Visual Representation of the Fraction 9/81: Match the Correct Image

Q: Why do I need to simplify 9/81 before looking at the visuals?

Simplifying makes it much easier! $ \frac{9}{81} = \frac{1}{9} $ means you're looking for 1 out of 9 parts, not trying to count 9 out of 81 tiny pieces.

Q: How do I find the greatest common divisor (GCD)?

Look for the largest number that divides both the numerator and denominator evenly. For 9 and 81: since 81 = 9 × 9, the GCD is 9.

Q: What should I look for in the correct visual?

Find a circle divided into 9 equal parts with exactly 1 part shaded. Count the total sections to make sure there are 9, not 4 or 8!

Q: What if the visual shows different numbers of sections?

4 sections = quarters ($ \frac{1}{4} $)8 sections = eighths ($ \frac{1}{8} $)9 sections = ninths ($ \frac{1}{9} $) ← This is correct!

Q: How can I double-check that 9/81 really equals 1/9?

Multiply back: $ \frac{1}{9} × \frac{9}{9} = \frac{9}{81} $ ✓ Or use decimals: $ \frac{9}{81} = 0.111... $ and $ \frac{1}{9} = 0.111... $

Fraction Simplification with Visual Representation

Choose the option that visually represents the following fraction:

$\frac{9}{81}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Choose the correct visual representation for the given fraction

00:03 In black, we see the number of parts into which the whole is divided

00:07 And in red is colored the given part, meaning the numerator

00:12 For each option, we'll find the mathematical representation and choose the appropriate one

00:44 Let's reduce the given fraction

00:49 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

Choose the option that visually represents the following fraction:

$\frac{9}{81}$

Step-by-step solution

To solve this problem, we'll simplify the fraction and identify the visual representation:

Step 1: Simplify the fraction $\frac{9}{81}$ .
Step 2: Recognize that $9$ is a common factor of both the numerator and the denominator.
Step 3: Divide both $9$ and $81$ by their GCD, which is $9$ .
Step 4: The simplified form $\frac{9 \div 9}{81 \div 9} = \frac{1}{9}$ .

Now, let's work through each step:
Step 1: Identify that $\frac{9}{81}$ can be simplified.
Step 2: Identify that the greatest common divisor between $9$ and $81$ is $9$ .
Step 3: Perform the division: $\frac{9 \div 9}{81 \div 9} = \frac{1}{9}$ .
Step 4: The simplified fraction represents one part out of nine equal parts in the visual representation.

Therefore, the solution to the problem is the visual representation that shows $\frac{1}{9}$ , which is Choice 3.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Simplification Rule: Find the GCD of numerator and denominator
Technique: Divide both 9 and 81 by their GCD of 9 to get $\frac{1}{9}$
Check: Verify the visual shows 1 out of 9 equal parts shaded ✓

Common Mistakes

Avoid these frequent errors

Choosing visuals without simplifying the fraction first
Don't look for 9 out of 81 parts in the visual = impossible to identify correctly! The fraction $\frac{9}{81}$ has too many parts to count accurately. Always simplify to $\frac{1}{9}$ first, then find the visual showing 1 out of 9 equal parts.

Practice Quiz

Test your knowledge with interactive questions

Write the fraction as a mixed number:

$\frac{10}{7}=$

FAQ

Everything you need to know about this question

Why do I need to simplify 9/81 before looking at the visuals?

Simplifying makes it much easier! $\frac{9}{81} = \frac{1}{9}$ means you're looking for 1 out of 9 parts, not trying to count 9 out of 81 tiny pieces.

How do I find the greatest common divisor (GCD)?

Look for the largest number that divides both the numerator and denominator evenly. For 9 and 81: since 81 = 9 × 9, the GCD is 9.

What should I look for in the correct visual?

Find a circle divided into 9 equal parts with exactly 1 part shaded. Count the total sections to make sure there are 9, not 4 or 8!

Can I use the original fraction 9/81 to check my visual choice?

It's much harder that way! With 81 parts, the sections would be too small to see clearly. Always simplify first to make visual identification easier.

What if the visual shows different numbers of sections?

4 sections = quarters ( $\frac{1}{4}$ )
8 sections = eighths ( $\frac{1}{8}$ )
9 sections = ninths ( $\frac{1}{9}$ ) ← This is correct!

How can I double-check that 9/81 really equals 1/9?

Multiply back: $\frac{1}{9} × \frac{9}{9} = \frac{9}{81}$ ✓ Or use decimals: $\frac{9}{81} = 0.111...$ and $\frac{1}{9} = 0.111...$

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