Problem 10 - Prealgebra

Question

Solve each problem using the percent equation. Find \(42 \%\) of 150

Step-by-Step Solution

Answer

42% of 150 is 63.

Step 1: Convert Percentage to Decimal

To use the percent equation, start by converting the percentage to a decimal. Move the decimal point two places to the left. For example, \(42\%\) becomes \(0.42\).

Step 2: Set Up the Equation

Use the percent equation \(\text{part} = \text{percent} \times \text{whole}\). Here, we want to find \(42\%\) of 150, so our equation becomes \(x = 0.42 \times 150\), where \(x\) represents the part of the whole.

Step 3: Solve the Equation

Multiply \(0.42\) by 150 to find \(x\). Calculating this gives \(x = 63\).

Step 4: Interpret the Result

Since \(x = 63\), this means that \(42\%\) of 150 is 63.

Key Concepts

Understanding Percentage Conversion

When you're working on a math problem involving percentages, the first step is converting the percentage into a decimal. This step is crucial as it allows you to perform mathematical operations easily. To convert a percentage to a decimal, move the decimal point two places to the left. For instance, if you have a percentage like 42%, changing it to a decimal gives 0.42.

• Move the decimal left: 42% becomes 0.42
• This conversion simplifies multiplication and other calculations
• Always ensure accuracy by double-checking the conversion

Remember, successfully converting the percentage sets the stage for applying the correct calculations and eventually solving the problem.

Decimal Multiplication Basics

After converting a percentage to a decimal, the next step often involves multiplication. Decimal multiplication requires precision but follows simple rules similar to those of multiplying whole numbers. In this context, you will multiply the decimal by the 'whole' or 'total' amount you are given in the problem. For example, if you want to find 42% of 150: 1. First convert 42% to a decimal; it becomes 0.42. 2. Then, multiply: 0.42 times 150. This calculation results in 63.

• Keep track of decimal places for correct placement in your final answer
• Practice makes perfect—use simpler examples if needed
• Make sure to line up the decimals correctly in manual computations

Decimal multiplication is essential in working with percentages, ensuring accurate results every time.

Effective Problem Solving Strategies

Mathematical problem solving can seem daunting, but with systematic approaches, it becomes much simpler. Start by clearly understanding the problem, identifying what is given, and what is needed. In our example problem, we are asked to find a percentage of a number, hence we ready ourselves to perform percentage conversion and multiplication.

• Write down known information and what needs to be calculated
• Break the problem into small, manageable steps
• Double-check the calculations to verify your answer makes sense

Consistent practice with these strategies helps build confidence and improves problem-solving skills over time.

Importance of Mathematics Education

Mathematics education is fundamental as it equips students with critical thinking and problem-solving skills. Understanding how to navigate various mathematical procedures like percentage conversion and decimal multiplication is crucial not just in academics, but also in real-life situations such as budgeting and data interpretation.

• Mathematics fosters logical reasoning and analytical skills
• It is applicable in diverse fields: science, technology, economics, etc.
• Building a strong foundation in math enhances future learning and career opportunities

Encouraging students to approach math positively, with an understanding of its real-world applications, makes it more accessible and less intimidating.