Problem 23 - Prealgebra

Question

Should be set up the same way. Then the actual calculations should be done on a calculator. Number of People Of \(7,892\) people attending an outdoor concert in Los Angeles, \(3,972\) are over 18 years of age. What percent is this? (Round to the nearest whole number percent.

Step-by-Step Solution

Answer

50% of the concert attendees are over 18.

Step 1: Identify the Total and Part

We need to find what percentage of the total number of people at the concert ( 7,892 people) are over 18 years of age ( 3,972 people). Identify these two numbers as the 'whole' and the 'part' for the percentage calculation.

Step 2: Set Up the Percentage Formula

Use the percentage formula: \( \text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100 \). Here, the 'Part' is 3,972 and the 'Whole' is 7,892.

Step 3: Substitute Numbers into the Formula

Substitute the values into the percentage formula: \( \text{Percentage} = \left( \frac{3,972}{7,892} \right) \times 100 \).

Step 4: Calculate the Division

Use your calculator to divide the part by the whole: \( \frac{3,972}{7,892} = 0.5032 \).

Step 5: Convert to Percentage

Multiply the result by 100 to convert the decimal to a percentage: \( 0.5032 \times 100 = 50.32 \).

Step 6: Round to the Nearest Whole Number

Round 50.32 to the nearest whole number, which is 50%.

Key Concepts

Prealgebra

Prealgebra serves as the foundational building block for understanding various mathematical operations, including percentages. At this stage, students engage with numbers and basic operations, setting the stage for more complex mathematical concepts. In the context of percentage calculation, prealgebra involves understanding what constitutes a 'part' and a 'whole' from a given situation.

For example, in the concert scenario, the total number of attendees (7,892) represents the 'whole', while the number of people over 18 (3,972) signifies the 'part'. This helps building a solid grounding for using percentages to describe portions of any whole. Mastery of such basic terms and concepts is crucial in developing the skill to solve real-world mathematical problems.

Mathematical Methods

Mathematical methods involve logical steps or formulas used to solve problems, such as percentage calculations. The method employed for finding a percentage involves the formula:

• \( \text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100 \)

This formula allows us to find out what portion of a whole a particular part represents, in percentage terms. It's important to accurately substitute the correct numbers into this formula and follow these steps diligently:
- Identify the total number (whole) and the specific number (part) from the problem.
- Substitute these values into the percentage formula.

Using these mathematical methods systematically can lead to accurate, real-world calculations.

Rounding Numbers

Rounding numbers is a common mathematical technique used to simplify numbers, making them easier to work with or understand. In the context of percentage calculation, once the decimal result is obtained, it is often rounded to a whole number for clarity and simplicity.

Rounding involves looking at the decimal part of a number. If it's 0.5 or above, you round up; if it's less than 0.5, you round down. For instance, in our exercise, the initial percentage calculated was 50.32%. Since the decimal part (.32) is less than 0.5, we round down to the nearest whole number, resulting in 50%.

Calculator Usage

Calculators are useful tools that expedite complex calculations, particularly when working with large numbers or intricate decimal places. In the context of percentage calculations, a calculator can quickly handle division and multiplication needed in the formula.

To use a calculator effectively for percentage calculations:

• First, input the part and the whole as demonstrated earlier (3,972 divided by 7,892).
• Understand that the result, a decimal, can be directly converted to a percentage by multiplying by 100.

It's essential to familiarize oneself with the calculator's basic functions to ensure accurate and efficient computation.