Compare Mixed Numbers with 1/8: Sorting 10%, 20%, 11/80, and More

Q: Should I convert everything to fractions or decimals?

Decimals are usually easier! Convert $ \frac{1}{8} = 0.125 $ as your benchmark, then convert percentages (10% = 0.10) and fractions ($ \frac{11}{80} = 0.1375 $) to decimals for simple comparison.

Q: How do I convert fractions like 97/800 to decimals?

Simply divide the numerator by denominator: 97 ÷ 800 = 0.12125. Use long division or a calculator, then compare to your benchmark of 0.125.

Q: What if two values are very close to 1/8?

Look at all decimal places! For example, $ \frac{97}{800} = 0.12125 $ vs $ \frac{1}{8} = 0.125 $. Since 0.12125 $ \frac{1}{8} $.

Q: Why can't I just look at the denominators to compare fractions?

Because the numerators matter too! $ \frac{11}{80} $ has a bigger denominator than $ \frac{1}{8} $, but 11/80 = 0.1375 is actually larger than 1/8 = 0.125 because 11 is much bigger than the equivalent numerator.

Q: How do I remember which group each value belongs to?

Make a simple list: smaller than 0.125 (10%, $ \frac{97}{800} $) and larger than 0.125 (20%, $ \frac{11}{80} $, 0.15). The benchmark 0.125 helps you see the pattern clearly!

Fraction Comparison with Mixed Number Forms

Organise the following into two groups of values smaller than $\frac{1}{8}$ and values larger than $\frac{1}{8}$ :

$10\%,20\%,\frac{11}{80},\frac{97}{800},0.15$

❤️ Continue Your Math Journey!

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

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Organise the following into two groups of values smaller than $\frac{1}{8}$ and values larger than $\frac{1}{8}$ :

$10\%,20\%,\frac{11}{80},\frac{97}{800},0.15$

Step-by-step solution

The problem requires us to organize values into two groups based on whether they are smaller or larger than $\frac{1}{8}$ , which equals $0.125$ .

First, convert the percentages to decimal form:

$10\% = 0.10$
$20\% = 0.20$

Now convert the fractions to decimal form:

$\frac{11}{80} = 0.1375$
$\frac{97}{800} = 0.12125$

The decimal $0.15$ is already given in decimal form.

We compare all values to $0.125$ (which is $\frac{1}{8}$ ):

$0.10 < 0.125$
$0.20 > 0.125$
$0.1375 > 0.125$
$0.12125 < 0.125$
$0.15 > 0.125$

Thus, we have:

Values smaller than $\frac{1}{8}$ : $10\%$ and $\frac{97}{800}$ .

Values larger than $\frac{1}{8}$ : $20\%$ , $\frac{11}{80}$ , and $0.15$ .

The correct grouping matches choice 1:
$10\%, \frac{97}{800} < \frac{1}{8}$
$20\%, \frac{11}{80}, 0.15 > \frac{1}{8}$

Final Answer

$10\%,\frac{97}{800}<\frac{1}{8}$

$20\%,\frac{11}{80},0.15>\frac{1}{8}$

Key Points to Remember

Essential concepts to master this topic

Convert First: Change all values to same format for easy comparison
Technique: Convert $\frac{1}{8}$ to 0.125 as benchmark decimal
Check: Verify $\frac{97}{800} = 0.12125 < 0.125$ ✓

Common Mistakes

Avoid these frequent errors

Comparing fractions without converting to common form
Don't compare $\frac{11}{80}$ directly to $\frac{1}{8}$ = wrong grouping! Different denominators make direct comparison impossible. Always convert all values to decimals or find common denominators first.

Practice Quiz

Test your knowledge with interactive questions

Approximately what is $\frac{11}{50}$ written as a percentage?

FAQ

Everything you need to know about this question

Should I convert everything to fractions or decimals?

Decimals are usually easier! Convert $\frac{1}{8} = 0.125$ as your benchmark, then convert percentages (10% = 0.10) and fractions ( $\frac{11}{80} = 0.1375$ ) to decimals for simple comparison.

How do I convert fractions like 97/800 to decimals?

Simply divide the numerator by denominator: 97 ÷ 800 = 0.12125. Use long division or a calculator, then compare to your benchmark of 0.125.

What if two values are very close to 1/8?

Look at all decimal places! For example, $\frac{97}{800} = 0.12125$ vs $\frac{1}{8} = 0.125$ . Since 0.12125 < 0.125, the fraction is smaller than $\frac{1}{8}$ .

Why can't I just look at the denominators to compare fractions?

Because the numerators matter too! $\frac{11}{80}$ has a bigger denominator than $\frac{1}{8}$ , but 11/80 = 0.1375 is actually larger than 1/8 = 0.125 because 11 is much bigger than the equivalent numerator.

How do I remember which group each value belongs to?

Make a simple list: smaller than 0.125 (10%, $\frac{97}{800}$ ) and larger than 0.125 (20%, $\frac{11}{80}$ , 0.15). The benchmark 0.125 helps you see the pattern clearly!

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Percentage 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