Problem 4 - Prealgebra

Question

Solve each problem using the percent equation. 12 is what percent of \(400 ?\)

Step-by-Step Solution

Answer

12 is 3% of 400.

Step 1: Understand the Percent Equation

The percent equation can be written as: \( \, \text{Part} = \text{Percent} \times \text{Whole} \, \). In this exercise, the part is 12, the whole is 400, and we need to find the percent.

Step 2: Set Up the Equation

We need to find what percent 12 is of 400 using the equation \( 12 = \text{Percent} \times 400 \). We are solving for the 'Percent'.

Step 3: Rearrange the Equation

To find the percent, rearrange the equation to solve for it: \( \text{Percent} = \frac{12}{400} \).

Step 4: Calculate the Percent

Calculate \( \frac{12}{400} \). To do this, divide 12 by 400: \( \frac{12}{400} = 0.03 \).

Step 5: Convert to Percentage

To convert the decimal to a percentage, multiply by 100. Therefore, \( 0.03 \times 100 = 3 \% \).

Key Concepts

Understanding the Part, Percent, Whole Relationship

The percent equation is a powerful mathematical tool that helps quantify relationships between parts of a whole. Break it down simply as:

• Part: This is the section of the whole you're focusing on.
• Percent: This is the proportion of the whole that corresponds to the part, usually expressed as a percentage.
• Whole: This is the total amount or number from which the part is derived.

So, in the percent equation, \[ \text{Part} = \text{Percent} \times \text{Whole} \]the part is obtained by multiplying the whole by the percent (expressed as a decimal). Knowing any two of these three can help you solve for the third.

Mastering Percentage Calculations

Percentage calculations are straightforward once you pay attention to detail. They often revolve around finding what part of a whole a particular number represents. To solve percentage problems effectively:

• Identify the 'whole' and the 'part' in your problem.
• Arrange the equation to solve for the percent, which involves dividing the part by the whole.
• Convert the result into a percentage by multiplying it by 100.

For example, if asked '12 is what percent of 400?', you start by dividing 12 by 400 to get the decimal, 0.03. Then by multiplying 0.03 by 100, you find that 12 is 3% of 400. A key takeaway is that the percent acts as a way to describe how large the part is relative to the whole.

Building Basic Arithmetic Skills

Basic arithmetic skills are essential for mastering more complex mathematical concepts. For percentage problems, mastery of division and multiplication is crucial.

• Division: It's useful for determining the part in relation to the whole. For instance, dividing the part by the whole gives you the necessary decimal for percentage conversion.
• Multiplication: Important when converting the decimal to a percentage by multiplying by 100.

Practicing these operations will not only help simplify percentage calculations, but also build a strong foundation for tackling various mathematical challenges. Remember, practice makes perfect, and accurately executing these basic operations is the key to success in mathematics.