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Chapter 7: Problem 1

Define the key term percent equation.

Short Answer

Expert verified
A percent equation is \[ \text{Part} = \frac{\text{Percent}}{100} \times \text{Whole} \] used to find the part, whole, or percent in percentage problems.

Step by step solution

01

- Understand 'percent'

To start, 'percent' refers to a part per hundred. For instance, 50% represents 50 out of 100, or half.
02

- Break down the term 'percent equation'

A percent equation is a mathematical expression used to find the part, whole, or percent in problems involving percentages.
03

- Write the general form of the percent equation

The general form can be written as \[ \text{Part} = \frac{\text{Percent}}{100} \times \text{Whole} \]. This equation helps convert a percentage into a mathematical operation.
04

- Identify components of the percent equation

In the equation \[ \text{Part} = \frac{\text{Percent}}{100} \times \text{Whole} \], 'Part' is the portion of the total, 'Percent' is the percentage, and 'Whole' is the total amount.
05

- Apply the equation

To use the percent equation, identify the known values (part, whole, or percent) and substitute them into the equation to solve for the unknown value.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

percent
A 'percent' is a way to express a number as a fraction of 100. It is denoted using the symbol '%'. For example, if you have 50%, it means you have 50 parts out of 100. This is equivalent to half or 0.5 in decimal form. Understanding percentages is crucial because they allow us to easily compare values. They are used in various real-world applications such as discounts, interest rates, and test scores.

mathematical expression
A 'mathematical expression' consists of numbers, variables, and operators (such as +, -, 脳, and 梅) that are grouped together to represent a value. In the case of a 'percent equation', the expression involves percentages and other values. By converting percent to a fraction of 100, you can perform calculations that help solve various problems involving parts, wholes, and percentages.

equation components
An equation is a statement that shows the equality between two expressions. For example, in the percent equation \(\text{Part} = \frac{\text{Percent}}{100} \times \text{Whole}\), there are three main components:
  • Part: This is the portion or segment of the total that we are interested in.
  • Percent: This represents the percentage value we are dealing with, converted into a fraction by dividing by 100.
  • Whole: This is the overall total value that the percent applies to.

problem-solving
Using the percent equation to solve problems involves identifying which values you know and which one you need to find. Here are some steps to follow:
  • Step 1: Write down the percent equation \(\text{Part} = \frac{\text{Percent}}{100} \times \text{Whole}\).
  • Step 2: Identify the known values (these could be part, percent, or whole).
  • Step 3: Substitute the known values into the equation.
  • Step 4: Solve for the unknown value.
For example, if you know the whole is 200 and the percent is 25%, you can find the part by substituting these values into the equation: \(\text{Part} = \frac{25}{100} \times 200 = 50\). Therefore, 25% of 200 is 50.

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