Compare Mixed Numbers: Sorting Fractions, Decimals, and Percentages Around 12%

Q: Which format should I convert everything to?

Choose the format that makes the math easiest! For this problem, percentages work well since 12% is already given as a percentage. You could also use decimals (12% = 0.12) or fractions ($ 12\% = \frac{12}{100} $).

Q: How do I convert fractions to percentages quickly?

Multiply the fraction by 100%! For example: $ \frac{6}{40} \times 100\% = \frac{600}{40}\% = 15\% $. Or convert to decimal first: $ \frac{6}{40} = 0.15 = 15\% $.

Q: Why is 0.1 less than 12% if 1 is bigger than 12?

Be careful with decimal place values! 0.1 = 0.10 = 10%, not 1%. The decimal 0.1 means "1 tenth" or 10%, which is indeed less than 12%.

Q: How can I double-check my percentage conversions?

Convert back to verify! If $ \frac{11}{100} = 11\% $, then $ 11\% = \frac{11}{100} $ should be true. Also, 11% should be smaller than 12%, which makes sense.

Q: What if I get confused about which group each number belongs to?

Make a simple list! Write 12% = 0.12 at the top. Then convert each number and ask: "Is this bigger or smaller than 0.12?" For example: 15% > 12% ✓, 10%

Converting Mixed Forms to Compare Values

Organise the following into two groups of values less than 12% and values greater than 12%.

$\frac{11}{100},0.1,0.13,\frac{6}{40},20\%$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Sorted into 2 groups

00:03 First, we'll convert percentages to fractions and decimal numbers, so we can compare

00:13 Now we'll sort each option as greater or less than the given value

01:07 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

Organise the following into two groups of values less than 12% and values greater than 12%.

$\frac{11}{100},0.1,0.13,\frac{6}{40},20\%$

Step-by-step solution

$12\%=\frac{12}{100}=0.12$

Now we will convert all values into percentages and see which are greater and which are less than 12%.

$\frac{6}{40}\times\frac{2.5}{2.5}=\frac{15}{100}=15\%$

$\frac{11}{100}=11\%$

$0.1=\frac{10}{100}=10\%$

$0.13=\frac{13}{100}=13\%$

Now we can observe which are greater and less than 12%.

Final Answer

$0.13,\frac{6}{40},20\%>12\%$

$\frac{11}{100},0.1<12\%$

Key Points to Remember

Essential concepts to master this topic

Conversion: Convert all values to same format before comparing
Technique: Change $\frac{6}{40}$ to percentage: $\frac{6}{40} \times 100\% = 15\%$
Check: Verify 12% = 0.12 = $\frac{12}{100}$ as reference point ✓

Common Mistakes

Avoid these frequent errors

Comparing different formats without converting
Don't compare 0.13 directly to 12% without converting = wrong groupings! Mixed formats make it impossible to see true size relationships. Always convert everything to the same format (all percentages, all decimals, or all fractions) before comparing.

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

Which format should I convert everything to?

Choose the format that makes the math easiest! For this problem, percentages work well since 12% is already given as a percentage. You could also use decimals (12% = 0.12) or fractions ( $12\% = \frac{12}{100}$ ).

How do I convert fractions to percentages quickly?

Multiply the fraction by 100%! For example: $\frac{6}{40} \times 100\% = \frac{600}{40}\% = 15\%$ . Or convert to decimal first: $\frac{6}{40} = 0.15 = 15\%$ .

Why is 0.1 less than 12% if 1 is bigger than 12?

Be careful with decimal place values! 0.1 = 0.10 = 10%, not 1%. The decimal 0.1 means "1 tenth" or 10%, which is indeed less than 12%.

How can I double-check my percentage conversions?

Convert back to verify! If $\frac{11}{100} = 11\%$ , then $11\% = \frac{11}{100}$ should be true. Also, 11% should be smaller than 12%, which makes sense.

What if I get confused about which group each number belongs to?

Make a simple list! Write 12% = 0.12 at the top. Then convert each number and ask: "Is this bigger or smaller than 0.12?" For example: 15% > 12% ✓, 10% < 12% ✓.

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