Chapter 6
6-2 Converting Percents to Fractions and Fractions to Percents
Section II Using the Percentage Formula to Solve Business Problems
6-4 Solving for the Rate
6-6 Determining Rate of Increase or Decrease
6-8 Understanding and Solving Problems Involving Percentage Points
Chapter Notes, Teaching Tips and Lecture Launchers
• Be sure students understand the importance of percents in business. Emphasize that percents
are the primary way of expressing parts of a whole, and measuring change among business
variables.
• The Collaborative Learning Activity for this chapter, “Percents, The Language of Business,”
will help reinforce the lesson of how frequently percents are used in the business world and
even our everyday lives. It also provides students with a chance to become familiar with
some popular business publications.
• Spotlight: The Business Decision at the end of the chapter, “Allocating Overhead
Expenses,” is an example of an important business concept, distribution of overhead. Point
out that overhead is a category of business expense that includes all expenses incurred during
an operating period except cost of goods sold. These might include salaries, rent, electricity,
insurance, advertising, general and administrative expenses, etc.
• Ask students, “In what ways can overhead expenses be allocated to various
departments of a manufacturing company?” Some typical responses might be by
number of employees, number of square feet, or number of machines.
• Students seem to relate well to changes in pay. Ask them what their new salary would be if
they were to get a 5.35% increase in pay. Similarly, ask them how many employees would
be out of work if their employer were forced to reduce the workforce by 15%.
• Many students have a hard time grasping the concept of a percent change “from” and “to,”
especially if it is a reduction. For a relevant class example, state that the price of gas went
from $3.47 per gallon to $3.23 per gallon, then ask them what is the percent reduction.
• PowerPoint slides for each chapter are available on the instructor’s website for this text. You
may wish to use these slides as you discuss definitions, concepts, and solutions.
Section I Understanding and Converting Percents
• Lecture Launcher: I begin the discussion of percents by asking students, “Has anybody ever
heard of a C-note?” Inevitably, someone will answer, “Oh, that’s street talk for a $100 bill.”
“Why C?” I ask. Nobody knows! This is the perfect opening to explain that C is a slang
abbreviation, derived from the Latin word Centum, which means “one hundred.”
Next, I ask, “How do we describe a period of 100 years?” “Century or centennial,” someone
will answer. I then explain, these also come from centum, one hundred. Finally, I ask, “How
about percent?” Usually, someone will catch on and answer, “Oh yes, If cent means one
$57.85.
.
• Point out that, just as with equations in Chapter 5, once the students have calculated the
portion, rate, or base, they can verify their solution by substituting their answer in a
rearranged version of the percentage formula. (Be aware of slight differences due to rounding
of the rate).
• For example, if the rate was found by
P
B
, it can be verified by substituting in P = RB.
R =
P
B
=
5
20
= 25% Verify: P = RB = .25 x 20 = 5
• Spotlight: Some students prefer using proportion to solve percentage problems rather than
the percentage formula. To do this, set up the proportion
rate
100 = portion
base
and cross-
multiply to solve for the unknown.
• For example: At a Circuit City store last week, 70 televisions were sold with DVDs
built in. If this represented 20% of all TVs sold, how many total TVs were sold?
20
100 = 70
base
20b = 100(70)
20b = 7,000
20
20
b = 7000
20
Total TV’s (base) = 350
• Collaborative Learning Activity: Have students break into groups of two’s or three’s to write
some business-related word problems that involve portion, rate, and base. Next, have each
group exchange and solve the problems of another group. Now have them compare answers
and resolve any differences.
Section III Solving Other Business Problems Involving Percents
• In percent change problems:
• Give emphasis to the fact that the percent change is added to 100% to form the rate
in percent “increase” problems, whereas the percent change is subtracted from 100%
to form the rate in percent “decrease” problems.
• Spotlight: Be sure students know that the original number is always the base, and
represents 100%. The portion is the difference between the original number and the
new one.
• Another way to express this concept is that the base is the number we’re moving
from, whether it’s higher or lower than the new number.
• As a shortcut, remind students of the following calculator sequence: 75 – 60 60 % = 25%.
• Note: Scientific and business calculators require pushing the = button after the %
key; common arithmetic calculators do not.
• Spotlight: Classroom Activity: Have students work Try-It Exercises 20 through 22 in pairs.
Some peer tutoring here can help those who don’t quite understand these procedures.
• Homework Activity: Percentage points are best used to illustrate a company’s change in
market share or a politician’s gains or losses in the polls.
• Ask students to research a company’s market share for two periods and calculate the
percentage change in business these numbers represent.
• During election periods, have students research a candidate’s poll standings for two
periods and calculate the percentage change in number of voters.
• Collaborative Learning Activity: Have students break into groups to write and solve word
problems involving percent increase, percent decrease, and percentage points.
• Next have the groups exchange and solve another group’s problems. When they are
done, have them check their answers and resolve any differences.
• Collaborative Learning Activity: Many people don’t bother reading stock market data in the
newspaper because they don’t understand it. The Business Decision, “Facts on Wheels” is a
good introduction, as well as being good practice in understanding percent change.
• Have students break into groups and work out the problem.
• Have them bring to class a newspaper clipping showing the highest Volume Change
they can find.
Questions Students Always Ask
“Why do you subtract the percent from 1?”
• If students are asking this question, go over the Fraction/Decimal/Percent chart again, so
that they comprehend that 1 is the same as 100%. 100% – 25% is the same as 1 – .25.
“I don’t understand why 3.5 isn’t 35%?”
and 3.5 = 350%. This is why is it helpful to just follow the rules when converting from
decimal to percent and vice versa; always move the decimal point either two places to the
right, or conversely, two places to the left.
“How do I know whether to add 100% to the rate?”
• Tell students to always ask themselves whether the question is asking only for the
difference between the old and the new, or whether it’s asking for the entire new amount,
which in increase situations includes 100% of the old plus the percentage change.
Illustrate this concept with a revenue problem. For example: If revenues were $110,000
in 2002 and are expected to increase by 35% in 2003, what will revenues be in 2003?
They will be not only 100% of the previous year’s revenues but also 35% more, or 135%.
“How do I know whether to use the rate given or the complement of that rate?”
• In problems where the rate for one subset of the whole is given and the question is asking
for the number of the remaining items, one must use the complement of the rate given. In
other words, if 95% of the population of a town of 10,000 eats meat, how many people in
the town are vegetarian? Emphasize that the rate and the portion being sought must
always correspond to each other. If 95% are carnivores, then the number of vegetarians
is 1 – .95.
“How can I keep from getting mixed up about which number is which?”