Simplify the Fraction 9/36: Step-by-Step Reduction

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

Start by dividing both numbers by any common factor you can see, then keep going! For example: $ \frac{9}{36} \rightarrow \frac{3}{12} \rightarrow \frac{1}{4} $. You'll get the same final answer!

Fraction Simplification with Common Factor Division

Simplify the given fraction to its simplest form:

$\frac{9}{36}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's simplify the fraction as much as we can.

00:08 Find the greatest common factor, then divide by it.

00:12 Remember, divide both the top number and the bottom number.

00:16 Now, calculate the results.

00:19 And there you have it! That's the solution!

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:

$\frac{9}{36}=$

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 9, therefore:

$\frac{9:9}{36:9}=\frac{1}{4}$

Final Answer

$\frac{1}{4}$

Key Points to Remember

Essential concepts to master this topic

Rule: Find the highest common factor that divides both numerator and denominator
Technique: Divide both parts by HCF: 9÷9 = 1, 36÷9 = 4
Check: Verify $\frac{1}{4}$ cannot be reduced further since 1 and 4 share no common factors ✓

Common Mistakes

Avoid these frequent errors

Dividing by different numbers for numerator and denominator
Don't divide 9 by 3 and 36 by 6 = $\frac{3}{6}$ which isn't fully simplified! This doesn't use the same divisor for both parts. Always divide both numerator and denominator by the exact same number (the 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 quickly?

List the factors of both numbers! For 9: 1, 3, 9. For 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. The largest number appearing in both lists is your HCF (which is 9).

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

Start by dividing both numbers by any common factor you can see, then keep going! For example: $\frac{9}{36} \rightarrow \frac{3}{12} \rightarrow \frac{1}{4}$ . You'll get the same final answer!

How do I know when my fraction is fully simplified?

Your fraction is fully simplified when the numerator and denominator have no common factors except 1. Since 1 and 4 only share the factor 1, $\frac{1}{4}$ cannot be reduced further.

Can I use prime factorization instead?

Absolutely! Break down both numbers: 9 = 3², 36 = 2² × 3². The common factors are 3², so HCF = 9. Then divide: $\frac{9÷9}{36÷9} = \frac{1}{4}$

What if the numerator is bigger than the denominator?

The same rules apply! Find the HCF and divide both parts by it. For example, $\frac{15}{10}$ becomes $\frac{3}{2}$ after dividing both by 5.

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