Simplify the Fraction 9/72 Using a Factor of 9

Q: What if I can't see that 9 goes into 72?

Try mental math tricks! Since 9 × 8 = 72, you know 9 divides evenly into 72. You can also use long division to check: 72 ÷ 9 = 8.

Q: How do I know 1/8 is fully simplified?

Check if 1 and 8 have any common factors. Since 1 only has itself as a factor, and 8 = 2 × 2 × 2, they share no common factors except 1. So $ \frac{1}{8} $ is in lowest terms!

Q: What does 'simplify by a factor of 9' mean exactly?

It means divide both parts of the fraction by 9. So $ \frac{9 ÷ 9}{72 ÷ 9} = \frac{1}{8} $. The fraction keeps the same value but becomes simpler!

Q: Why is 9/18 wrong as an answer?

That would mean you only divided the denominator by 4, not by 9! Remember: $ \frac{9}{72} ≠ \frac{9}{18} $. You must divide both numbers by the same factor.

Fraction Simplification with Common Factors

Simplify the following fraction by a factor of 9:

$\frac{9}{72}=$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 First, let's reduce the fraction by dividing it by 9.

00:09 Divide both the top and bottom numbers by this factor.

00:13 Make sure to divide both the numerator and the denominator.

00:18 Now, calculate the results of these divisions.

00:21 And there you have it! This is the solution to the problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Simplify the following fraction by a factor of 9:

$\frac{9}{72}=$

Step-by-step solution

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

$\frac{9:9}{72:9}=\frac{1}{8}$

Final Answer

$\frac{1}{8}$

Key Points to Remember

Essential concepts to master this topic

Simplification Rule: Divide both numerator and denominator by the same factor
Technique: Find the GCF first: $\frac{9}{72}$ , GCF is 9
Check: Verify 9 × 1 = 9 and 9 × 8 = 72 ✓

Common Mistakes

Avoid these frequent errors

Dividing only the numerator by the common factor
Don't divide just 9 by 9 to get $\frac{1}{72}$ = wrong answer! This creates an unequal fraction that doesn't represent the original value. Always divide both numerator AND denominator by the same factor.

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

What if I can't see that 9 goes into 72?

Try mental math tricks! Since 9 × 8 = 72, you know 9 divides evenly into 72. You can also use long division to check: 72 ÷ 9 = 8.

How do I know 1/8 is fully simplified?

Check if 1 and 8 have any common factors. Since 1 only has itself as a factor, and 8 = 2 × 2 × 2, they share no common factors except 1. So $\frac{1}{8}$ is in lowest terms!

Can I simplify by a different factor first?

Yes! You could divide by smaller factors like 3, then 3 again. But using the greatest common factor (9) gets you to the answer in one step, which is faster and less error-prone.

What does 'simplify by a factor of 9' mean exactly?

It means divide both parts of the fraction by 9. So $\frac{9 ÷ 9}{72 ÷ 9} = \frac{1}{8}$ . The fraction keeps the same value but becomes simpler!

Why is 9/18 wrong as an answer?

That would mean you only divided the denominator by 4, not by 9! Remember: $\frac{9}{72} ≠ \frac{9}{18}$ . You must divide both numbers by the same factor.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Simple Fractions questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime