Number Classification: Sorting Values Around 2/5 Threshold

Q: Should I convert everything to decimals or fractions?

Either works! Decimals are usually easier for comparison. Convert $ \frac{2}{5} = 0.4 $ and compare each value to 0.4.

Q: How do I convert percentages to decimals quickly?

Move the decimal point two places left! So 41% becomes 0.41, and 18% becomes 0.18. Easy!

Q: Why is 24/20 greater than 2/5?

$ \frac{24}{20} = 1.2 $ and $ \frac{2}{5} = 0.4 $. Since 1.2 > 0.4, we have 24/20 is much larger than our benchmark!

Q: How can I double-check my groupings?

Convert all to decimalsCompare each to 0.4Values less than 0.4 go in first groupValues greater than 0.4 go in second group

Fraction Comparison with Mixed Number Forms

Organise the following into two groups of values smaller than $\frac{2}{5}$ and values larger than $\frac{2}{5}$ :

$\frac{1}{3},41\%,0.38,\frac{24}{20},\frac{18}{100}$

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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 Let's multiply to find a common denominator

00:25 This fraction appears smaller than the given one

00:42 Now let's convert the given number to percentages and compare

01:06 These percentages are larger than the given number

01:14 Let's convert from fraction to decimal and compare

01:32 This number is smaller than the given one

01:46 Let's multiply to find a common denominator with the fraction

01:59 This fraction is larger than the given one

02:17 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 smaller than $\frac{2}{5}$ and values larger than $\frac{2}{5}$ :

$\frac{1}{3},41\%,0.38,\frac{24}{20},\frac{18}{100}$

Final Answer

$\frac{1}{3},0.38,\frac{18}{100}<\frac{2}{5}$

$41\%,\frac{24}{20}>\frac{2}{5}$

Key Points to Remember

Essential concepts to master this topic

Convert First: Change all values to same form (decimals or fractions)
Benchmark: $\frac{2}{5} = 0.4$ so compare each to 0.4
Check: $\frac{1}{3} \approx 0.333 < 0.4$ and $41\% = 0.41 > 0.4$ ✓

Common Mistakes

Avoid these frequent errors

Comparing different number forms directly
Don't compare 1/3 to 41% without converting = impossible comparison! You're mixing fractions with percentages which have different scales. Always convert all numbers to the same form first (all decimals or all fractions).

Practice Quiz

Test your knowledge with interactive questions

Approximately what is $\frac{6}{25}$ as a percentage?

FAQ

Everything you need to know about this question

Should I convert everything to decimals or fractions?

Either works! Decimals are usually easier for comparison. Convert $\frac{2}{5} = 0.4$ and compare each value to 0.4.

How do I convert percentages to decimals quickly?

Move the decimal point two places left! So 41% becomes 0.41, and 18% becomes 0.18. Easy!

What if I get confused with fraction to decimal conversion?

Just divide the numerator by denominator! For $\frac{1}{3}$ , calculate 1 ÷ 3 = 0.333...

Why is 24/20 greater than 2/5?

$\frac{24}{20} = 1.2$ and $\frac{2}{5} = 0.4$ . Since 1.2 > 0.4, we have 24/20 is much larger than our benchmark!

How can I double-check my groupings?

Convert all to decimals
Compare each to 0.4
Values less than 0.4 go in first group
Values greater than 0.4 go in second group

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