1.9: Interpreting Statements about Percentages

INTRODUCTION

Mathematicians like to shorten things. Sometimes a capital letter (like C or Q) is used as a common variable to indicate that you are talking about two similar quantities. The numbers 1 and 2 indicate that the quantities represent two different quantities, but their values might still be the same. For example, if C1 represents students in one class and C2 represents students in a second class, it is possible that C1 = C2, even though they represent different things. Note: Remember, an inequality means that two quantities are not equal. Also, remember the inequality symbol (> or <) always points to the smaller of the two quantities.

Quick Check-in:

Please discuss the following questions in your group:

What specific concept from Unit 1.7 do you feel fairly confident about?
Are there any specific concepts in Unit 1.7 that you find challenging?

SPECIFIC OBJECTIVES

By the end of this collaboration, you should understand that

percentages involve a numerator (comparison value) and a denominator (reference value).

By the end of this collaboration, you should be able to

correctly identify the quantities involved in a verbal statement about percentages.
convert between ratios and percentages.
convert between the decimal representation of a number and a percent.
read and use information presented in a two-way table.

PROBLEM SITUATION: THE LANGUAGE OF PERCENTAGES

The World Health Organization (WHO) is the part of the United Nations that oversees health issues in the world. The WHO leads numerous studies on tobacco use around the world. In its study called, “Gender and Tobacco,” the organization learned that tobacco use among females is increasing.²⁸ For example, recent research shows that just as many young girls smoke as young boys. The report is filled with information about percentages of females who smoke, percentages of males who smoke, and the percentage of smokers who start smoking by age 10. The language used to describe this information can be difficult to understand; therefore, pay close attention to the language used to describe a percent at the beginning of this collaboration. This will help you to understand the findings reported in the WHO study.

Consider the following two quantities:

Quantity 1 (Q1): The percentage of females who smoke.
Quantity 2 (Q2): The percentage of smokers who are female.

(1) (a) Are these two quantities equal (Q1 = Q2)?

(b) Could Q1 be greater than Q2 (Q1 > Q2)?

(c) Could Q1 be less than Q2 (Q1 < Q2)?

(d) Explain your reasoning.

(2) What information would you need to calculate these percentages?

Smoking on Two College Campuses

Questions 3 and 4 present two situations with data about smoking. You can use these situations to test your ideas from Questions 1 and 2.

(3) Suppose a study on smoking was conducted at Midland University. The following table indicates the results of the study.

	Males	Females
Smokers	4,572	5,362
Nonsmokers	10,284	12,736

(a) What percentage of females smoke at Midland University? Round to the nearest percent.

(b) What percentage of smokers at Midland University are female? Round to the nearest percent.

(4) Suppose a study was conducted at Northwest College. The following table indicates the results of the study.

	Males	Females
Smokers	1,256	536
Nonsmokers	1,028	1,053

(a) What percentage of females smoke at Northwest College? Round to the nearest percent.

(b) What percentage of smokers at Northwest College are female? Round to the nearest percent.

(c) A newspaper stated that 40% of the male students at Northwest College are smokers. Is that claim reasonable?

(5) In 2021, the World Health Organization conducted a study about the prevalence of tobacco use worldwide.²⁹ The organization reported that 2.1% of the adult females in China smoke tobacco products. In the United States, 15.2% of adult females smoke.

(a) Out of 100 adult females in China, about how many are smokers?

(b) Out of 1,000 adult females in China, about how many are smokers?

(c) Out of 100 adult females in the United States, about how many are smokers?

(d) Out of 1,000 adult females in the United States, about how many are smokers?

(e) Suppose you read that 478 out of 1,000 males in China smoke. Based on this data, what percentage of males in China smoke?

(f) Are there more female smokers in China or the United States? Discuss in your group before recording your answer in the space below.

FURTHER APPLICATIONS

The following questions are included in Exercise 1.8. After you complete (a) and (b) below, be sure to transfer your answers to Exercise 1.8, Question 5.

(6) A teacher has collected data on the grades his students received in his morning and afternoon classes. The following tables show two different ways to represent the same data as percentages.

Table 1

	Grade A	Grade B	Grade C	Grade D	Grade F
Morning Class	12.5%	25.0%	37.5%	6.3%	18.7%
Afternoon Class	14.3%	20.0%	37.1%	8.6%	20.0%

Table 2

	Grade A	Grade B	Grade C	Grade D	Grade F
Morning Class	44.4%	53.3%	48.0%	40.0%	46.2%
Afternoon Class	55.6%	46.7%	52.0%	60.0%	53.8%

(a) Which table could be used to answer the following question: What percentage of the students who received an “A” is in the morning class? Explain your answer.

(b) Which table could be used to answer the following question: What percentage of the students in the morning class received an “A”? Explain your answer.

MAKING CONNECTIONS

Record the important mathematical ideas from the discussion.

______________________________________

²⁸ https://apps.who.int/iris/handle/10665/43657

²⁹ https://www.who.int/publications/i/item/9789240039322

Contents

Text