Algebra

Chapter 2B: Ratios, Proportions, and Percents

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Table of Contents

Chapter 2-6: Ratios, Rates, and Proportions SWBAT: Write and use ratios, rates, and unit rates. Write and solve proportions. Homework: Page #5

Chapter 2-7: Applications of Proportions SWBAT: Use proportions to solve problems involving geometric figures. Use proportions and similar figures to measure objects indirectly. Homework: Pages #10-11

Quiz on Lessons 2-6 to 2-7

Sprial review of lessons 2.6 and 2.7 Homework: Pages #12-13

Chapter 2-8: Percents SWBAT: Solve problems involving percents. Homework: Page #18

Chapter 2-9: Applications of Percents SWBAT: Use common applications of percents. Homework: Page #24

Chapter 2-10(A): Percent Increase and Decrease SWBAT: Find percent increase and decrease. Homework: Page #29

Chapter 2-10(B): Applications of Percent Increase and Decrease SWBAT: Apply knowledge of percent increase and decrease to real world problems. Homework: Page #35

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Chapter 2-6

SWBAT: Write and use ratios, rates, and unit rates. Write and solve proportions.

Warm Up

1. 2.

2

Example 1: Using Ratios

1. The ratio of faculty members to students at a college is 1:15. There are 675 students. How many faculty members are there? 2. The ratio of games won to games lost for a baseball team is 3:2. The team won 18 games. How many games did the team lose?

Example 2: Unit Rates A rate is a ratio of two quantities with different units.

Example: gal

mi

2

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A unit rate is a rate with a second quantity of 1 unit.

Example: gal

mi

1

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3. Cory earns $52.50 in 7 hours. Find the unit rate.

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4. If a 16oz box of Bran costs $3.16 and a 12oz box of Corn flakes cost $2.64, which cereal is the better buy?

Example 3: Converting Rates

Commonly Used Conversion Charts

12 inches = 1 foot

1 yard = 3 feet

1 mile = 5280 feet

1 hour = 60 min

1 min = 60 sec

5. Serena ran a race at a rate of 10 kilometers per hour. What was her speed in kilometers per minute?

6. A cheetah can run at a rate of 60 miles per hour in short bursts. What is this speed in feet per minute?

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Challenge

Summary

Exit Ticket

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Chapter 2.6 Homework: #1-18

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Chapter 2-7

SWBAT: Use proportions to solve problems involving geometric figures. Use proportions and similar figures to measure objects indirectly.

Applications of Proportions

Similar figures have exactly the same shape but not necessarily the same size.

Corresponding sides of two figures are in the same relative position, and corresponding angles are in the

same relative position. Two figures are similar if and only if the lengths of corresponding sides are proportional

and all pairs of corresponding angles have equal measures.

You can use proportions to find missing lengths in similar figures.

Warm Up

Evaluate each expression for a = 3, b = –2, and c = 5.

1. 4a – b 2. 3b2 – 5 3. ab – 2c

Solve each proportion.

4. 5.

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Example 1: Similar Figures

Proportion

a.

b.

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You can solve a proportion involving similar triangles to find a length that is not easily measured. This method

of measurement is called indirect measurement. If two objects form right angles with the ground, you can

apply indirect measurement using their shadows.

Example 2: Indirect Measurement Problems

Example c: A forest ranger who is 150 cm tall casts a shadow 45 cm long. At the same time, a nearby tree casts

a shadow 195 cm long. Write and solve a proportion to find the height of the tree.

Example d: A woman who is 5.5 feet tall casts a shadow 3.5 feet long. At the same time, a building casts a

shadow 28 feet long. Write and solve a proportion to find the height of the building.

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Challenge Problem

Summary

Exit Ticket

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Chapter 2.7 Homework: #1-10, 14-18

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12

Spiral Review of Chapter 2.6 and 2.7

Chapter 2.6 Review

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Chapter 2.7 Review

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Chapter 2-8

SWBAT: Solve problems involving percents.

A percent is a ratio that compares a number to 100.

For example, 100

25%25 = 0.25

5.0100

5%5

Warm Up 1. Find the value of x in each diagram.

∆ABC ~ ∆MLK

2. A girl that is 5 ft tall casts a shadow 4 ft long. At the same time, a tree casts a

shadow 24 ft long. How tall is the tree?

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Example 1: Finding the Part

Find 30% of 80.

Part:

Whole:

Percent:

a. You Try: Find 120% of 15.

Example 2: Finding the Percent

What percent of 45 is 35?

Part:

Whole:

Percent:

b. You Try: What percent of 35 is 7?

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Example 3: Finding the Whole

38% of what number is 85?

Part:

Whole:

Percent:

c. 120% of what number is 90?

APPLICATIONS:

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Challenge Problem

Summary

Exit Ticket

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Chapter 2.8 Homework: #3-47 (odds)

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Chapter 2-9

SWBAT: Use common applications of percents.

A commission is money paid to a person or a company for making a sale. Usually the commission is a percent

of the sale amount.

Example 1: Commission Problems

Mr. Cortez earns a base salary of $26,000 plus a sales commission of 5%. His total sales for one year were

$300,000. Find his total pay for the year.

a. A telemarketer earns $350 per week plus 12% commission on sales. Find her total pay for a week in which

her sales were $940.

Warm Up 1. Find 20% of 80.

2. What percent of 160 is 20?

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Example 2: Interest Problems

Find the simple interest paid for 3 years on a $2500 loan at 11.5% per year.

b. Find the simple interest earned after 2 years on an investment of $3000 at 4.5% interest earned annually.

Example 2-Part II: Interest Problems

After 6 months, the simple interest earned on an investment of $5000 was $45. Find the interest rate.

c. The simple interest paid on a loan after 6 months was $306. The annual interest rate was 8%. Find the

principal.

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A tip is an amount of money added to a bill for service. It is usually a percent of the bill before sales tax is

added. Sales tax is a percent of an item’s cost.

Example 3: Estimating tip

Lunch at a restaurant is $27.88. Estimate a 15% tip.

c. Estimate a 20% tip on a check for $21.98.

Example 3-Part II: Estimating Sales Tax

The sales tax rate is 7.25%. Estimate the sales tax on a book that costs $19.97.

d. Estimate the tax on shoes that cost $68.50 when the sales tax rate is 8.25%.

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Challenge Problem

Summary

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Exit Ticket

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Chapter 2.9 Homework#2-12

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Chapter 2-10(A) – Percent Increase/Decrease

SWBAT: Find percent increase and decrease.

A percent change is an increase or decrease given as a percent of the original amount. Percent increase describes an amount that has grown. Percent decrease describes an amount that has been reduced.

Example 1: Percent Increase and Decrease

Find each percent change. Tell whether it is a percent increase or decrease.

From 8 to 10

Warm Up 1.

2. The sales tax rate is 6.25%. Find the sales tax on a shirt that costs $29.50.

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Find each percent change. Tell whether it is a percent increase or decrease.

a. From 200 to 110 b. From 40 to 50

Example 2: Finding the result of a Percent Increase and Decrease

Find the result when 12 is increased by 50%. Find the result when 55 is decreased by 60%.

c. Find the result when 72 is increased by 25%. d. Find the result when 10 is decreased by 40%.

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Challenge Problem

SUMMARY

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Exit Ticket

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Chapter 2-10 Homework: #3 - 35 (odds)

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Chapter 2-10(B) – Applications of Percent Increase/Decrease

SWBAT: Apply knowledge of percent increase and decrease to real world problems.

Applications: A discount is an amount by which an original price is reduced.

Percent DISCOUNT Problems Example 1: Admission to the museum is $8. Students receive a 15% discount. How much is the discount? How much do students pay?

Warm Up 1.

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a. A coat is on sale for 25% off the original price. If the original price of the coat is $75, what is the

discounted price? A markup is an amount by which a wholesale cost is increased.

Percent Markup Problems

b. Customers of a utility company received notices in their monthly bills that heating costs for

the average customer had increased 125% over last year because of an unusually severe

winter. In January of last year, the Garcia’s paid $120 for heating. What should they expect

to pay this January if their bill increased by 125%?

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Tax and discount combined Sue bought a picnic table on sale for 50% off the original price. The store charged her 10% tax and

her final cost was $22.00. What was the original price of the picnic table?

c. d.

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Relative Error – shows how large an error is made in measurement in relation to the correct value.

Skeeter the dog weighs exactly 36.5 pounds. When weighed on a defective scale, he weighed 38 pounds. What is the percent of error in measurement of the defective scale to the nearest tenth?

d. Ryan estimates the measurement of the volume of a popcorn container to be 282 cubic inches. The actual

volume of the popcorn container is 289 cubic inches. What is the relative error of Ryan's measurement to

the nearest thousandth?

Challenge

A student mistakenly measures the length of a radius to be 24 inches. The actual radius is 25

inches.

a. What is the student's percent of error on this measurement?

b. If the student uses this measurement to compute the area of a circle with this radius, what is the student's

percent of error on the area computation, to the nearest tenth of a percent?

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Summary

Exit Ticket

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Chapter 2-10(B) – Applications of Percent Increase/Decrease

25. The actual length of this field is 500 feet. A measuring instrument shows the length to be 508 feet.

a.) the relative error in the measured length of the field.

b.) the percentage error in the measured length of the field