Classify Fractions and Percentages: Sorting Values Around 25%

Converting Mixed Formats to Percentages

Organise the following into two groups of values greater than 25% and values less than 25%:

1350,34,34%,24100,0.28 \frac{13}{50},\frac{3}{4},34\%,\frac{24}{100},0.28

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Sorted into 2 groups
00:06 First, we'll convert from percentages to fractions and decimal numbers, so we can compare
00:41 Now we'll classify each option as greater or smaller than the given value
01:44 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Organise the following into two groups of values greater than 25% and values less than 25%:

1350,34,34%,24100,0.28 \frac{13}{50},\frac{3}{4},34\%,\frac{24}{100},0.28

2

Step-by-step solution

To solve this problem, we'll convert each given value to a percentage and compare it with 25%.

  • 1350 \frac{13}{50} : Calculate as (1350)×100=26% \left(\frac{13}{50}\right) \times 100 = 26\% .
  • 34 \frac{3}{4} : Calculate as (34)×100=75% \left(\frac{3}{4}\right) \times 100 = 75\% .
  • 34% 34\% : This value is already in percentage form as 34%.
  • 24100 \frac{24}{100} : Calculate as (24100)×100=24% \left(\frac{24}{100}\right) \times 100 = 24\% .
  • 0.28 0.28 : Calculate as 0.28×100=28% 0.28 \times 100 = 28\% .

Now, we compare each percentage to 25%:

  • 1350=26%\frac{13}{50} = 26\% which is greater than 25%.
  • 34=75%\frac{3}{4} = 75\% which is greater than 25%.
  • 34%34\% which is greater than 25%.
  • 24100=24%\frac{24}{100} = 24\% which is less than 25%.
  • 0.28=28%0.28 = 28\% which is greater than 25%.

Thus, grouping these values gives us:

  • Values greater than 25%: 1350,34,34%,0.28 \frac{13}{50}, \frac{3}{4}, 34\%, 0.28
  • Values less than 25%: 24100 \frac{24}{100}

Therefore, the correct answer is:

1350,34,34%,0.28>25% \frac{13}{50},\frac{3}{4},34\%,0.28>25\%

24100<25% \frac{24}{100}<25\%

3

Final Answer

1350,34,34%,0.28>25% \frac{13}{50},\frac{3}{4},34\%,0.28>25\%

24100<25% \frac{24}{100}<25\%

Key Points to Remember

Essential concepts to master this topic
  • Conversion Rule: Multiply fractions and decimals by 100 for percentages
  • Technique: 1350×100=26% \frac{13}{50} \times 100 = 26\% for fraction conversion
  • Check: Compare all converted values to 25% benchmark ✓

Common Mistakes

Avoid these frequent errors
  • Comparing different number formats directly
    Don't compare 34 \frac{3}{4} directly to 25% without converting = wrong groupings! Different formats can't be compared accurately. Always convert all values to the same format (percentages) 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

Why do I need to convert everything to percentages?

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Converting to percentages gives you a common format for comparison! It's much easier to see that 26% > 25% than comparing 1350 \frac{13}{50} to 25%.

How do I convert a fraction like 13/50 to a percentage?

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Multiply the fraction by 100: 1350×100=26% \frac{13}{50} \times 100 = 26\% . You can also divide first: 13 ÷ 50 = 0.26, then multiply by 100.

What about decimals like 0.28?

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For decimals, just multiply by 100: 0.28 × 100 = 28%. Move the decimal point two places to the right and add the % symbol!

Is 24/100 the same as 24%?

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Yes! 24100 \frac{24}{100} means 24 out of 100, which is exactly 24%. Any fraction with denominator 100 converts directly to a percentage.

What if I get confused about which group a value belongs to?

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Always convert first, then compare! Write down: 26%, 75%, 34%, 24%, 28%. Now it's easy to see which are greater or less than 25%.

Can I use a different method to compare these values?

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You could convert everything to decimals instead (comparing to 0.25), but percentages are usually clearer for this type of problem since 25% is already given as a percentage.

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