1, you're done.

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