Compare and Group Numbers: Sorting Fractions, Decimals, and Percentages Around 20%

To solve this problem, we'll proceed with the following steps:

• Step 1: Convert each given value to a decimal form for consistent comparison.
• Step 2: Compare each decimal to 0.20, sort values into the categories: greater than 20% and less than 20%.

Let's convert each value:
- $\frac{18}{50} = 0.36$
- $0.24$ is already in decimal form.
- $0.19$ is already in decimal form.
- $45\%$ in decimal form is $0.45$.
- $\frac{28}{100} = 0.28$.

Now we compare each with 0.20:

• $\frac{18}{50} = 0.36$ is greater than $0.20$.
• $0.24$ is greater than $0.20$.
• $0.19$ is less than $0.20$.
• $45\%$ or $0.45$ is greater than $0.20$.
• $\frac{28}{100} = 0.28$ is greater than $0.20$.

Based on these comparisons, we organize them into two groups:

Greater than 20%: $\frac{18}{50}, 0.24, 45\%, \frac{28}{100}$

Less than 20%: $0.19$

Therefore, the values sorted into their respective categories are:

$\frac{18}{50},0.24,45\%,\frac{28}{100}>20\%$

$0.19<20\%$