Calculating Discounts math worksheet for students to practice finding new prices after applying percentage discounts.

Problem Overview:

The task involves calculating the new price of various items after applying different discount percentages. The goal is to determine the discounted price for each item based on its original price and the given discount rate.

Solution Approach:

To calculate the new price after a discount, we use the formula:
\[
\text{New Price} = \text{Original Price} \times (1 - \text{Discount Rate})
\]
Where:
- Original Price is the initial price of the item.
- Discount Rate is the percentage discount expressed as a decimal (e.g., 25% = 0.25).

Step-by-Step Calculations:

#### Item (a): Skateboard
- Original Price: $9
- Discount Rate: 25% = 0.25
\[
\text{New Price} = 9 \times (1 - 0.25) = 9 \times 0.75 = 6.75
\]
So, the new price is $6.75.

#### Item (b): Baseball bat
- Original Price: $23
- Discount Rate: 10% = 0.10
\[
\text{New Price} = 23 \times (1 - 0.10) = 23 \times 0.90 = 20.70
\]
So, the new price is $20.70.

#### Item (c): Leather jacket
- Original Price: $85
- Discount Rate: 25% = 0.25
\[
\text{New Price} = 85 \times (1 - 0.25) = 85 \times 0.75 = 63.75
\]
So, the new price is $63.75.

#### Item (d): Digital watch
- Original Price: $120
- Discount Rate: 50% = 0.50
\[
\text{New Price} = 120 \times (1 - 0.50) = 120 \times 0.50 = 60.00
\]
So, the new price is $60.00.

#### Item (e): Soccer ball
- Original Price: $18
- Discount Rate: 10% = 0.10
\[
\text{New Price} = 18 \times (1 - 0.10) = 18 \times 0.90 = 16.20
\]
So, the new price is $16.20.

#### Item (f): Roller skates
- Original Price: $78
- Discount Rate: 15% = 0.15
\[
\text{New Price} = 78 \times (1 - 0.15) = 78 \times 0.85 = 66.30
\]
So, the new price is $66.30.

#### Item (g): Men's tie
- Original Price: $4.5
- Discount Rate: 15% = 0.15
\[
\text{New Price} = 4.5 \times (1 - 0.15) = 4.5 \times 0.85 = 3.825
\]
Rounding to two decimal places, the new price is $3.83.

#### Item (h): Running shoes
- Original Price: $50
- Discount Rate: 10% = 0.10
\[
\text{New Price} = 50 \times (1 - 0.10) = 50 \times 0.90 = 45.00
\]
So, the new price is $45.00.

Final Answers:

\[
\boxed{
\begin{array}{ll}
\text{(a) Skateboard} & \$6.75 \\
\text{(b) Baseball bat} & \$20.70 \\
\text{(c) Leather jacket} & \$63.75 \\
\text{(d) Digital watch} & \$60.00 \\
\text{(e) Soccer ball} & \$16.20 \\
\text{(f) Roller skates} & \$66.30 \\
\text{(g) Men's tie} & \$3.83 \\
\text{(h) Running shoes} & \$45.00 \\
\end{array}
}
\]