Question

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a new bicycle sells for $300. it is on sale for $\frac{1}{4}$ off the regular price. select all the expressions that represent the sale price of the bicycle in dollars.
a) $300 cdot \frac{1}{4}$
b) $300 cdot \frac{3}{4}$
c) $300 cdot (1 - \frac{1}{4})$
d) $300 - \frac{1}{4}$
e) $300 - \frac{1}{4} cdot 300$

Explanation:

Step1: Understand discount logic

The sale price is regular price minus $\frac{1}{4}$ of regular price, or equivalently, $\frac{3}{4}$ of regular price.

Step2: Analyze each option

• A: $300 \cdot \frac{1}{4}$: This calculates the discount amount, not sale price.
• B: $300 \cdot \frac{3}{4}$: This is $\frac{3}{4}$ of the regular price, which equals sale price.
• C: $300 \cdot (1 - \frac{1}{4})$: Simplifies to $300 \cdot \frac{3}{4}$, same as above, valid.
• D: $300 - \frac{1}{4}$: Subtracts a fraction, not the discount amount, invalid.
• E: $300 - \frac{1}{4} \cdot 300$: Subtracts the discount amount from regular price, valid.

Answer:

B) $300 \cdot \frac{3}{4}$, C) $300 \cdot (1 - \frac{1}{4})$, E) $300 - \frac{1}{4} \cdot 300$