AAA000 Course Title

## Introduction: Connecting Your Learning

As a network administrator, you must constantly monitor network traffic to ensure that employees can access the Internet and company resources to do their jobs. You may have to analyze comparisons between departments to see where the heaviest load is so you can compensate for any congestion that might be occurring. By using percentages, you can quickly compare the differences between departments and potentially even users to determine how the network is being utilized. This module discusses applications of percents. By the end of the module, you should be able to distinguish between the base, percent, and percentage, and calculate the percentage, the percent, and the base.

## Lesson Objectives

By the end of this lesson, you should be able to:

1. Identify the percentage, the base, and the percent
2. Find the unknown percentage, base, or percent.

## Key Terms

Review the flashcards to learn the key terms for this lesson.

## Presentation

### Base, Percent, and Percentage

Three basic types of percent problems are most common. Each type involves a base, a percent, and a percentage, and when they are translated from words to mathemati­cal symbols, each becomes a multiplication statement. Examples of these types of problems are the following:

1. What number is 30% of 50? (Missing product statement)
2. 15 is what percent of 50? (Missing factor statement)
3. 15 is 30% of what number? (Missing factor statement)

In Problem 1, the product is missing.

To solve the problem, you represent the missing product with P.

P = 30% ⋅ 50

Percentage

The missing product P is called the percentage. Percentage means part or por­tion.

In P = 30% ⋅ 50, P represents a particular part of 50.

In Problem 2, one of the factors is missing. Here the missing factor is represented with Q.

15 = Q ⋅ 50

Percent

The missing factor is the percent. Percent, you know, means per 100, or part of 100. In 15 = Q ⋅ 50, Q indicates what part of 50 is being taken or considered. Specifi­cally, 15 = Q ⋅ 50 means that if 50 were to be divided into 100 equal parts, then Q indicates 15 are being considered.

In Problem 3, one of the factors is missing. Represent the missing factor with B.

15 = 30% ⋅ B

Base

The missing factor is the base. Some meanings of base are a source of supply or a starting place. In 15 = 30% ⋅ B, B indicates the amount of supply. Specifically, 15 = 30% ⋅ B indicates that 15 represents 30% of the total supply.

Each of these three types of problems is of the form (percentage) = (percent) ⋅ (base).

You can determine any one of the three values given the other two.

### Finding the Percentage

Example

Problem

What number is 30% of 50?

 What number is 30% of 50? Missing product statement. (percentage) = (percent) x (base) P = 30% x 50 Convert 30% to a decimal. P = .30 x 50 Multiply. P = 15

15 is 30% of 50.

Example

Problem

What number is 36% of 95?

 What number is 36% of 95? Missing product statement. (percentage) = (percent) x (base) P = 36% x 95 Convert 36% to a decimal. P = .36% x 95 Multiply. P = 34.2

34.2 is 36% of 95.

### Finding the Percent

Example

Problem

15 is what percent of 50?

 15 is what percent of 50? Missing factor statement. (percentage) = (percent) x (base) 15 = Q x 50 = Q Divide 15 by 50. 0.3 = Q 30% = Q Convert to a percent.

15 is 30% of 50.

Example

Problem

4.32 is what percent of 72?

 4.32 is what percent of 72? Missing factor statement. (percentage) = (percent) x (base) 4.32 = Q x 72 = Q Divide 4.32 by 72. 0.06 = Q 6% = Q Convert to a percent.

4.32 is 6% of 72.

### Finding the Base

Example

Problem

15 is 30% of what number?

 15 is 30% of what number? Missing factor statement. (percentage) = (percent) x (base) 15 = 30% x B Convert to decimal. 15 = 0.30 x B Divide 15 by .3 = B 50 = B

15 is 30% of 50.

Example

Problem

56.43 is 33% of what number?

 56.3 is 33% of what number? Missing factor statement. (percentage) = (percent) x (base) 56.43 = 33% x B Convert to decimal. 56.43 = .33 x B Divide 56.43 by .33 = B 171 = B

56.43 is 33% of 171.

Using the three methods listed above you can now solve problems like these:

Example

Problem

Jeff has a coupon at an electronics store for 15% off any purchase of \$100 or more. He wants to buy a 17-inch monitor with a price tag of \$220. Jeff wonders how much money the coupon will take off the \$220 original price.

 What number is 15% of \$220 Missing product statement. (percentage) = (percent) x (base) P = 15% x 220 Convert 15% to a decimal. P = .15 x 220 Multiply. P = 33

The coupon will take \$33 off the original price.

Example

Problem

Evelyn bought some CDs at the local bookstore. Her total bill was \$31.50, which included 5% tax. How much did the books cost before tax?

 What number + 5% of that number is \$31.50? \$31.50 is 105% of what number? Missing factor statement. (percentage) = (percent) x (base) \$31.50 = 105% x B Convert to decimal. \$31.50 = 1.05 x B Divide \$31.50 by 1.05 = B 30 = B

The CDs cost \$30 before tax.

Watch the following Khan Academy videos about how to solve percent problems. You will see additional examples that can help you better understand how to solve percent problems.

 Math Video Toolkit: View the following Khan Academy video lessons. Solving Percent Problems Solving Percent Problems 2 Solving Percent Problems 3

## Exercise:

 Now you get a chance to work out some problems. You will need to get out a piece of paper and a pencil to complete the practice problems. Study each of these problems carefully; you will see similar problems on the lesson knowledge check. Select the following link to complete the practice activity. Translating Problems with Percent Practice Problems Once you complete the practice activity, check to see how well you did by selecting the following link: Solutions: Translating Problems with Percent Practice Problems

## Summarizing Your Learning

Each of these three types of problems is of the form (percentage) = (percent)(base). You can determine any one of the three values given the other two.

## Assessing Your Learning

 Now that you have read over the lesson carefully attempted the practice exercises, it is time for a knowledge check. Please note that this is a graded part of this lesson so be sure you have prepared yourself before starting.
1. Complete the Percents: Translating Problems.

Resource: