lesson 6: percents - faculty website index valencia …fd.valenciacollege.edu/file/sbowling6/class 2...

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Lesson 6: Percents

Lesson 6: Objectives

Lesson Objective Related Examples

Convert percent to decimal 2, YT3

Convert percent to fraction 2, YT3

Convert decimal to percent 2, YT3

Convert fraction to percent 2, YT3

Solve equations of the form x = a ⋅b WE4

Solve equations of the form a ⋅x = b WE5

Create and solve percent equations: Type I 6, YT7

Create and solve percent equations: Type II 8, YT9

Create and solve percent equations: Type III 10, YT11

Solve applications involving percent 1, 12-14, YT15

Determine percent increase or decrease 16, 17, YT18

Determine percent discount 19, YT21a

Compute simple interest 20, YT21b

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Lesson 6: Mini Lesson Videos and Embedded You Try Answers

Example 1:

40

Example 2:

YOU TRY

3. Complete the missing parts of the table. Round decimal part to FOUR decimal places as

needed. Simplify all fractions. Show all work.

Fraction Decimal Percent

a. 1

9 0.1111 11.11%

b. �

�� 0.0625 6.25%

c. �

�

0.8 80%

Example 4: Worked Example (not included)

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Example 5

Example 6:

42

YOU TRY

7. Determine the missing number in each of the following. Round to two decimals as needed.

a. What is 15% of 324? b. 25.12% of 132 is what number?

Answer: 48.6 Answer: 33.16

Example 8:

YOU TRY

9. Determine the missing number in each of the following. Round to TWO decimals as needed.

Show all work.

a. 40% of what number is 20? b. 105 is 15.15% of what number?

Answer: 50 Answer: 693.07

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Example 10:

YOU TRY

11. Determine the missing number in each of the following. Round to TWO decimals as needed.

Show all work.

a. What % of 12 is 8? b. 105 is what percent of 123?

Answer: 66.67% Answer: 85.37%

Example 12:

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Example 13:

Example 14:

YOU TRY

15. To win the election as president of the United States of America, a person must obtain 270 out of 538 possible votes from the electoral college. What percentage of the overall electoral votes is this? Round to 4 decimals initially. Be sure to set up your percent statement and equation as in the examples. Given Goal 270 is what percent of 538? 270 = x • 538

x = ��

�≈ �. ��

x = 50.19% To win the election as president of the United States, a person must obtain 50.19% of the possible votes from the electoral college.

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Example 16:

Example 17:

YOU TRY

18. Determine the percent increase or decrease for each of the following. Round % to the

nearest hundredth.

a. the change from 54 to 62 b. the change from 50 to 40

Answer: 14.81% increase Answer: 20% decrease

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Example 19: A $725 couch is on sale for 20% off. Find the amount of the discount and the sale price. Round to the nearest cent. [Circle GIVENS and underline GOAL]

Example 20:

YOU TRY

21a. An $85 pair of sunglasses is on sale for 30% off. Find the amount of the discount and the sale price. Round to the nearest cent. [Circle GIVENS and underline GOAL]

Given Goal Answers: Amount of discount: $25.50 Sale Price: $59.50 21b. Calculate the simple interest and the final balance on $14,000 borrowed at 3% interest over 10 years. Round to the nearest cent. [Circle GIVENS and underline GOAL] Answers: Simple Interest: $4200 Final Balance: $18,200

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Lesson 7: Ratios, Rates and Proportions



Write and simplify ratios 1, 2, YT5a

Write and simplify rates 3, 4, YT5b

Compute unit rates 6, 7, 8, YT9

Solve proportions using cross-products 10, 11, 12, YT13

Solve applications using proportional reasoning 14, YT15

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Examples 1 and 2:

Examples 3 and 4:

48

YOU TRY

5. Use the information to write a ratio in simplest form. Indicate if the ratio is also a rate.

a. 5 feet:10 feet b. 12 geese to 15 ducks

Answer: 1:2 Answer: ��

��

Example 6:

Example 7:

Example 8:

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YOU TRY

9. Amazon.com recently advertised the following choices for ibuprofen tablets (200mg). Use

unit rates to determine which is the better buy.

Option 1: 360 pills for $15.45 Option 2: 300 pills for $12.98

Answers:

Option 1: �. �� or �. ��

Option 2: �. �� or �. ��

Option 1 is a better buy

Example 10:

Example 11:

50

Example 12:

YOU TRY

13. Solve the proportions showing all possible steps. Round your answer to the nearest

hundredth as needed.

a. x

12=

3

6 b.

6

5=

10

p

Answer: 6 Answer: 8.33

Example 14:

51

YOU TRY

15. Mary earned $112.50 last week working 12 hours at her part-time job. If she works 15 hours

this week and is paid the same rate, how much will she earn? Use proportional reasoning to

determine your result. Round to the nearest cent.

GIVEN: Mary earned $112.50 last week working 12 hours at her part-time job

If she works 15 hours this week and is paid the same rate

GOAL: How much will Mary earn?

MATH WORK: $��.��

��=

$

�� x = $143.63

CHECK: varies

FINAL RESULT AS A COMPLETE SENTENCE: Mary will earn $143.63 if she works 15 hours

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Lesson 8: Statistics



Define and compute three different measures of central tendency 1, YT2

Define and compute weighted averages 3, 4, YT5

Discuss data variability and compute the range of a data set 6, 7, YT8

Compute measures of central tendency with data sets that contain

outliers

9

Use tables and graphs to interpret and analyze data 10, 11, YT12, 13,

YT14

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Example 1:

YOU TRY

2. Find the mean, median, and mode of the data set 5 2 7 11 6 0 3 3.

Begin by writing the data set in increasing order.

0 2 3 3 5 6 7 11

Mean Median Mode

Answers: 4.625 4 3

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Example 3:

Example 4:

YOU TRY

5. Compute the student’s GPA for the term.

Course Credits Grade

MAT082 3 A

ENG071 4 B

PSY 100 3 C

RDG 061 3 A

Answer: 3.23

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Examples 6 and 7:

YOU TRY

8. Find the range of the following data set 5 2 7 11 6 0 3 3. Start by writing the data

set in increasing order.

0 2 3 3 5 6 7 11

Answer: 11

Example 9:

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Example 10:

Example 11:

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YOU TRY 12. In 2009, the Bureau of Labor Statistics reported a surge in volunteerism. At this time, there

were a reported 63,361volunteers in the U.S. The pie chart below shows the different

categories in which these people volunteered.

Find the number of people who volunteered in an Educational capacity. Round your answer to

the nearest whole number.

Answer: 16,537 people

Example 13:

57

You Try

14. a. How many students made a B on the Midterm?

Answer: 9

b. How many students were in the class? Answer: 35

c. What percentage of the class made a B on the midterm? Round to hundredths.

Answer: 25.71% d. What percentage of students made a passing grade (A, B, or C) on the Midterm? Round to hundredths. Answer: 71.43%

Lesson 8:

Midterm Exam Grades

0

2

4

6

8

10

12

14

A B C D F

Nu

mb

er

of

Stu

den

ts

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Lesson 9: Units and Conversions



Perform one-step conversions of U.S. units 1, 2, YT10

Convert using U.S. mixed units 3, 4, 5, 6, YT10

Perform multi-step conversions of U.S. units 7, 8, 9, YT10

Add and subtract U.S. units of measure 11, 12, YT13

Perform conversions within the metric system 14, 15, YT16

Perform conversions between the U.S. and metric system 17, 18, YT19

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Example 1:

Example 2:

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Examples 3 and 4:

Examples 5 and 6:

Example 7:

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Example 8:

Example 9:

YOU TRY

10. Perform each of the following conversions within the U.S. system. Round to tenths as

needed. Show complete work.

a. A young girl paced off the length of her room as approximately 8 feet. How many inches

would that be?

Answer: 96

b. 18 oz = _____ lb c. 100 yd = _____ ft d. 10,235 lb = _____ tons

Answers: 1.1 33.3 5.1

e. How many inches are in 6 feet, 8 inches?

Answer: 80

f. How many square inches are in 10 square feet?

Answer: 1440

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Examples 11 and 12:

YOU TRY

13. Rayene needs a board that is exactly 8 inches long to add a little security to the window in

her room. She has a board that is 1 ft, 3 inches long to work with. How much, in inches, would

she have to cut in order to use the board?

Answer: 7 inches

Example 14:

Example 15:

62

YOU TRY

16. Perform each of the following conversions within the metric system. Show complete work.

a. 1510 m = ________ mm b. 13.50 ml = _______ l c. 5k = ________ m

Answers: 1,510,000 0.01350 5000

Example 17:

Example 18:

YOU TRY

19. Perform each of the following U.S. to metric or metric to U.S. conversions. Round to

hundredths as needed.

a. Soda pop is often sold in 2-liter containers. How many quarts would this be? How many

gallons?

Answers: 2.2 qt 0.55 gal

b. Your friend Leona is planning to run her first 10km race in a few weeks. How many miles will

she run if she completes the race?

Answer: 6.21 mi

c. A roll of Christmas wrapping paper is 3 meters long. How long is this in yards?

Answer: 2.7 yd

d. Convert 10 ml to cups.

Answer: 0.0421 c

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Lesson 10: Geometry I: Perimeter and Area



Compute perimeter of different shapes 1, 2, YT5

Compute circumference of a circle 3, YT5

Explain the difference between rounded form and exact form WE4

Compute distance around closed objects of unusual shape 6

Solve applications involving perimeter or circumference 7

Compute area of different shapes 8, 9, 10, YT11

Compute area of nonstandard shapes 12

Solve applications involving area and/or perimeter 13

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Example 1:

64

Example 2:

Example 3:

Worked Example 4 (not included here)

lesson 6: percents - faculty website index valencia …fd.valenciacollege.edu/file/sbowling6/class 2...

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