Problem 22 - Prealgebra

Question

If 12 of the 75 animals in a pet store are parakeets, what percent are parakeets?

Step-by-Step Solution

Answer

16% of the animals are parakeets.

Step 1: Understand the Problem

We want to find the percentage of animals in the pet store that are parakeets. There are 12 parakeets out of a total of 75 animals.

Step 2: Use the Percentage Formula

The formula to find the percentage is:\[\text{Percentage} = \left( \frac{\text{Number of Desired Items}}{\text{Total Number of Items}} \right) \times 100\]For this problem, the desired items are the parakeets.

Step 3: Insert the Numbers into the Formula

Insert the numbers into the formula:\[\text{Percentage} = \left( \frac{12}{75} \right) \times 100\]

Step 4: Perform the Division

Calculate \( \frac{12}{75} = 0.16 \).

Step 5: Convert Division Result to Percentage

Multiply the result of the division by 100 to find the percentage:\[ 0.16 \times 100 = 16 \]

Step 6: State the Answer

Therefore, 16% of the animals in the pet store are parakeets.

Key Concepts

Understanding Arithmetics in Percentage Calculation

Arithmetics, the art of working with numbers, forms the backbone of percentage calculations. At the heart of these calculations lies the simple process of division and multiplication. When we talk about finding a percentage, we essentially deal with two operations:

• Division: This helps us determine what fraction of a whole we are focusing on.
• Multiplication: By multiplying the fraction by 100, we convert it into a percentage, a friendlier format for expressing proportions.

Each arithmetic operation serves a specific purpose. For example, dividing 12 by 75 gives us the fraction of animals that are parakeets. Then, multiplying by 100 converts this fraction into a readable percentage. Knowing when and how to apply these arithmetic operations is crucial for solving percentage problems effectively.

The Role of Fractions in Calculating Percentages

Fractions are fundamental in percentage calculations as they represent parts of a whole. In the context of the given problem, the fraction \( \frac{12}{75} \) determines the portion of the store's animals that are parakeets. Here's how fractions are particularly helpful:

• Fractions provide an exact way of representing division, often more meaningfully than a decimal.
• They make it easy to see the ratio between parts and the whole, crucial for understanding proportions.

Transforming a fraction into a percentage involves straightforward steps. First, perform the division to convert the fraction to a decimal. In our example, \( \frac{12}{75} = 0.16 \). Then, turning decimals into percentages by multiplying by 100 simplifies the comparison between different ratios or fractions. It's a clean and efficient way of communicating how large one number is in relation to another.

Effective Problem Solving Approach in Percentage Problems

Problem-solving in mathematics often starts with understanding the problem at hand. With percentages, the first step is identifying the 'whole' and the 'part' of interest. Let's explore the problem-solving strategy using our 16% parakeet example:Identifying Components:

• The 'whole' refers to the total number of items, which is 75 animals.
• The 'part' is the count of items of interest, 12 parakeets in this case.

Using a formula makes problem-solving systematic. By identifying important numbers and plugging them into \[ \text{Percentage} = \left( \frac{\text{Number of Desired Items}}{\text{Total Number of Items}} \right) \times 100 \], you create a methodical approach to finding solutions.Finally, finishing the problem involves carrying out the arithmetic and interpreting the results. Calculating \( \frac{12}{75} \) and then moving to \( 0.16 \times 100 \) provides a clear path to the solution, ensuring that each step in the process contributes to understanding and solving the problem. This approach not only helps in percentage problems but enhances overall problem-solving skills.