Problem 28 - Prealgebra

Question

Find the discount to the nearest cent. \(25 \%\) off a \(\$ 74\) baseball glove

Step-by-Step Solution

Answer

The discount is $18.50.

Step 1: Identify the Discount Rate

The problem states that we need to find the discount using a rate of 25%. This means the discount rate, as a decimal, is 0.25.

Step 2: Calculate the Discount Amount

To find the discount, multiply the original price of the baseball glove by the discount rate. Discount amount = Original price × Discount rate Therefore, Discount amount = 74 × 0.25 = 18.50.

Step 3: Ensure the Discount is Rounded Correctly

According to the problem, the discount should be rounded to the nearest cent. Since $18.50 is already at two decimal places, it does not require further rounding.

Key Concepts

Calculation of Discounts

Calculating discounts is a useful skill, especially when you are out shopping or planning purchases. A discount is essentially a reduction in the original price of an item. To determine the amount of discount, you'll need two key pieces of information: the original price of the product and the discount rate. In our example, the discount rate is 25% and the original price is $74.

To find the discount amount, convert the discount rate from a percentage to a decimal by dividing by 100. For a 25% discount, this converts to 0.25. Then, multiply the original price by this decimal. For different real-world situations:

• Check the store ad or tag to confirm the discount percentage.
• Use mental math or a calculator for quick conversions to decimals.
• Remember that discount calculations help in budgeting and saving money.

Percentage Problems

Percentage problems might seem tricky at first, but they become straightforward once you understand the basics. Percent means 'per hundred', so a percentage represents a part out of a total of 100. For instance, 25% means 25 parts out of 100.

To tackle percentage problems efficiently:

• Familiarize yourself with converting percentages to decimals by dividing the percentage by 100. In our example, this translates 25% into 0.25.
• Apply these conversions in practical scenarios, like applying discounts or calculating interest rates.
• Percentages are also handy for comparing quantities or measuring increases and decreases over time.

It is helpful to regularly practice diverse percentage problems to build confidence in handling them effectively.

Basic Arithmetic Skills

Mastering basic arithmetic skills is essential, as they form the foundation of many mathematical concepts. Arithmetic involves operations such as addition, subtraction, multiplication, and division. Let's focus on multiplication for this example, used to calculate the discount.

Here’s a quick guide to improve arithmetic skills:

• Start with simple, real-world tasks: such as calculating prices after a discount or combining totals from multiple purchases.
• Use methods like breaking numbers into simpler components to make multiplication easier (e.g., multiplying by 0.25 can be seen as multiplying by 1/4).
• Optimize learning with both mental calculations and calculator use for fast and accurate results.

Developing strong arithmetic skills will help tremendously, both in academics and daily life calculations.