Section 4.4

Percents

 


What you should learn

To solve percent problems

To solve problems involving simple interest

NCTM Curriculm Standards 2, 6 - 9

 

In doing this the teacher wants to make sure that the following words are incorporated into the introductory lesson:

Percent

Percentage

Base

Rate

Simple Interest

 

 

 

Introduction: Three out of 5 teenage girls wear mascara. What is the rate of teenage girls wearing mascara per 100 girls?

You can solve this problem by using a proportion. The ratio of teenage firls who wear mascara to the total number of teenage firls is 3/5. Write a proportion that sets 3/5 equal to the ratio with a denominator of 100.

3/5 = n/100

60 = n

Teenage girls wear mascara at a rate of 60 per 100, or 60 percent. A percent is a ratio that compares a number to 100. Percent also means per hundred, or hundredths. Percents can be expressed with a percent symbol (%), as fractions, or as decimals.

60% = 60/100 = 0.60

 

 

 

Exercise 1: Write 3/4 as a percent

3/4 = n/100

300 = 4n

75 = n

Thus, 3/4 is equal to 75/100 or 75%

 

 

Proportions are often used to solve percent problems. One of the ratios in these proportions is always a comparision of two numbers called the percentage and the base. The other ratio, called the rate, is a fraction with the denominator of 100.

 

Percent Proportion: percentage/base = rate or percentage/base = r/100

 

 

 

 

Exercise 2:

a. 30 is what percent of 50?

Use the percent proportion.

percentage/base = r/100

30/50 = r/100

3000 = 50r

60 = r

Thus, 30 is 60% of 50.

b. 20 is what percent of 30?

 

 

You can also write equations to solve problems with percents.

 

 

 

Exercise 3:

a. 60% of what number is 54?

(60/100) * x = 54

0.6x = 54

x = 90

Thus, 60% of 90 is 54.

b. What number is 40% of 37.5?

 

 

Percents are also used in simple interest problems. Simple interest is the amount earned for the use of money. The formula I = prt is used to solve problems involving simple interest. In the formula, I represents the interest, p represents the amount of money invested, called the principal, r represents the annual interest rate, and t represents time in years.

 

 

 

Activity: Making Circle Graphs

Materials: compass and protactor

You can use a circle graph to compare parts of a whole. Follow the steps to display the data below in a circle graph.

Where's the Remote?
 Number of Times TV Remote Misplaced Per Week Number of People Responding 

 Never

1 - 5

5 or more

Don't Know

 220

190

85

5

YOUR TURN

a. Find the total number of people surveyed.

b. Find the ratio that compares the nubmer of people that responded for each category to the total number of people that responded.

c. Since there are 360 degrees in a circle, multiply each ratio by 360 to find the number of degrees for each section of the graph. Round to the nearest degree.

d. Use a compass to draw a circle and a radius.

e. Use a protractor to draw angles. Start with the least number of degrees. Repear for the remaining sections. Label each section and give the graph a title.

f. What is the sum of the percents in your graph?

 

 

 

Exercise 4:

a.Luis Hernandez has some money he has saved over the summer from mowing lawns. He wants to put some of it in a 6-month certificate of deposit (CD) account that would pay 6% annual interest. He doesn't want to put all of his money in the CD because he wants some spending money. He is hoping to earn $45 in interest to buy a new video game. How much money should Luis put in the CD?

Explore

Let p = the amount of money Luis should deposit.

Plan

I = prt

45 = p(0.06)(0.5)

Solve

45 = 0.03p

1500 = p

Examine

When p is 1500, I = (1500)(0.06)(0.5) or $45. Luis should deposit $1500.

b. Whitney Williamson has $30,000 she would like to invest. She has a choice of two-interest-paying bonds, one offering a 6% annual interest and the other paying 7.5% annual interest. She would liek to earn $2100 in interest in one year. If she earns any more than $2100, she would need to pay a higher rate of income tax. How much money should she invest in each bond?

 

 

 

Closing Activity: Check for understanding by using this as a quick review before class is over. It should take about the last five to ten minutes. I would use it for my students as their 'ticket out the door'. Click Here.

 

 

 

Homework: The homework to be assigned for tonight would be: 17 - 45 odd, 46, 47 - 53 odd, 55 - 64

 

Alternative Homework: Enriched: 16 - 44 even, 46 - 64

 

Extra Practice: Students book page 765 Lesson 4-4

 

Extra Practice Worksheet: Click Here.

 

 

 


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