To determine how much time Jasmine spends preparing snacks, let's break the problem down into smaller steps.
1. Total Time Available:
Jasmine has a total of [tex]\(2 \frac{1}{2}\)[/tex] hours until her friends arrive. We can convert this mixed number into an improper fraction or a decimal to make calculations easier.
[tex]\[
2 \frac{1}{2} = 2 + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2} \text{ hours} = 2.5 \text{ hours}
\][/tex]
2. Time Spent Cleaning:
Jasmine spends [tex]\(\frac{2}{5}\)[/tex] of her total time cleaning. To find this, we multiply the total time by the fraction of time spent cleaning:
[tex]\[
\text{Time spent cleaning} = 2.5 \text{ hours} \times \frac{2}{5} = 2.5 \times 0.4 = 1.0 \text{ hour}
\][/tex]
3. Time Spent Preparing Snacks:
To find the time spent preparing snacks, we subtract the time spent cleaning from the total time:
[tex]\[
\text{Time spent preparing snacks} = 2.5 \text{ hours} - 1.0 \text{ hour} = 1.5 \text{ hours}
\][/tex]
Thus, Jasmine spends [tex]\(1.5\)[/tex] hours, or [tex]\(1 \frac{1}{2}\)[/tex] hours, preparing snacks. Therefore, the final answer is:
[tex]\[
\boxed{1 \frac{1}{2}}
\][/tex]
