To find the current value of the bicycle, we need to account for the price change of $-\frac{1}{5}$ of the original price.

Step-by-Step Solution:

1. Original price of the bike: $450.

2. Value change: The value has decreased by $\frac{1}{5}$ of the original price. To calculate the amount of the price decrease: $\text{Decrease} = \frac{1}{5} \times 450 = \frac{450}{5} = 90$

3. Current value of the bike: The value has decreased by $90 from the original price, so we subtract this from $450: $\text{Current value} = 450 - 90 = 360$

Final Answer:

The current value of the bike is $360.

Would you like more details or have any questions?

Here are 5 related questions to deepen your understanding:

1. If the value of the bike had decreased by $\frac{1}{10}$ of its original price, what would the current value be?
2. What percentage decrease does $\frac{1}{5}$ represent?
3. If the bike's value increases by $50 after reaching $360, what is its new value?
4. How much would the bike be worth if the value decreased by $\frac{1}{4}$ of the original price?
5. If Delaney decides to sell the bike for $400, what would the difference between this price and the current value be?

Tip: When dealing with fractional changes, always multiply the fraction by the original value to find the change amount.