BLoCK 1 ~ dAtA AnALYsIs - Oregon Focusoregonfocus.com/Inside/media/OnlineBook/DA_Block_1.pdf · Block 1 ~ Data Analysis ~ Ratios, Proportions And Percents 1 BLoCK 1 ~ dAtA AnALYsIs

Block 1 ~ Data Analysis ~ Ratios, Proportions And Percents 1

BLoCK 1 ~ dAtA AnALYsIs ratiOs, prOpOrtiOns anD percents

unit rAte

word wAll

scAle

rAtio

BAr grAPh

similAr figures

raTe

ProPortion

Pie chArt

Percent

PictogrAPh

freQuency

Lesson 1 raTios and raTes - ---------------------------------------------------- 3Lesson 2 ProPorTions ----------------------------------------------------------- 8

Explore! Proportions and Cross ProductsLesson 3 PercenTages ---------------------------------------------------------- 13Lesson 4 creaTing and anaLYzing Bar graPHs -------------------------------- 18Lesson 5 creaTing and anaLYzing Pie cHarTs --------------------------------- 23

Explore! Easy As Piereview BLock 1 ~ raTios, ProPorTions and PercenTs ------------------------ 29

2 Block 1 ~ Ratios, Proportions And Percents ~ Tic - Tac - Toe

BLoCK 1 ~ rAtIos, ProPortIons And PerCents

tic - tac - tOetic - tac - tOetic - tac - tOeTo the rescue

Write a children’s story where the main character

uses ratios and proportions to save the day.

See page for details.

Percent eQuAtions

Use percent equations to solve a variety of problems.


sPreAdsheets And Pie charTS

Conduct a survey of classmates. Create a pie

chart of the results.


A Perfect Pie chArt

Conduct a survey of classmates. Learn to use angle measures to make your pie chart just right.


counting critters

Research how the capture-recapture method is used to

determine populations of diff erent types of wildlife.


Percent of chAnge

Use proportions to solve a variety of problems involving percents of increase or decrease.


sodA Price comPArison

Compare the unit costs for sodas of various sizes.


Are they ProPortionAl?

Make a brochure showing diff erent ways to determine

if two ratios form a proportion.


douBle BAr grAPhs

Conduct a survey of classmates. Construct a

double bar graph.


%

Lesson 1 ~ Ratios And Rates 3

Caroline loves summer break. She asked her friends to name their favorite thing about summer vacation. She organized the information as shown in the table below.

My Friends’ Favorite Th ings About summer Vacation

Caroline wants to compare the number of her friends who enjoy hanging out with friends during the summer to the number who enjoy summer vacation because of the weather. She uses a ratio. A ratio uses division to compare two numbers.

Caroline’s ratio is: hanging out with friends

_________________ the weather = 8 + 5 ____ 5 + 3 = 13 __ 8

use the table above to fi nd the following ratios. Write each ratio all three ways in simplest form.a. ratio of girls to all students b. ratio of boys to girls

a. Find the total number of girls. 3 + 7 + 5 + 5 = 20 Find the total number of students. 5 + 6 + 8 + 3 + 20 = 42

Write the ratio. girls ________ all students = 20 __ 42 = 10 __ 21 , 10 : 21 or 10 to 21

b. Find the total number of boys. 5 + 6 + 8 + 3 = 22

Write the ratio. boys

____ girls = 22 __ 20 = 11 __ 10 , 11 : 10 or 11 to 10

Th e weather going on family vacation

hanging out with friends going to camp

Boys 5 6 8 3girls 3 7 5 5

example 1

solutions

ratiOs anD rates

Lesson 1

4 Lesson 1 ~ Ratios And Rates

Some ratios involve quantities with diff erent units. If the units represent the same type of measurement (for example, length), then convert the ratio so the units are common units.

A rectangular picture frame measures 4.5 feet long and 18 inches wide. What is the ratio of the frame’s length to width?

Convert one unit to match the other. Th ere are 12 inches in one foot; change 4.5 feet into inches by multiplying by 12. 4.5 ∙ 12 = 54 inches

Th e ratio of length to width: length

_____ width = 54 __ 18 = 3 _ 1

Sometimes ratios have units that cannot be converted to the same units. For example, miles cannot be converted into hours. Dollars cannot be converted into years. Ratios comparing two numbers with diff erent units are called rates. Some examples of rates are:

125 miles _______ 3 hours 200 words ________ 3 minutes $1.60 ________ 8 teeth lost

Rates are most useful when they are converted to unit rates. A unit rate is a rate with a denominator of 1 in the fraction. Th ey are stated using the word “per.” Sixty-two miles per hour or $18 per portrait are typical ways of stating a unit rate. Unit rates are helpful when comparing two or more amounts.

super Cinemas sells a movie pass for $50 for admission into 8 movies. Movie Land sells a similar pass for $60 for admission into 10 movies. Which movie theater has the better deal?

Write the information in the Super Cinemas’ Rate = $50 _______ 8 movies problem as rates. Movie Land’s Rate = $60 ________ 10 movies

$50 _______ 8 movies = $6.25 ______ 1 movie Convert the rates into unit rateswith a denominator of 1. Divide by the denominator in each rate. $60 ________ 10 movies = $6 ______ 1 movie

Super Cinemas costs $6.25 per movie. Movie Land costs $6 per movie. Th e price at Movie Land is less than the price at Super Cinemas. Movie Land has the better deal.

example 2

solution

example 3

solution

÷ 8

÷ 8÷ 10

÷ 10


exercises

Identify each as either a ratio or rate.

1. 20 inches _______ 12 inches 2. 140 miles : 1 hour 3. 55 seconds to 70 seconds

4. $115000 ______ 3 years 5. 4 feet : 27 inches 6. 2.5 points

_______ 1 point

7. 3 cars to $42,000 8. 65 words _______ 1 minute 9.

10 boys ______ 15 girls

10. Which rates in exercises 1-9 are unit rates?

simplify each ratio. Write each simplifi ed ratio in all three forms. 11. 12 __ 15 12. 18 to 14

13. 4 : 20 14. 24 __ 42

Convert each ratio to common units and simplify.

15. 6 yards

______ 2 feet 16. 45 minutes to 3 hours 17. 20 inches _______ 1 yard

Convert each rate to a unit rate. state each unit rate using the word “per”.

18. $36 ______ 3 pallets 19. $102 for 8.5 hours of work 20. 8 inches over 3 years

use the table to fi nd each ratio. Write each answer as a fraction in simplest form.

21. seventh graders to eighth graders

22. eighth graders to all students

23. favorite subject of English to favorite subject of math

24. favorite subject of social studies to all students

25. seventh graders whose favorite subject is math to eighth graders whose favorite subject is math

26. eighth graders whose favorite subject is science to all eighth graders

Favorite subject by grade Level7th 8th

english 9 22Math 8 14

science 12 7social studies 5 11

6 Lesson 1 ~ Ratios And Rates

Write a ratio in simplest form for each situation.

27. Fift een of 24 dentists surveyed recommend using DentaWhite toothpaste. a. What is the ratio of dentists who did not recommend DentaWhite to the dentists

who recommended DentaWhite? b. What is the ratio of dentists who did not recommend DentaWhite toothpaste to

all dentists surveyed?

28. Th ere are 156 eighth graders and 6 eighth grade teachers at Arbor Middle School. What is the ratio of students to teachers?

29. Th ree students in Mrs. Schaub’s class ride their bikes to school. Twelve students ride the bus. Nine students walk to school and three ride with their parents. What is the ratio of students who ride the bus to all students in the class?

30. In a survey of forty shoppers at Save-Time, twenty-fi ve said they used coupons. What is the ratio of shoppers who used coupons to those who did not use coupons?

31. Th e bottom of each triangle is called the “base.” Th e dashed line represents the “height”. A B C

a. Which triangle has the greatest ratio of base to height? Explain.b. Which triangle has the smallest ratio of base to height? Explain.c. Which triangle has a ratio of base to height closest to 1 : 1? Explain.

32. Which triangle would you expect to have the greatest ratio of base length to height? Explain.

X Y Z

use unit rates to compare.

33. It costs $0.89 for a 20-ounce soda and $1.09 for a 32-ounce soda. Which is the better deal?

34. Bobby ran one mile in 8 minutes. Julia ran 6.75 miles in 1 hour. Who ran at a faster rate?

35. Maia typed a 2,000-word paper in 45 minutes. Lonnie typed his 2,400-word paper in 65 minutes. Who can type faster?

36. A car travels 270 miles on 16.5 gallons of gas. a. Find the miles per gallon.

b. Find the gallons per mile.

12

3

5

610

2


tic-tAc-toe ~ sodA Pr ice com PA r ison

step 1: Soda comes in a variety of sizes. Go to a grocery store and fi nd at least four diff erent containers (sizes) of a particular brand of soda. Record the brand of soda.

Use a 2-liter bottle, a 20-ounce bottle, and a 6-pack as three of your sizes. You choose the fourth size. Copy and complete the table below to fi nd the unit price (cost per ounce) for each size of soda. Remember: you do not need to buy the soda. Just collect the data. 1 liter ≈ 33.8 ounces

step 2: Which size of soda container provides the best deal? Which size has the highest cost per ounce? Explain.

step 3: Complete a similar table for a second brand of soda.

step 4: How do the two brands compare? Is the same size container of soda the cheapest per ounce? Most expensive per ounce? Make at least two other comparisons.

Brand of Soda: ______________________

Size of Soda Total Number of Ounces Total Cost Unit Price (Cost per

ounce)2-liter bottle20-ounce bottle6-pack

tic-tAc-toe ~ to the re scue

Write a children’s story where the main character(s) uses ratios and proportions to save the day. Th e story should include the following terms: ratio, rate, unit rate and proportion. Include illustrations where appropriate. Present the story in book form and include a cover page.

8 Lesson 2 ~ Proportions

Bela and Lindsay are planning a school dance. Th ey are unsure about how many students to plan for. Th ey surveyed 30 random students at school. Of the 30 students surveyed, 21 said they will attend the dance. Th ere are 820 students in the school. How many students should Bela and Lindsay plan for?

Problems like this are solved with proportions. A proportion is an equation stating that two ratios are equivalent. Th e ratio of students coming to the dance from the survey is approximately the same as the ratio of all students who will attend the dance. Here is the proportion they can use.

21 students coming to the dance

_______________________ 30 total students surveyed = x students coming to the dance

______________________ 820 students

step 1: Write each proportion on paper. Cross multiply each numerator with the opposite denominator for each proportion. Part A is completed.

A. 2 _ 3 = 10 __ 15 B. 1 _ 2 = 25 __ 50 C. 7 __ 10 = 21 __ 30 d. 6 _ 8 = 27 __ 36

2 ∙ 15 = 30 3 ∙ 10 = 30

step 2: What do you notice about the cross products in each proportion?

step 3: Use cross products to determine which of the following pairs of ratios form a proportion.

A. 4 _ 5 , 7 _ 9 B. 4 _ 9 , 20 __ 45 C. 5 _ 6 , 27.5 ___ 33

step 4: Find x in each proportion based on the fi ndings in steps 1 and 2.

A. 2 _ 3 = x __ 12 B. 8 __ 16 = 2 _ x

explOre! prOpOrtiOns anD crOss prODucts

prOpOrtiOns

Lesson 2

Lesson 2 ~ Proportions 9

solve Bela and Lindsay’s proportion. Find the number of students they can expect to attend the dance.

21 students coming to the dance

__________________________ 30 total students surveyed = x students coming to the dance

______________________ 820 students

Set the cross products equal to each other. 21 ∙ 820 = 30 ∙ x

Simplify each side of the equation. 17220 = 30x

Divide each side by 30 to isolate x. 17220 _____ 30 = 30x ___ 30 574 = x

Bela and Lindsay can expect about 574 students at the dance.

Stacy earned $44 for 5.5 hours of work. How many hours will she need to work to earn $500? It is important to match corresponding parts and units correctly when solving proportion problems.

Jeremy’s car travels 260 miles on 16 gallons of gas. how many miles can the car travel on 3 gallons of gas?

Set up two ratios with the corresponding parts in the same position. Correct Incorrect

260 miles _______ 16 gallons = x miles _______ 3 gallons 260 miles _______ 16 gallons = 3 gallons _______ x miles

OR OR 16 gallons

_______ 260 miles = 3 gallons

_______ x miles 260 miles _______ x miles = 3 gallons

_______ 16 gallons

Use the fi rst proportion above. Set the cross products equal to each other. 260 ∙ 3 = 16 ∙ x

Simplify and divide by 16 on each side of 780 = 16xthe equation. 48.75 = x Jeremy’s car can travel 48.75 miles on 3 gallons of gas.

example 1

solution

example 2

solution

Correct Proportions Incorrect Proportions

$44 _______ 5.5 hours = $500 ______ x hours $44 _______ 5.5 hours = x hours ______ $500

$44 ____ $500 = 5.5 hours _______ x hours $44 ____ $500 = x hours _______ 5.5 hours

260 miles_______16 gallons

3 gallons_______ miles

OR OR

260 miles_______x milesx milesx

3 gallons_______16 gallons

_______16 gallons

OR OR

3 gallons_______16 gallons


Proportions can also be used to solve problems involving similar figures. Similar figures are two figures that have the exact same shape, but not necessarily the exact same size. Similar figures have equal corresponding angles. The corresponding sides are proportional.

use the similar triangles to answer each question.

a. Which side on the smaller triangle corresponds with the 8 meter side on the larger triangle?b. What is the value of x?c. What is the value of y?

a. The 8 meter side is next to the 90° angle. The corresponding side on the smaller triangle is the 3 meter side.

b. Set up a proportion with corresponding sides. 8 _ 3 = x __ 12 Since the 8 meter side corresponds with the 3 meter side, that is the first ratio. The missing side, x, corresponds with 12 meters on the smaller triangle. Find the cross products and solve. 96 = 3x

The value of x is 32 meters. 32 = x

c. Set up a proportion with corresponding sides. 8 _ 3 = 15 __ y Find the cross products and solve. 8y = 45 The value of y is 5.625 meters. y = 5.625

Proportions are also used for scale drawings. Maps, blueprints and models are examples of objects drawn or designed to scale. Scale means there is a common ratio of a length on a map or model to the actual object.

Jerry’s model of a spacecraft has a 1 inch : 4.5 feet ratio. one of the wings on Jerry’s model is 3.75 inches long. how long is the wing on the actual spacecraft?

Write the proportion. Match model _____ actual = 1 inch ______ 4.5 feet = 3.75 inches ________ x feet

the corresponding parts on the model to the spacecraft.

Find the cross products and solve for x. 1x = 4.5 ∙ 3.75 x = 16.875

The wing of the actual spacecraft would be 16.875 feet.

example 3

solutions

15 m

8 m

x90°

12 m

3 my

90°

example 4

solution

Lesson 2 ~ Proportions 11

exercises

1. How are proportions related to ratios?

2. Kebede is supplying juice boxes for the class holiday party. He is not sure how many to bring. He asked 6 random students if they would want a juice box. Four students told him they wanted juice boxes. There are 27 students in Kebede’s entire class. Which proportions represent this situation? State all possible answers.

A. 6 _ 4 = 27 __ j B. 4 _ 6 = 27 __ j C. 4 _ j = 27 __ 6 d. 4 _ 6 = j __ 27 e. 4 _ j = 6 __ 27

use cross products to determine whether each pair of ratios forms a proportion.

3. 5 __ 15 , 30 __ 90 4. 23 __ 30 , 7 _ 9 5. 8 __ 13 , 25.6 ___ 41.6

solve each proportion. round each answer to the nearest tenth. 6. 2 _ 9 = 8 _ x 7. h __ 32 = 4 _ 5 8. 45 __ m = 10 __ 3

9. 15 __ 65 = 12 __ y 10. i ___ 100 = 42 __ 37 11. 28 __ 38 = p ___ 100

12. Jacqueline made a pastry requiring 2 cups of flour for eight servings. She made a larger batch for 15 servings. How many cups of flour did she use?

13. Kayla looked at the floor plan of the new house her family just purchased. The scale on the floor plan said 0.5 centimeters represented 2 feet in real-life. She measured the length and width of her new room on the floor plan. It measured 3.75 centimeters by 3 centimeters. What are the dimensions of the actual room in feet?

14. A map of Oregon’s Willamette Valley has a scale of 2 centimeters : 8 miles. Corvallis and Eugene are approximately 12 centimeters apart on the map. What is the actual distance between the two cities?

15. A fish and wildlife worker found there were 5 owls in a 1.5 square mile section of forest. About how many owls will there likely be in a 10 square mile section of forest?

16. Use the two rectangles at right. a. What is the ratio of the longer side on the large rectangle to the longer side on the small rectangle? Write the answer in simplest form. b. What is the ratio of the shorter side on the large rectangle to the shorter side on the small rectangle? Write the answer in simplest form. c. Are the two rectangles similar? Explain.

24

12

18

9


17. Th e triangles are similar. Find the value of x.

18. Th e pentagons are similar. Find the value of x and y.

19. Julian typed 200 words in 3 minutes. How long will it take him to type 2,800 words at this rate?

review

20. Identify each as either a ratio or rate.

a. 80 words _______ 2 minutes b. 18 inches : 12 inches c. 1.5 feet ______ 5 yards d. 25 lawns _______ $120


21. 520 calories burned in 20 minutes on the treadmill

22. 98.8 miles ________ 3.8 gallons

23. 63 ounces of trail mix cost $3.50

24. Karen rode her bike 25 miles in 45 minutes during a race. Chris completed a 35-mile bike race in an hour and fi ve minutes. Who rode at a faster pace?

42

3248

x

y cm

18 cm

24 cm

x cm9 cm

20 cm

tic-tAc-toe ~ Ar e the y ProPortionA l?

In Lesson 2, cross products were used to determine if two ratios were proportional. Th ere are other ways to determine if two ratios form a proportion. One method involves equivalent fractions. Another method uses decimals. Research these methods. Make a brochure illustrating all three ways. Your brochure should explain each method and give several examples.

Lesson 3 ~ Percentages 13

A percent is a ratio that compares a number to 100. If 80% of the students in your school attend the football game, it means that 80 out of every 100 students or 80 ___ 100 of all students attend.

Percentages are ratios. Th ey can be used in proportions to solve problems. You can set up a percent problem with a proportion, as shown.

percent ______

100 =

part _____

whole

A store held a fundraiser for the local high school. Fift een percent of one day’s profi t went to the school. Th e store had a profi t of $2,450 that day. What amount did the high school receive?

Set up the proportion. Write the percent, 15, over 100. Th e profi t for the day was $2,450. Th is is the “whole”. Th e “part” is the unknown. Represent it with a variable.

Write the proportion. 15 ___ 100 = x ____ 2450

Set the cross products equal to one another. 15 ∙ 2450 = 100 ∙ x

Solve the equation for x. 36750 = 100x 367.5 = x

Th e high school received $367.50 from the store’s fundraiser.

Th e key to solving a proportion problem is correctly setting up the proportion. Be careful to identify which number represents the “part” and which is the “whole”.

example 1

solution

percentages

Lesson 3

14 Lesson 3 ~ Percentages

use a proportion to answer each question.a. What number is 30% of 80?b. sixty percent of what number is 24?c. What percent of 40 is 75?

a. Th e whole is represented by 80. Th e percent is 30. Th e “part” is unknown. Write the proportion. 30 ___ 100 =

p __ 80

Find cross products and solve. 2400 = 100p Th irty percent of 80 is 24 . 24 = p b. Write the proportion. 60 ___ 100 = 24 __ w Find cross products and solve. 60w = 2400 Twenty-four is 60% of 40 . w = 40 c. Write the proportion. x ___ 100 = 75 __ 40

Find cross products and solve. 40x = 7500 Seventy-fi ve is 187.5% of 40. x = 187.5

Percents are commonly used to describe increases or decreases in amounts. Sales taxes and tips are examples of increases. Sales or discounts are examples of decreases.

use proportions to solve the following problems.a. Amaury bought a pair of shoes at a store that has a sales tax. Th e shoes originally cost $55. how much did Amaury pay, including tax?b. Jacob bought an MP3 player on sale for $90. It originally cost $150. Find the percent discount for the MP3 player.

a. Write the proportion. 6.5 ___ 100 = t __ 55 Find cross products and solve. 357.5 = 100t 3.575 = t Round to the nearest hundredth. $3.58 = t

Add the original price and the sales tax. $55 + $3.58 = $58.58

Amaury paid a total of $58.58 for the shoes.

b. Find the discount amount 150 − 90 = 60 for the MP3 player. Write the proportion and solve. x ___ 100 = 60 ___ 150

150x = 6000 Th e MP3 player discount was 40%. x = 40

example 2

solutions

example 3

solutions


exercises

determine which proportion can be used to solve each problem.

1. Approximately 28% of students at Archwood Middle School are in art class. There are 110 students in art class. How many students attend school at Archwood?

A. 110 ___ 100

= 28 __ x B. 28 ___

100 = x ___

110 C. 28 ___

100 = 110 ___

x

2. A class has 28 students. Sixteen students in the class participate in after school activities. What percent of students participate in after school activities?

A. x ___ 100

= 16 __ 28

B. 16 ___ 100

= x __ 28

C. x ___ 100

= 28 __ 16

3. Everyone in a town of 24,800 people voted for their favorite Italian restaurant. Serrano’s Ristorante received 72% of the votes. How many people voted for Serrano’s as their favorite restaurant?

A. 72 ___ 100 = 24800 _____ x B. x ___ 100 = 24800 _____ 72 C. 72 ___ 100 = x _____ 24800

use proportions to answer each question. 4. What number is 45% of 250? 5. Fifteen percent of what number is 66?

6. Eighty is what percent of 200? 7. What percent of 48 is 60?

8. Ten percent of 205 is what number? 9. One hundred is 25% of what number?

10. Seventy-two percent of the students at Kingsley Middle School have cell phones. There are 525 students at Kingsley. How many have cell phones?

11. Diego earned 54 out of 62 points on the latest test. What percent did Diego earn on the test? Round to the nearest whole percent.

12. Tuition for a particular college is $9,500 per year. Tuition accounts for about 75% of all expenses at the school. How much is the total expense for one year? Round to the nearest penny.

13. Use percents and proportions to find the approximate answer to each question. a. Portland’s population (556,370) was about 15% of Oregon’s total population in 2005. What was Oregon’s 2005 population? Round to the nearest whole number. b. Salem had 147,250 people in 2005. Use the answer from part a to find the percent of Oregon’s population from Salem. Round to the nearest whole percent. c. Harney County is Oregon’s largest county in terms of land area. It has almost 11% of

Oregon’s land area. Oregon’s land area totals 97,060 square miles. About how many square miles is Harney County? d. Multnomah County has Oregon’s smallest land area with only 465 square miles. Multnomah County is what percent of Oregon’s total land area? Round to the nearest tenth of a percent.

16 Lesson 3 ~ Percentages

14. Xian used a 20% off coupon to buy a $65 fl oral arrangement. How much did she pay for the fl owers?

15. LeeAnne went out to dinner with a friend. Th e bill came to $18.65. Th ey left a 15% tip. How much did dinner cost, including the tip? Round to the nearest penny.

16. Talia bought a scarf in Idaho. She paid $19.17 for the scarf, including sales tax. Th e price on the tag was $17.95. What was the percent of sales tax? Round to the nearest tenth of a percent.

17. Jamal bought a laptop computer on sale. Th e original cost was $750. Th e sale price was $600. What percent had the computer been discounted?

review

simplify each ratio. Write each simplifi ed ratio in all three forms.

18. 24 __ 40 19. 36 : 28 20. 100 to 120


21. 1 _ 4 , 7.5 ___ 30 22. 24 __ 22 , 120 ___ 112 23. 11 __ 20 , 50.6 ___ 92

tic-tAc-toe ~ counti ng cr itte rs

Fish and Wildlife workers oft en use a process called “Capture-Recapture” to estimate the populations of fi sh, deer and other wildlife. Th e fi rst step in the process is to collect a sample of the animal (fi sh, for example) and tag them. Th e fi sh are then released and allowed to mix with the population again. At a later time, the workers return and collect another sample of fi sh. From this sample, they fi nd the ratio of tagged fi sh to total fi sh. It is assumed that this ratio in the sample is

similar to the ratio in the whole population.

Tagged Fish in Sample ________________ Total Fish in Sample = Tagged Fish in Population

__________________ Total Fish in Population

Research how the capture-recapture method is used with at least two diff erent types of animals (fi sh, deer, bears, birds, etc.). Write a 1-2 page summary of your fi ndings. State the sources of your information.


tic-tAc-toe ~ Pe rce nt of ch A nge

Sales taxes, pay raises and tips left at a restaurant are all examples of percents of increase. Discounts, depreciation and decay are all examples of percents of decrease. Th ese situations can be dealt with easily using a percent of change proportion:

new percent _________ 100

= new amount ____________ original amount

To fi nd the “new percent” for each problem, either add the percent of increase to 100 or subtract the percent of decrease from 100. Here are a few examples:

use proportions to solve the following percent of change problems.

1. A car depreciates in value by 12% per year. Th e car is now worth $22,000. How much will it be worth in one year?2. Kevin took his family out for dinner. Th e total bill came to $65. He left a 15% tip. How much did Kevin end up paying including the tip?3. With a 9% sales tax, Irene pays $19.33 for a new set of headphones. How much did the headphones cost originally?4. Gavin was excited because he found a pair of jeans that originally cost $45 on sale for $28. What is the percent of discount on the jeans?5. Haleb received a pay raise from $9.10 to $9.95 per hour. What was the percent of her pay raise?6. A radioactive material decays at 20% per day. Th ere are 200 milligrams of the material today. How many milligrams will there be tomorrow?7. Another radioactive material decays at 15% per day. Th ere are 400 milligrams of the material today. How many milligrams were there yesterday?8. In 2007, a car was worth $17,500. A year later the car was worth $16,850. What is the percent of depreciation of the car?9. Lisa took a group of her co-workers out for dinner to discuss a new project they were working on. Th e total bill for the meals came to $174.80. Th is included a 15% gratuity (tip). a. How much did the meals cost before the gratuity? b. Th ere were eight people in the group. How much did each person’s meal cost, on average?

Max bought an MP3 player in Washington state, where there is a 7% sales tax. If the MP3 player cost $99, how much did Max pay with the tax?

A sales tax is an increase, so 100 + 7 = 107%.

107 ___ 100 = x __ 99

Set cross products equal. 10593 = 100x 105.93 = x

Th e MP3 player cost $105.93 with the sales tax.

Kira took a friend out for lunch. She had a 15% off coupon which made the fi nal cost of their meals $12.35. How much would Kira have paid without the coupon?

Since this is a discount, 100 – 15 = 85%.

Th e problem is asking for the original amount of the meals.

85 ___ 100 = 12.35 ____ x 85x = 1235 x ≈ 14.53

Th e meals cost $14.53 before the discount.

James took a friend out for dinner. Th eir meals cost $29.85, but James left a tip which brought the cost to $35. What was the percent of the tip that James left ?

$29.85 is the original amount and $35 is the new amount.

x ___ 100 = 35 ____ 29.85 x = 117.25%

Compare 117.25% to 100% to fi nd the percent of increase.

117.25 − 100 = 17.25

James left a tip of 17.25%.

18 Lesson 4 ~ Creating And Analyzing Bar Graphs

Irma’s school had money to fund a new aft er school sport team. Th e committee was not sure which sport would be most popular among students. Irma conducted a survey and reported the results. She put the data into a table aft er surveying the students.

Irma displayed the data for the committee with a pictograph. A pictograph is a graph using pictures to compare the amounts represented in each category. Th e categories are represented by the diff erent sport choices.

Th e key explains how to interpret each picture in the pictograph. Each football represents two students who voted for that sport. A half football represents one student.

sport Soccer Volleyball Dance Flag Football Basketballnumber of students 10 6 3 7 4

Soccer Volleyball Dance Flag Football

Basketball

= 2 students

creating anD analyZing Bar graphs

Lesson 4

Lesson 4 ~ Creating And Analyzing Bar Graphs 19

Another type of graph uses bars to compare the quantities in each category instead of pictures. This type of graph is a bar graph. Bar graphs can have either horizontal or vertical bars.

Irma surveyed the staff about which after school sport each would be willing to coach. she put the data into a bar graph.

a. Which after school sport has the most staff members willing to coach? Which has the fewest staff members?b. What percent of staff members would be willing to coach soccer?c. There are 55 staff members at Irma’s school. how many would be willing to coach volleyball after school?

a. The bar which represents basketball is the tallest (30%). Basketball has the most staff members willing to coach. Dance has the fewest staff members (10%) willing to coach.

b. Fifteen percent of the staff members are willing to coach soccer.

c. Solve by using a proportion. The survey showed that 20% of the staff members are willing to coach volleyball. There are 55 staff members. This represents the “whole”. The “part” is the unknown. 20 ___ 100 = v __ 55 Set cross products equal and solve. 20 ∙ 55 = 100v 11 = v

Eleven staff members are willing to coach volleyball after school, according to Irma's survey.

Bar graphs are created in much the same way as pictographs. Place the categories along one of the axes. Scale the other axis appropriately so all values are included (instead of using pictures). Bar graphs show quantities as percents, like the example above, or frequency. The frequency is the number of times an item occurs in a data set.

example 1

solutions

0

5

10

15

20

25

30

35

Soccer Volleyball Dance Flag Football Basketball

Perc

ent o

f Sta

ff


Students' Favorite Ways to Communicate with Friends

02468

10121416182022242628

Talk on Phone Text Message InstantMessage

Email

Num

ber o

f Stu

dent

s

Melody was curious about how many of her classmates were involved in music. she conducted a survey. use the data to make a bar graph and a pictograph.

Place the categories along the horizontal axis.

exercises

1. How are pictographs and bar graphs similar? How are they different?

2. Use the bar graph at the right. a. How many students were surveyed? b. What is the students’ favorite way to communicate with friends? c. How many more students prefer instant messaging over email? d. How many times more students prefer instant messaging over talking on the phone? e. What percent of students prefer text messaging? Round to the nearest percent. f. What percent of students prefer talking on the phone? Round to the nearest percent.

3. Make a pictograph using the data from the bar graph in exercise 2. Each picture in your pictograph should represent two students.

example 2

solution

Orchestra Band Choir None7 8 10 3

The bar graph has a vertical axis that shows the frequency for each category.

Students in Music

0

2

4

6

8

10

12

Orchestra Band Choir None

Num

ber o

f Stu

dent

s

The pictograph uses a double music note to represent two students.

= 2 students

Orchestra Band Choir None

Lesson 4 ~ Creating And Analyzing Bar Graphs 21

4. Harvey Middle School collected data about how students travel to school each day. Use the pictograph to answer each question. a. How many students are included in this pictograph? b. How many students ride bikes to school each day? c. How many more students get a ride to school than walk? d. How many times more students ride the bus than walk? e. What percent of students get a ride to school each day? Round to the nearest percent. f. Harvey Middle School has 520 students. How many students would likely arrive by bicycle? Round to the nearest whole number.

5. Use proportions to convert all amounts in each category in exercise 4 to percents. Make a bar graph using percents on the vertical axis.

6. Mr. Carlisle surveyed his 24 seventh grade students. He asked what type of chores they do at home at least once per month. Some students had more than one type of chore per month. a. How many of Mr. Carlisle's students dust at least once a month? b. What is the ratio of students who wash dishes to students who vacuum? Write the answer in simplest form. c. What percent of students wash the car at least once per month? Round to the nearest percent. d. There are 200 seventh graders at Mr. Carlisle's school. How many would you expect to dust at least once per month? Round to the nearest whole number.

7. Seventy freshmen students at Bennett High School took a survey. The survey asked which academy they planned to enroll in. Use the bar graph at the left to answer each question. a. What is the ratio of students planning to enroll in the applied trade academy to the arts academy? b. A total of 90 freshmen enrolled in the social services academy. How many would you expect to enroll in the business academy? c. Based on the survey, what percent of the

freshman class enrolled in the science and technology academy from the survey? Round to the nearest percent.

= 10 students

Walk

Ride the bus

Bicycle

Get a ride

02468

1012141618202224

Business SocialServices

Science /Technology

Applied Trade Arts

Num

ber

of S

tude

nts

0

4

8

12

16

20

24

Vacuum Wash Dishes Wash the Car Dust

Num

ber

of S

tude

nts


8. Samantha analyzed her monthly budget. She made a table to compare her expenses.

Category Rent Groceries Utilities Gas Insurance EntertainmentAmount $450 $100 $70 $150 $60 $80

a. What is the total amount Samantha spends per month?b. How many times more money does Samantha spend on rent than on gas?c. What is the ratio of the amount Samantha spends on utilities to the amount she spends on groceries?d. Use proportions to convert all amounts in each category to percents. Round each answer to the

nearest percent. Make a bar graph using percents on the vertical axis.

review

9. What is 85% of 320? 10. What percent of 40 is 35?

11. Th irty percent of what number is 90? 12. One hundred fi ft y is what percent of 120?

13. Jillian made muffi ns for her co-workers. Th e recipe she used requires 1 _ 2 cup of sugar for 12 muffi ns. She has 45 co-workers. How many cups of sugar will she need to make one muffi n each for everyone?

14. Cody bought 4.5 pounds of trail mix to take on a fi eld trip. Cody had $20. Th e trail mix cost $2.99 per pound. How much money did he have left over?

tic-tAc-toe ~ douBle BA r gr A Phs

Conduct a survey of at least 40 students at your school, half boys and half girls. Ask the question, “What is your favorite _______?” Off er between four and six possible responses. Keep a tally of your classmates’ responses as well as their gender. For example, "What is your favorite color?" might have blue, red, green, purple or orange as possible responses:

Gender Blue Red Green Purple OrangeBoys 4 2 9 1 4Girls 4 4 3 3 6

Use your data to construct a double bar graph (or double pictograph) comparing the number of boys and girls giving each response. Write a half-page summary of your graph. How are boys' and girls' answers similar? How are their answers diff erent? What surprised you about the data you collected? If you were to conduct the survey again, what would you do diff erently? 0

123456789

10

Blue Red Green Purple Orange

BoysGirls

example

Lesson 5 ~ Creating And Analyzing Pie Charts 23

You learned how to use bar graphs to display data in Lesson 4. Another graph used to compare amounts represented in several categories is a pie chart. A pie chart is a circle graph that shows information as sectors, or slices, of a circle.

A pie chart is labeled with category names and the percentage represented by each category.

Jeff fi gured out his monthly budget. He made a list of monthly expenses from last month. He put them into categories. He found the total amount of money spent in each category and recorded that data in a table.

rent groceries gas Bills entertainment$800 $160 $140 $500 $200

Jeff wants to display the data in a pie chart. Follow the steps below to make a pie chart for the data set.

step 1: Copy the table below. Enter the total amount of money Jeff spent last month.

rent groceries gas Bills entertainment totalAmount $800 $160 $140 $500 $200Percent 44%

step 2: Convert each of the amounts into percents using proportions. Round answers to the nearest percent. Complete the table with the percent for each category. Th e “Rent” category has been done for you. Write the proportion. Rent: x ___ 100 = 800 ____ 1800 Use cross products and solve. 1800x = 80000 x ≈ 44%

step 3: Trace the circle at the right. Use a straight-edge to create sectors for each category. Use the chart below to estimate the appropriate size for each category. Label each sector with the budget category and the percent of the total budget.

Common Percents and sectors25% 33% 67% 75%

explOre! easy as pie

creating anD analyZing pie charts

Lesson 5

Yellow20%

Blue15%

Green40%

Red25%

24 Lesson 5 ~ Creating And Analyzing Pie Charts

Data displayed in pie charts can be used to answer questions about the data set. The example below shows how to read and analyze a pie chart.

The pie chart shows students’ post high school plans. use the data to answer each question.

a. What do most students plan to do after high school? b. What percent of students want to join the Armed Forces after high school?c. There are 65 students who plan to attend community college. how many students are there in the school? d. use the answer from part c to approximate how many students intend to get a job after high school.

a. The largest section of the pie chart represents what most students plan to do after high school. Most students plan to attend a 4-year college.

b. Ten percent of students plan to join the Armed Forces.

c. The pie chart shows 20% of students plan to attend community college. Since 65 students plan to attend community college this represents the “part”. Find the total number of students, the “whole.” Write the proportion. 20 ___ 100 = 65 __ x Set the cross products equal 20x = 6500 to each other and solve. x = 325

There are 325 students in the school.

d. The pie chart shows 25% of students plan to get a job after high school. There are 325 students in the school. Write the proportion. 25 ___ 100 =

j ___ 325

Set the cross products equal 8125 = 100j to each other and solve. 81.25 = j There are about 81 students who plan to get a job after high school.

example 1

solutions

Community College

20%

4-Year College

45%

Armed Forces10%

Get A Job25%


exercises

1. The table shows the percent of students who chose each animal as their favorite at the zoo. Use the percentages to create a pie chart. Estimate the size of each sector. Label the pie chart.

giraffe Bear Monkey elephant sea Lion15% 9% 34% 17% 25%

2. Residents of Masonville responded to a survey about their favorite recreational activity. The responses were put into a table. Convert each amount into a percent.

Fishing skiing hiking Boating5 12 8 15

3. Summarize how to make a pie chart, in your own words.

4. Students at Kingsman Middle School were asked about their favorite type of movie. Use the pie chart to answer the questions. a. Which type of movie was most popular among students at Kingsman? b. How many times more popular were drama than action movies? c. Sixty students picked comedy as their favorite. Approximately how many students were surveyed? d. Use the answer from part c. How many students picked romance as their favorite type of movie?

5. Mr. Caldwell surveyed his class to find the number of siblings each student had. He recorded the results as percentages.

no siblings 1 sibling 2 siblings 3 or more siblings12% 40% 30% 18%

a. There are 720 students at Mr. Caldwell’s school. Approximately how many students in the entire school have 3 or more siblings? b. Mrs. Engstrom has 28 students in her class. Based on Mr. Caldwell’s findings, predict how many of her students have no siblings. c. Make a pie chart from the data from Mr. Caldwell’s class.

6. A nutritionist collected data about students’ choices of beverages at lunch. The pie chart shows the results of her study. a. What percent of students chose either milk or bottled water? b. Forty-five students selected juice. How many total students were included in the study? c. Use your answer from part b. How many students chose to drink milk?

Juice25%

Soda20%

Bottled Water40%

Milk15%

Comedy35%

Musical10%

Romance15%

Action10%

Drama30%

Favorite type of Movie


7. Several students were asked to name their favorite type of food. The results are displayed in the pie chart. a. What was the ratio of students who preferred Mexican food to those who preferred Chinese food? b. Nine students preferred Italian food. How many students were included in the survey? c. Use your answer from part b. How many students preferred American food? d. Five hundred students will be attending a leadership workshop. Use the pie chart to predict how many would choose seafood as their favorite

type of food?

8. Hoi sells jewelry at the Saturday Market. She took inventory of what she had sold at the end of the day. Create a pie chart to show Hoi’s percent of sales for each item.

Bracelets necklaces earrings Anklets20 9 22 5

9. Mrs. Huber collected data on students’ favorite after school sports to participate in. She surveyed 48 students. She made a pictograph to display the data. a. Copy and complete the table.

Football Basketball track VolleyballFrequency

Percent b. Use the percentages from part a. Create a pie chart. c. There are 496 students at the school. Approximately how many students’ favorite after school sport is track?

review

10. Valerie’s Vinyl sells used records. Valerie tracked the busiest times of day. She made the following pictograph. a. How many records did Valerie sell between noon and 4 p.m.? b. How many records did Valerie sell on this particular day? c. Valerie sold 120 records over the next week. How many of them would you expect to be sold before noon?

= 4 students

Football Basketball VolleyballTrack

Before noon Between noon and 4 p.m.

After 4 p.m.

= 4 records

Mexican28%Seafood

6%

Chinese18%

American25%

Italian23%


use cross products to determine whether each pair of ratios forms a proportion. 11. 7 _ 9 , 31.5 ___ 49.5 12. 41.25 ____ 127.5 , 11 __ 34

13. Jenny bought a book for 30% off the original price. Th e original price was $19.99. a. How much was the book discounted? b. How much did Jenny actually pay for the book?

14. Vicente took his family out to dinner. Th e bill came to $38.75. He left a 15% tip for the server. a. How much was the tip he left ? b. What was the total cost of the dinner, including the tip?

tic-tAc-toe ~ sPr e A dshe e ts A n d Pi e ch A rts

Conduct a survey of at least 30 classmates, asking the question, “What is your favorite _______?” Off er between four and six possible responses. For example, “What is your favorite color?” might include blue, red, green, purple or orange as possible responses. Keep a tally of your classmates’ responses.

Enter the fi nal data into a computer spreadsheet program. Th e spreadsheet should include your answer categories in one row and the total tally of students in the second row. For example:

Blue Red Green Purple Orange5 7 2 6 10

Use the computer soft ware to create a pie chart of your data. If needed, consult the “Help” tool on your spreadsheet soft ware to learn how to create the chart. Turn in a printout of your spreadsheet table as well as the pie chart.


tic-tAc-toe ~ A Pe r fect Pi e ch A rt

In this Block you learned how to make a pie chart by fi nding the percents for each category and estimating the size of each sector. To make a more accurate pie chart, you can convert the percents into degrees and measure the size of each sector using a protractor.

To complete the table below, convert the amounts into percents as you learned in Lesson 3. For example, the amount of people who chose chocolate as their favorite can be converted to a percent.

10 __ 20 = x ___ 100 → 1000 = 20x → 50 = x → 50%

Since there are 360 degrees in a circle, the amount of people who chose chocolate as their favorite can be converted into degrees.

10 __ 20 = x ___ 360 → 3600 = 20x → 180 = x → 180°

1. Copy the table. Use proportions to complete the percents and degrees for Vanilla and Strawberry fl avors.

2. Use a compass to draw a circle with a radius of 2 inches. Use a protractor to measure the correct degrees for each of the three sectors in the table. Label each sector with the ice cream fl avor and the percent of students who chose that fl avor as their favorite.

Follow the steps below to conduct your own survey. Create a pie chart of the results.

step 1: Survey at least 30 students. Ask them a question, such as “What is your favorite _____?”

step 2: Give no more than ten possible answers to choose from.

step 3: Tally students’ responses and put them into a table (as above).

step 4: Convert the number of tallies into percents and degrees using proportions.

step 5: Use a protractor to accurately measure the number of degrees for each sector of the pie chart. Label each sector with the response and the percentage of students.

In this Block you learned how to make a pie chart by fi nding the percents

Favorite Ice Cream FlavorsChocolate Vanilla strawberry total

Amount 10 6 4 20Percent 50%degrees 180°

Block 1 ~ Review 29

Lesson 1 ~ Ratios and Rates

Identify each as either a ratio, rate or unit rate. 1. 60 miles per hour 2. $84 ___ $60 3. 9 students : 15 students

4. 20 lawns _______ $140 5.

75 text messages ____________ 1 month 6. 600 words in 12 minutes

simplify each ratio. Write each simplifi ed ratio in all three forms. 7. 36 __ 21 8. 15 : 40


9. 22 televisions for every 8 households

10. $42 _________ 6 car washes

use the table to fi nd each ratio. Write each answer as a fraction in simplest form.

11. boys to girls 12. monkeys to all animals

13. boys who preferred sea lions to girls who preferred sea lions

14. girls who preferred elephants to all students who preferred elephants

Favorite Animal at the ZooBoys girls

Monkey 8 2elephant 5 6sea Lion 1 9

Bear 4 3

review

bar graph pie chart ratio frequency proportion scale percent rate similar fi gures pictograph unit rate

vocabulary

BLoCK 1

30 Block 1 ~ Review

Compare each situation using unit rates.

15. Callyn hiked 7 miles in 66.5 minutes. Graham hiked 4 miles in 41 minutes. Who hiked at a faster pace?

16. Hiro bought fi ve bananas for $1.85. Nina bought seven bananas for $2.31. Which person paid less per banana?

Lesson 2 ~ Proportions


17. 9 __ 14 , 11 __ 16 18. 8 __ 12 , 32 __ 48 19. 12 __ 17 , 40.8 ___ 57.8

solve the following proportions. 20. 3 _ 8 = 24 __ v 21. h __ 10 = 5 _ 6 22. 48 __ 50 = p

___ 100

23. Use the two rectangles at right. a. What is the ratio of the longer side on the large rectangle to the longer side on the smaller rectangle? Write your answer in simplest form. b. What is the ratio of the shorter side on the large rectangle to the shorter side on the small rectangle? Write your answer in simplest form. c. Are the two rectangles similar? Explain.

use proportions to solve the following problems.

24. Tamiqua organized a blood drive at her school. Fourteen students donated blood during the fi rst 20 minutes of the blood drive. Th e blood drive lasted for 3 hours. Approximately how many students donated blood?

25. Gerad checked his hiking map of the Pacifi c Crest Trail. He is hiking to a nearby town to stay overnight. Th e town is 1.75 inches away from his current location on the map. Th e map scale states that 1.5 inches equals 8 miles. How far will Gerad hike to the town?

26. Maven cut weight before the next wrestling weigh-in. He cut 0.2 pounds by jogging for 15 minutes. How long did he jog to cut 1.5 pounds by weigh-in?

27. Ian made a scale drawing of his bedroom which measures 12 feet by 13.5 feet. His drawing had a scale of 3 feet : 1.5 inches. What were the dimensions of his bedroom in the drawing?

21

12

9

14

Block 1 ~ Review 31

28. The triangles are similar. Find the value of x.

Lesson 3 ~ Percentages

use proportions to answer each question. 29. Twenty percent of what number is 55? 30. Eighty is what percent of 180?

31. What is 70% of 220? 32. What percent of 65 is 90? Round to the nearest percent.

33. Sixty percent of students at Glendale Middle School participate in extra-curricular activities. Three hundred eighty-one students participate in extra-curricular activities. How many students are in the school?

34. Silvio collected permission slips for a class field trip. He has collected slips from 21 of the 27 students. What percent has Silvio collected? Round to the nearest percent.

35. Christy is a professional wedding photographer. She charges $800 for taking wedding photos. She charges friends 65% of this amount. How much does she charge her friends to take their wedding photos?

36. Bragg bought a pair of concert tickets on sale for $60. The original price was $75. What was the percent of discount?

37. Dana bought a pair of running shoes. They cost $79. The sales tax was 6.5%. How much did she pay for the shoes, including sales tax? Round to the nearest penny.

38. Marcos and Maddie’s dinner cost $24.85. Marcos left a tip of $4.15. What percent did he leave as a tip? Round to the nearest tenth of a percent.

Lesson 4 ~ Creating and Analyzing Bar Graphs

39. Students participated in a survey on the type of reading they prefer in their free time. The bar graph shows the results. a. How many students were surveyed? b. Which is the students’ least favorite type of reading? c. How many more students prefer fiction to biographies? d. What percent of students preferred to read magazines?

35

x36

45

0

1

2

3

4

5

6

7

8

9

Fiction Non-Fiction Biographies Magazines

Num

ber

of S

tude

nts

32 Block 1 ~ Review

40. Make a pictograph from the bar graph in exercise 39. Let each picture in the pictograph represent two students.

41. Th e pictograph shows the results of a survey students participated in. Th e topic was “favorite cell phone company”.

a. How many students are represented in the pictograph?

b. How many times more students preferred Far-Tel over CellSpan?

c. What percent of students preferred Wire-Free?d. Two hundred forty students attend Mt. Hood

Academy. Based on this survey, about how many students would choose Mobi-Fone as the favorite cell phone company?

42. Otto asked several students about their favorite class. He put the data in a table.

subject English Math Science Social Studies Music# of students 5 7 2 12 8

Percent

a. How many students did Otto survey?b. Copy the table. Convert each amount in the table to a percent. Write each percent in the empty row.

Round to the nearest tenth of a percent.c. Make a bar graph of the data. Use percents on the vertical axis.

Lesson 5 ~ Creating and Analyzing Pie Charts

43. Marcie’s digital picture frame holds a variety of pictures. Th e table shows the percentage of each type of picture she stores in the digital frame. Create a pie chart to show these percentages.

Photos of Friends Photos of Family scenic Photos Photos of Pets22% 38% 25% 15%

44. Students were asked to name their favorite form of exercise. Th e results of the survey are shown in the pie chart. a. Which form of exercise was most popular among students? b. How many times more popular was aerobics than bicycling? c. Eighty students were surveyed. How many of them chose lift ing weights as their favorite form of exercise? d. One school has 36 students who prefer bicycling as their favorite form of exercise. About how many students would you estimate are in the school?

Far-Tel Mobi-Fone CellSpan Wire-Free

= 2 students

Aerobics16%

Team Sports28%

Lift ing Weights18%

Walking/Running

30%

Bicycling8%

Block 1 ~ Review 33

45. Noelle sold fruit smoothies at the county fair. Th e table shows the sales for each fl avor. Convert each amount into percents. Make a pie chart from the percentages.

Banana strawberry raspberry Peach7 18 1 11

46. Ryan tracked the number of calories he consumed one day. He fi gured out the protein, carbohydrate and fat make-up of the calories. He made a pie chart to display the results. a. What was Ryan’s ratio of protein to carbohydrates? b. Ryan consumed 240 fat calories. How many total calories did he consume? c. How many protein calories did Ryan consume? Use the answer from part b as the total calories.

tic-tAc-toe ~ Pe rce nt eQuAtions

In Lesson 3, proportions were used to solve problems such as, “What is 25% of 120?” A percent equation can also be used to solve this type of problem. Set up percent problems with an equation as follows.

part = percent ∙ wholeExamples: What is 125% of 60? What percent of 160 is 12? Eighty is 40% of what number?

Write the percent as a decimal.p = 1.25 ∙ 60

p = 75

12 = t ∙ 160Divide by 160 on both sides.

0.075 = tConvert the decimal to a

percent.t = 7.5 %

80 = 0.4 ∙ wDivide by 0.4 on both sides.

200 = w

use percent equations to solve the following problems. 1. Fift een is what percent of 40? 2. What is 75% of 240?

3. Five percent of what number is 50? 4. Ninety percent of 500 is what number?

5. What percent of 120 is 150? 6. Two hundred is 85% of what number?

7. Th irty fi ve percent of Marty’s monthly paycheck is spent on rent. Marty pays $700 per month for rent. How much is his monthly paycheck?

8. Heidi spends $120 per month on groceries. Her monthly paycheck is $2,200. What percent of her monthly paycheck is spent on groceries?

9. Carl’s car payment is $250 per month. Th is is 8% of his monthly paycheck. How much does Carl get paid each month?

, proportions were used to solve problems such as, “What is

%

Fat15%

Protein55%Carbohydrates

30%

34 Block 1 ~ Review

BriAn coach

PortlAnd, oregon

I am a volleyball coach. I do many things to make sure that our team is as successful as they can be. I plan and oversee practice each day. I evaluate my players and decide who is playing the best at what position. I also oversee the assistant coaches on my team.

Many coaches use statistics to evaluate their game performance and practice efficiency. Statistics give me a clear and unbiased picture of how well we are doing. By looking at the numbers I have kept, I can adjust strategy on the court during a game or at practice. It is also helpful for athletes to see their own statistics. By looking at their own performance, athletes can work on specific skills and take extra practice on the areas they are not as strong in.

In volleyball, players rotate through positions on the court. I use math to analyze rotations and determine the most effective line-up for our team. Two other important components of volleyball are the points my team has scored and the points we have given up. By tracking those numbers throughout the season, I can evaluate our team’s trends and help better our odds of competing.

There are no educational requirements for being a coach. Many coaches have received training or college degrees in exercise or fitness management. You can even get a coaching minor at some colleges. Other coaches work their way up through experience.

Salaries for coaches vary greatly depending on the level you coach at. Coaches of middle or high schools can make up to $6,000 per season. Coaches at the professional level can make millions of dollars per year.

I really enjoy being a coach. It is a daily challenge to come up with a practice and game plan to help my team be as successful as possible. It is also great to see individual athletes work hard and improve. The relationships and experiences I have while coaching make it a very rewarding career.

CAreer FoCus

Documents

BLoCK 1 ~ dAtA AnALYsIs - Oregon Focusoregonfocus.com/Inside/media/OnlineBook/DA_Block_1.pdf · Block 1 ~ Data Analysis ~ Ratios, Proportions And Percents 1 BLoCK 1 ~ dAtA AnALYsIs