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Probability, Percent, Rational Number Equivalence

Math A Honors HW Keys

Module #1

Created in collaboration with Utah Middle School Math Project

A University of Utah Partnership Project

San Dieguito Union High School District

SDUHSD Math A Honors – Module #1 - TEACHER EDITION 4

1.0A Homework: American Football Name: Period:

Complete by showing all of your work. Do NOT use a calculator. Box your final answer.

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

Spiral Review:

13. Add:

14. Subtract:

15. | | 5

16. 5 + 3(2) – 4 7


1.0B Homework: Fraction Review Name: Period:

1. Fill in the boxes below to show how you can convert between fractions, decimals, and percentages.

Show how to use the steps you described to complete the following problems.

2. Write 45% as a fraction in simplest form.

3. Write as a decimal. 0.6

4. Write as a decimal.

5. Write 0.45 as a percent. 45%

6. Write 1 as a percent.

100%

7. Write 0.002 as a fraction.

Answer the following questions. Show your work. Answer in a complete sentence. 8. Your food costs are $2,500. Your total food

sales are $17,500. What fraction of your food sales do the food costs represent? 1/7 of the food sales

9. James hired a new employee to work in his bakeshop. In one hour, the employee burned 625 chocolate chip cookies. If this represented 25% of the day’s production, how many cookies did James plan on producing that day?

2,500 cookies

10. In order to select new board members, the French Club held an election. 56 out of the 80 members of the French club voted in the election. What percentage of the members voted? 70% of the French Club voted

11. There are 18 empty seats and 54 occupied seats on a train. What percentage of the seats on the train are empty? 25%

12. A serving of ice cream contains 1200 calories. One hundred forty-four calories come from fat. What percent of the total calories come from fat?

3

5

1

9

b. How can you write a fraction as a decimal?

Understand that a decimal is ―out of 100,‖ convert fraction to n/100 or use bar model. Divide the numerator by the denominator.

c. How can you write a decimal as a percent?

Understand that decimal is out of 100; move the decimal point to the right two places and put in the percentage symbol.

a. How can you write a percent as a fraction?

Write the percent as a whole number over 100, then simplify the fraction.


12%

Fill in each blank with the equivalent fraction, decimal or percent. Use bar notation for repeating decimals.

Fraction Decimal Percent

13. 0.6 60%

14. 0.16 16%

15.

0.42 42%

16.

0.8 80%

17.

0.32 32%

18. 0.45 45%

19.

0.21 21%

20.

0.06 6%

21.

0.07 7%

22. 0.125 12.5%

23.

0.99 99%

24.

0.75 75%

25. 0.25 25%

26.

0.2 20%

27.

0.4 40%

28.

1.5 150%

29.

2.5 250 %

30.

3.0 300%

31.

0. %

32.

0. %

6

10

4

25

9

20

1

8

1

4

Show and number your work over here!


1.1A Homework: Solve Probability Predictions* Name: Period:

Find the probability of each roll if you use a single die with 8 sides. Express your answer as a simplified fraction, decimal, and percent.

1. P(5)

, 0.125, 12.5% 2. P(odd number)

, 0.5, 50%

3. P(a number less than 7)

, 0.75, 75% 4. P(a number greater than 4)

, 0.5, 50%

5. P(a multiple of 2)

, 0.5, 50% 6. P(a number less than 9) 1, 1, 100%

Each of the 12 cards shown below has a letter, a number, and a color. Each card is equally likely to be drawn. Find each probability. Express your answer as a simplified fraction, decimal, and percent.

A 1

A 2

A 3

A 4

B 1

B 2

B 3

B 4

C 1

C 2

C 3

C 4

7. P(C)

, ,

8. P(gray)

, 0.5, 50%

9. P(not C)

, ,

10. P(not 1, or 2, or 3)

, 0.25, 25%

11. P(prime number)

, 0.5, 50% 12. P(not 1)

, 0.75, 75%

13. Adrienne flipped a coin 50 times and got 23 heads. What is her experimental probability of getting a

head? Write your answer as a simplified fraction, decimal and percent.

14. Based on Adrienne’s flips from #13: What if she flipped the coin 100 times, how many heads could she

expect to get? Explain your answer. Answers will vary a little. They may say 46 times since ( ) so multiply 23 by 2. Or they may say 50 times since they would expect to get a head about ½ of the time. Discuss their answers as a class.


15. You want to use 800 marbles and you want six different colors—blue, red, green, yellow, purple, and pink. You also do not want more than two colors to have the same probability. State the number of each color you are going to put in the bag and what the theoretical probability of drawing the color will be (answers will vary.) (Answers will vary.) Here is one possibility. a. Blue: P(B)__1/2 _____ and actual number of blue _____400______

b. Red: P(R)___1/4_____ and actual number of red ______200______

c. Green: P(G)__1/8____ and actual number of green _____100_______

d. Yellow: P(Y)_1/16__ and actual number of yellow ____50________

e. Purple: P(P)__1/40___ and actual number of purple ____20_______

f. Pink: P(P)___3/80 __ and actual number of pink ______30______

g. To check your answer, the sum of the fractions should be _______. Explain.

h. To check your answer, the sum of the marbles should be _______. Explain.

16. Order the following fractions from least to greatest. Place and label the fractions on the number line

below. Explain how you decided where the fractions would be placed on the number line. What was your method? Explanations will vary.

Spiral Review:

17.

(

)

18. ( ) 38

19. | | | | 10

20.


1.1A Extra Practice: Probably Probability Name: Period:

This should not be an optional activity, rather can be inserted as extra in or out of class practice anytime within section 1. Directions: Follow each set of instructions below; write each answer as a simplified fraction, decimal and percent. Find the probability of each event happening if the spinner is spun once.

1) P (9)

2) P (multiple of 2)

3) P (even number)

4) P (prime number)

5) P (number < 8)

6) P (factor of 8)

7) Given an example of a spin that has a probability of

. Explain.

Example: P(4, 6) =

A laundry basket contains 3 red socks, 5 orange socks, 4 blue socks, and 8 black socks. Without looking, choose a sock. What is the probability for each event?

8) P (orange)

9) P (red)

10) P (not red)

11) P (white) 0

12) What do you notice about numbers 9 and 10? Explain.

The sum of the probabilities is one. You will either get a

red sock or not a red sock. No other option is available.

If you roll a die and toss a dime, what is the probability of each event occurring? Start by listing out all the possible outcomes. List: 1H, 2H, 3H, 4H, 5H, 6H, 1T, 2T, 3T, 4T, 5T, 6T

13) P (1, head)

14) P (2, tail)

15) P (6, heads or tails)

16) P (even, tail)

17) P( odd, heads or tails)

18) P (even, heads and tails)


1.1B Homework: Probability*

Name: Period

Write all probabilities as a fraction, decimal and percent. 1.

a. What is the sample space when flipping a coin (heads or tails) FOUR times? {HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, TTTT}

b. How many total possible outcomes are there? Justify by showing your Fundamental Counting

Principle work. 16 possible outcomes

c. Draw a tree diagram representing this situation. Allow students to use whatever model they choose to compute the sample space. Have students display their models to the class and explain how they systematically ensured they found all possible outcomes. Connect the outcomes from the model to the idea of ―theoretical probability.‖ 2. Based on #1, what is the theoretical probability, written as a simplified fraction, decimal, and percent,

that you:

a. Get HEADS for all four flips?

b. Get HEADS at least once in four flips?

c. Get HEADS exactly three times in four flips?

3. Seek and Win The fast food chain, Macduff’s, is running a contest. With every order, you get a card which has 12 covered circles. You can scratch off up to four circles. You win if 3 or more palm trees are revealed, but lose if 2 or more crabs are revealed. If you win, you can then scratch off one of the three squares (on the shell) to reveal what you have won. One of the cards is shown below with all the circles and all the squares revealed. Macduff’s wants the game to be both fun to play and relatively easy to win. a. What is the ratio of palm trees to crabs? 2 to 1

If all the circles are then covered up, find the probability (as a simplified fraction) that your first choice is:

b. P(revealing a palm tree)

c. P(revealing a crab)


Assume that you revealed a palm tree on your first go, then on the second go, find the probability (as a simplified fraction) your second choice is:

d. P(revealing a palm tree)

e. P(revealing a crab)

4. Draw a tree diagram illustrating the outcomes of throwing two 6-sided dice. 5. Two dice are rolled. How would the sample space for the product of two

dice be the same/different from the sample space of the sum of two dice? Use the tree diagram above to find the probability that this sum shows. Write your answer as a simplified fraction, decimal, and percent.

6. P(5 or 11)

7. P(less than 8)

8. P(1) 0 9. P(at most 7)

Answer the following questions using your knowledge of probability. Hint: A tree diagram may help. 10. Three coins are tossed. Find the probability (as a simplified fraction) of obtaining the following: a. at least two tails b. exactly 1 tail c. at most 2 heads

11. You have one penny, one nickel, one dime, and one quarter in your pocket. You select two coins at

random. What is the probability (as a simplified fraction) that you have taken at least 25 cents from your pocket?

Spiral Review:

12. Find the area of a rectangle with a length of 10 inches and a height of 4 inches. 40 in2

13. Simplify: 24

14. Simplify: ( )

8

15. Use a bar model to represent

.

See Tree Diagram off to the right as an example of the answer.


1.1C Homework: Probability and Fair Game?* Name: Period:

Express all probabilities as a simplified fraction, decimal, and percent. 1. Jenn told her friend Alice to choose what she wants to do to celebrate her birthday. Alice gets to pick

the restaurant and an activity for the day. Jenn will choose a gift for her. The local restaurants will include Mexican, Chinese, or Italian. The activities Alice can choose from are Putt Putt, bowling, or movies. Jenn will buy her either candy or flowers.

a. How many outcomes are there for these three decisions? 18

b. Draw a tree diagram to illustrate the choices and their associated costs.

Cost of Dinner for Two Activity Cost for Two Gift Cost

Mexican - $20 Putt Putt - $14 Flowers - $25

Chinese - $25 Bowling - $10 Candy - $7

Italian - $15 Movie - $20

2. If all the possible outcomes are equally likely, what is the probability that the celebration will cost Jenn

at least $50?

3. What is Jenn’s maximum cost for the day? $70 4. What is Jenn’s minimum cost for the day? $32 5. To the nearest dollar, what is Jenn’s average cost for this day? $51

6. What is the probability that the day costs exactly $60?

7. What is the probability that the day costs under $40?

8. A bag of marbles contains 3 red marbles, 5 blue marbles, and 2 yellow marbles.

Start


a. What is P(red)?

b. What is P(blue)?

c. What is P(yellow)?

d. What is the most likely outcome when drawing a marble out of the bag? Explain. Blue, P(B) is greater than either P(R) or P(Y)

e. What is the least likely outcome when drawing a marble out of the bag? Explain. Yellow, P(Y) is less than either P(R) or P(B)

f. Have you been computing theoretical or experimental probabilities? Explain. Theoretical

9. A spinner contains three letters of the alphabet.

a. How many outcomes are possible if the spinner is spun 3 times? 27

b. What is the sample space when the spinner is spun 3 times? {TTT, TTV, TVT, TTH, THT, TVH, THV, HHH, HHV, HVH, HHT, HTH, HVT, HTV, VVV, VVH, VHV, VVT, VTV, VHT, VTH, TVV, THH, HVV, HTT, VHH, VTT}

c. What is the probability of getting exactly one H?

d. What is the probability of getting exactly two V’s?

e. What is the probability of getting three T’s?

f. What outcome(s) is/are most likely for 3 spins? All individual outcomes are equally likely with a 1/27 probability.

Spiral Review: Simplify the following

10.

11. (5.2)(3.25) 16.9

12. 24

13. | | 17


Section 1.1 Review Name: Period:

Be sure to write all fraction answers in simplest form. Write probabilities as simplified fractions unless otherwise instructed.

1. A company manufactures phones. The quality control department checks 700 phones and

discovers that 72 of them are defective. What is the probability that a phone is not defective?

( )

2. After 40 spins, Chris landed on blue 16 times.

a. What is the experimental probability of landing on a

blue?

( )

b. What is the theoretical probability of landing on a

blue?

( )

c. What are all of the different possible outcomes of 1

spin? {Red, Blue, Green, Orange, Yellow}

3. Create a table showing the sums of two six-sided dice.

a. How many different outcomes are possible? 36 outcomes

b. What is the probability of rolling a sum of 10? ( )

c. What is the probability of the sum being less than 4? ( )

d. What type of probability is this? Theoretical Probability

e. What is the probability of the sum being at least 10? ( )

4. Chloe and Angelo rolled a pair of dice ten times. Their sums are recorded below.

Roll # 1 2 3 4 5 6 7 8 9 10

Sum 5 3 7 9 7 8 6 7 5 9

a. What is the experimental probability of rolling a sum of 9? ( )

b. Explain why the theoretical and experimental probabilities for rolling a sum of 9 are the

same/different.

The experimental probability is

and the theoretical probability is

. The experimental

probability is greater than the experimental probability. An experiment will not always mimic

theoretical.

5. There is a bag of pink, purple, and black marbles. There is an 18% possibility of randomly picking

a pink marble and a 60% chance of randomly picking a black marble. What is the probability of

picking a purple marble? Write your answer as a fraction, decimal, and percent.

100% - 18% - 60% = 22%

( )


6. Talia has a bag containing 5 black tiles, 6 pink tiles, and 4 yellow tiles. If one tile is drawn and then

replaced:

a. What is the sample space of one draw? {black, pink, yellow}

b. What is the probability that Talia will pick a pink tile? ( )

c. What is the probability that Talia will pick a black or yellow tile? ( )

d. If Talia picks a tile from the bag and returns it 30 times, predict how many times you would

expect her to pick a black tile. Explain your reasoning.

( )

, Talia can expect to get a black marble 10 times out of 30 draws. If the

number of trials is doubled, then the number of times black can be pulled is also doubled.

7. Place the fractions on the number line below. Be sure to label your points.

{

}

8. Order the fractions from least to greatest.

{

}

9. Lulu has a box full of magnets. The box has 2 yellow magnets, 7 black magnets, 4 red magnets, 6

pink magnets, 3 green magnets, and 8 brown magnets. If Lulu is randomly choosing magnets out of the box one at a time and then returning them, circle all of the statements that are true. Show your reasoning for each part.

A. Lulu has a

chance of picking a pink magnet.

B. Lulu will more likely pick a brown magnet than a red magnet.

C. Lulu has a

chance of picking a magnet that is NOT brown.

D. Lulu has an equal chance of choosing any color magnet.

E. Lulu has a

chance of choosing a green magnet.

10. Ryan flips three coins.

a. Create a tree diagram to show all of the possible outcomes.

b. How many different outcomes are possible? 8 outcomes

c. What is the probability of getting at most 2 tails? ( )


1.2A Homework: Equivalent Fractions* Name: Period:

1. Simplify each fraction. Draw a bar model for questions ―a‖ and ―b‖ to show equivalent fractions.

a.

b.

c.

d.

e.

f.

2. Write an equivalent fraction. Draw a bar model for questions ―a‖ and ―b‖ to show the equivalent

fractions. If you need more space to draw the bar models, use the back of this page.

a.

b.

c.

d.

e.

f.

3. Change each fraction to a mixed number. Draw a bar model for questions ―a‖ and ―b‖. If you need

more space to draw the bar models, use the back of this page.

a. 3

b. 7

Key for B on next page.

c. 2

4

6

3

9

10

18

14

21

9

21

7

35

1

2 6

2

5 15

2

3 15

4

7 14

5

8 24

3

4 24

10

3

29

4

25

9


d. 2

e. 2

f. 3

Answer to 3b. 4. Complete the table:

Decimal Fraction in Simplest Form Percent

A. 0.45

45%

B. 0.25

25%

C. 0.55

55%

D. 0.4

40%

E. 0.65

65%

F. 1.25

125%

G. 0.96

96%

H.

I. 0.13

13%

J. 0.02

2%

K. 0.04

4%

25

12

20

7

19

5


1.2B Homework: Rational Number Ordering and Estimation* Name: Period:

1. Peter has one half dollar, one quarter, and two dimes. Express the total value as a fraction of a dollar.

2. Rick pays five cents of every dollar he earns to the government for taxes. Jason pays 1/20 of his

earnings for taxes. Do they pay equivalent fractions of their earnings for taxes? Explain.

Yes,

or 5%

3. In an 8th grade class of 30 students, there are 15 students who can speak both Spanish and English.

There are 12 others who can speak both French and English. The rest speak only English.

a. What fraction of the class can speak Spanish?

b. What fraction of the class can speak French?

c. What fraction of the class can speak English? 1

d. What fraction of the class can speak a second language? 9/10

4. Ned jogged for one-third of a mile, Trey jogged for one-half of a mile, and Steven jogged for one-fifth of

a mile. Order these distances from least to greatest. What is the sum of their distances?

Total:

miles

5. A magazine sells one advertisement that is seven-eighths of a page and another advertisement that is five-sixths of a page. If both advertisements cost the same amount, which one is the better deal? 7/8 is a better deal because it is a larger ad for the same cost

6. Derek’s dad travels one and a half hours each way to work. What part of his day is spent commuting to and from work? 1/8 of his day

7. Order the following set of numbers from least to greatest:

8. Order the following set of numbers from least to greatest:

10

9. Plot each rational number on the number line. Write them in order from least to greatest:


ESTIMATE each of the following. Justify your answer with either words or a model. Indicate if your estimate is larger or smaller than the exact answer.

Fraction ≈ Decimal ≈ Percent Justification

10.

% This is close to

. The estimate is a little high.

11.

0.9 90% This is close to

. This estimate is a little low.

12.

% This is close to

This estimate is a little low.

Fill in the blank with <, >, or =. Justify each with a picture or number-line or explanation.

13. < 1.2 Justification:

= 1.16 < 1.2

14. > -1.2 Justification:

= -1.16 > -1.2

15. -2.34 > Justification: -2.34 >

=

16. = Justification:

=

17. < -3.94 Justification:

= -3.95 < -3.94

Spiral Review:

18. Write

as a decimal and percent.

19. Simplify: 114.5 – (6.3 + 2.7)2 33.5

20. Use =, <, or > to make a true statement. Show your work. __=___ ( )

21. Simplify:

16

25

41

25

41

25

42

11

5

110.45

193

20


1.2C Homework: Probability, Fractions, Percentage, & Ratio* Name: Period:

Express each fraction as a percent.

1. 20%

2. 90%

3. 15%

4. 40%

Express each percent as a fraction in simplest form. 5. 60% =

6. 80% =

7. 75% =

8. 10% =

9. 5% =

10. 25% =

Solve each using a model. Show your work: 11. Find 80% of 150. 120 12. Find 40% of 40. 16 13. What percent of 30 is 15? 50%

14. What percent of 80 is 60? 75%

15. 40 is 8% of what number? 500 16. 60 is 30% of what number? 200

1

5

9

10

3

20

2

5

40

8 8 8 8 8

15 15

30

150

30 30 30 30 30

80% =

80

20 20 20 20

75% =

500

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

8% =

200

20 20 20 20 20 20 20 20 20 20

30% =

, 60 into 3 parts is 20 per part


Use a model to ESTIMATE each of the following. Indicate if your estimate is slightly higher or lower than the exact answer. Answers may vary. 1. Estimate 74% of 24.

18, high estimate 24

6 6 6 6

75% =

2. Makayla got a score of 77% on her English final. If there were 48 questions on the test, approximately

how many questions did she get right? Assume that each question is worth one point. 36 questions, low estimate 48

12 12 12 12

75% =

Use a model to SOLVE each of the following. Answer in a complete sentence 3. Milo can run 10 miles in 60 minutes. If he needs to reduce his time by 20%, how many minutes does

he have to take off his time? 12 minutes 60 minutes

12 12 12 12 12

20% =

20. The bike store has a bicycle regularly priced at $660. Tom negotiated a

% discount. How much

money will Tom save buying the bike on sale? How much will he have to pay for the bike? Saved: $220, Pay: $440

$660

220 220 220

% =

Spiral Review:

21. Write

as a decimal and percent.

22. How does a number line help you order

fractions? 23. Compare these two fractions using < or >. Explain.


1.2D Homework: Rational Numbers in Applications with Models* Name: Period:

Use a model to fill in the table below:

Fraction Decimal Percent SHOW YOUR WORK HERE:

1.

0.6 60%

2.

0.16 16%

3.

0.15 15%

4.

%

5.

0.45 45%

Use a model to solve each problem. 6. Fletcher paid $287.50 in taxes this year to his school district. This year’s taxes were a 15% increase

from last year. What did Fletcher pay in school taxes last year?

The greatest common factor of 100 and 115 is 5. There are 23 intervals of 5% in 115% and 287.5/23 = 12.5 So 12.5 corresponds with 5%. There are 20 intervals of 5% in 100% and 20(12.5) = 250. Fletcher paid $250 in school taxes last year.

7. Marisa earned money for helping a local business with organizing their inventory. She spent half of

her earnings on accessories for her phone, and half of the remaining money on a gift for her mother. If she has $15 left, how much did she make organizing the inventory? $60

$15 was remaining. It is ½ of the remaining, so was $30. $30 is ½ of the total, so the total is $60.

3

5

4

25

2

3


8. Pedro has $80 left from the money he earned during the summer helping at his father’s business. He

had spent of his earnings on climbing equipment, on camping gear and of the remainder on

entertainment during the summer. How much did he earn during the summer? 80 x 2 x 3 = $480 Pedro’s Total Earnings

Climbing Equip. Camping Gear Entertain-ment $80 Left

1/3 of Earnings 1/3 of Earnings ½ of the remainder on entertainment 9. A snowmobile manufacturer claims that its newest model is 15% lighter than last year’s model. If this

year’s model weighs 799 pounds, how much did last year’s model weigh?

15% lighter than last year’s model means 15% less than 100% of last year’s model’s weight, which is 85%. The greatest common factor of 85 and 100 is 5. There are 17 intervals of 5% in 85% and 799/17 = 47, so 47 corresponds with 5%. There are 20 intervals of 5% in 100% and 20(47) = 940. So, last year’s model weighed 940 pounds.

10. Nick estimates that 50% of his income goes toward living expenses (rent, utilities and food). Of the rest, 50% goes to paying for his car and 25% of what is left goes to his other expenses. If Nick has $300 left at the end of the month, how much does he earn?

(300 ÷ 3) × 4 × 2 × 2 = $1600 Nick’s Total Earnings

Living Expenses Car

50% of income $300 left at the end of the month 50% of the rest 25% to other expenses

1

3

1

3

1

2


11. Urivan earned $360 helping his grandfather at his business. He spent of his earnings on a gift for

his mother and put of the rest into a savings account. How much does Urivan have left over for fun?

(360 ÷ 4) x 3 ÷ 3 = $90 Urivan earned $360

Gift for Mom

For Fun

¼ of his earnings 2/3 of the rest in savings account 12. A color of paint used to paint a race car includes a mixture of yellow and green paint. Scotty wants to

lighten the color by increasing the amount of yellow paint by 30%. If a new mixture contains 3.9 liters of yellow paint, how many liters of yellow paint did he use in the previous mixture?

The greatest common factor of 130 and 100 is 10. There are 13 intervals of 10% in 130% and 3.9/13 = 0.3 and 0.3 corresponds to 10%. There are 10 intervals of 10% in 100% and 10(0.3) = 3. So, the previous mixture included 3 liters of yellow paint.

13. Julia found a great pair of boots for $240, but that was more than she wanted to spend. A few months

later they were on sale for 40% off. She searched online and found a coupon for an additional 25% off the sale price. How much will she pay for the boots? $108

1

4

2

3

$96 off $36

40% off Sale Price = $144

$240 Boots

$36 $36 $36


14. Bjorn is a supervisor and spends 20% of his typical work day in meetings and 20% of that meeting time in his daily team meeting. If he starts each day at 7:30 a.m., and his daily team meeting is from 8:00 a.m. to 8:20 a.m., when does Bjorn’s typical work day end?

20 minutes is 1/3 of an hour. Bjorn spends 1/3 hour in his daily team meeting so 1/3 corresponds to 20% of his meeting time. There are 5 intervals of 20% in 100% and 5(1/3) = 5/3. So, Bjorn spends 5/3 hours in meetings. 5/3 of an hour corresponds to 20% of Bjorn’s work day.

There are 5 intervals of 20% in 100% and 5(5/3) = 25/3. So, Bjorn spends 25/3 hours working. 25/3 hours = 8 1/3 hours. Since 1/3 hour = 20 minutes, Bjorn works a total of 8 hours 20 minutes. If he starts at 7:30 a.m., he works 4 hours 30 minutes until 12:00 p.m., and since 8 1/3 – 4 ½ = 3 5/6, Bjorn works another 3 5/6 hours after 12:00p.m. 1/6 hour = 10 minutes and 5/6 hour = 50 minutes. So, Bjorn works 3 hours 50 minutes after 12:00p.m., which is 3:50 p.m. Bjorn’s typical work day ends at 3:50 p.m.

Spiral Review: Simplify the following expressions:

15. ( ) 10

16. ( ) 158

17. 3(2)2 12

18. Round to the hundredths place: 132.934 132.93 19. Round to the tenths place: 429.372 429.4

20. Round to the tens place: 285.286 290


Section 1.2 Review Name: Period:

Show all work. Be sure to write all fraction answers in simplest form. Read the directions carefully! Write each in fraction, decimal, and percent form.

1.

.0625 = 62.5%

2. 2.45

= 245%

3. 38%

0.38 =

4.

=

5. 0.006

0.6% =

6. 82%

0.82 =

For #7-12, solve using a model. Show all work. Answer in a complete sentence. 7. What is 40% of 85? 34 8. What percent of 60 is 15? 25%

9. 45 is what percent of 270?

10. What is 150% of 40? 60

11. You get 75% correct on a science quiz with 80 questions. Assuming each question is worth 1 point each, how many questions did you get correct? 60 questions correct

12. A) A blue sweater normally sells for $120. George has a coupon he can use to get 40% off the original price. How much will George have to pay for the sweater? $72 B) The store that sells the sweater wants customers to come in early so they decide to offer an Early Bird

Special. Anyone shopping before 10:00am can take an additional 15% off their total bill. If George gets to the store early, how much will he have to pay for the sweater? $61.20

13. Which of the following is NOT equivalent to the other three? Explain your reasoning.

A)

B) 6.5% C)

D) .065


14. Plot the following on a number line: 1.65, -0.4,

,

, .25

15. Using the bar model below, name the two equivalent fractions being shown.

16. Find the equivalent fraction. Draw a bar model to show the equivalence between the original fraction

and the new one.

? = 16

17. At Nellie’s BBQ restaurant, 15 out of 60 customers ordered their BBQ extra spicy. What percent did

not order the extra spicy BBQ? Draw a model to find the solution. 75%

18. At Kentucky Fried Chicken, customers ordered either extra crispy, crispy, original, or grilled chicken.

of the customers ordered extra crispy chicken, 20% ordered crispy chicken, and

ordered original

chicken. If 75 customers ordered grilled chicken, how many total customers were there? 500 total customers

Spiral Review: 19. Evaluate if a = 4 and b = 2:

A) ab

8 B) 4a – b

14 C) a2 – b2

12

20. What is the probability of drawing a red marble out of a bag with 6 green marbles, 4 purple marbles, 3

black marbles, and 2 red marbles?

( )

, -0.4, .25,

, 1.65


1.3A Homework: Model Percent and Fraction Problems* Name: Period:

Use a model to answer #1-3 below. Then write a number sentence that reflects your model and answer. For #4-11, use a method of your choice to solve. Show your work. 1. A) Last year Stella harvested 42 tomatoes from her backyard garden. This year, her harvest increased

by 1/3. How many tomatoes did she harvest this year? 42 ÷ 3 + 42 = 56 tomatoes B) If next year, she harvests 1/3 less than this year, will the number of tomatoes harvested return to 42? Why or why not? Justify your answer. No A)

B)

2. Adam is taking care of a vacant lot in his neighborhood. There are approximately 64 dandelions in the

lot. He decided to try a homemade weed killer his grandmother suggested. Five weeks later, the dandelions have decreased by 75%. Approximately how many dandelions are in the vacant lot now?

16 dandelions

3. Maria is learning to play golf. She has been working particularly hard on driving. Before lessons, her

drives average 240 yards. After her first lesson, her drives increased 25%. After her second lesson, her new average increased 25%. How far are her average drives after her two lessons?

375 yards 4. Two stores have the same necklace on sale. The original price of the necklace is $200. At store AAA,

it’s on sale for 30% off with a rewards coupon that allows the purchaser to take an additional 20% off the sale price at the time of purchase. At store BBB, the necklace is on sale for 50% off. Will the price for the necklace be the same at both stores? If not, which store has the better deal?

AAA: sale price $140, with rewards $112

BBB: sale price $100

BBB has the better deal.


5. Two schools start with 1000 students. The first school’s enrollment increases 20% in 2012 and then decreases 20% in 2013; the second school’s enrollment stays constant in both 2012 and 2013. Which school has the most students now?

First school: 2012 enrollment 1200 students, 2013 enrollment 960

Second school: 2012 enrollment 1000 students, 2013 enrollment 1000

The second school has more students in 2013 6. Twelve percent of the total worth of a retirement fund is invested in oil stocks. If $45 million is invested

in oil stocks, what is the total worth of the fund? $375 million

7. A shirt costs $8.00 to manufacture. If the designer, distributor, and wholesaler each add a 50%

markup of the price paid, what is the final price of the shirt? $27

8. The Sound Off Siren Company tests every fifth siren for sound quality and every eighth siren for

mechanical quality. The daily output is 350 sirens. a. What percent is tested for sound quality?

20%

b. What percent is tested for mechanical quality?

12.5%

c. What percent is tested for both types of quality at the same time?

2.5%

9. A bag of candy contains 300 pieces of which 28% are red. a. How many pieces are NOT red?

216 pieces are not red

b. What is the probability that you pull a red piece of candy out?

P(red) = 28% or 0.28


10. Sydney inflated 24 balloons for decorations at the middle school dance. a. If Sydney inflated 15% of the balloons that need to be inflated for the dance, how many balloons

are there in total?

160 balloons total

b. What is the probability that a balloon chosen at random is a balloon that Sydney did not inflate?

P(balloon Sydney did not inflate) = 85% or 0.85 11. Haley is making admission tickets to the middle school dance. So far she has made 112 tickets on

purple paper, and her plan is to make 320 tickets total. Haley ran out of purple paper and needs to make the rest on gold paper.

a. What percent of the admission tickets has Haley produced so far?

35%

b. What is the probability that a ticket pulled at random is purple?

P(purple) = 35% or 0.35 or

Spiral Review: Write all probabilities as fractions, decimals and percentages. 12. Suppose you were to roll a fair number cube once, then flip a coin. List the sample space.

{1H, 2H, 3H, 4H, 5H, 6H, 1T, 2T, 3T, 4T, 5T, 6T}

13. What is the P(2, H)?

14. What is the probability that you would roll an even number and flip heads?

15. What is the probability that you would roll an even number or flip heads?

16. Find the area of the triangle below: 40 m2

5 m

16 m


1.3B Homework: Transition to Numeric Expressions* Name: Period:

For each problem below, use a model to answer the question.

Context Model Fraction Change

Fraction of

Original

Percent Change

Percent of

Original

1. At the beginning of the year there were 32 students in Ms. Herrera’s class. There are now 36 students in her class.

They increased

by

They

have

their original

class size

They increased by 12.5%

They have

112.5% their

original class size

2. During the school year, Jose worked 15 hours a week. During the summer he works 30 hours a week.

Hours

increased

by

.

Jose

works

as much

Hours increased by 100%

Jose works

200% as much

For each question write a fraction change expression and percent change expression.

Context Fraction Change Expression Percent Change Expression

3. In a small town in Utah, 40,000 homes use to have land-line phones. Now 35,000 homes have land-line phones.

( ) (

)

(

)

( ) ( ) ( )

4. A small business’s profits in 2011 were $120,000. In 2012 they were $150,000

( ) (

)

(

)

( ) ( ) ( )

For each question, write the appropriate expression(s) and solve. State your answer in a complete sentence. 5. The weight of a granola bar was decreased by 20%. What is the new weight if the original weight was

4.5 oz? 3.6 oz

6. The number of seats on the new Jet Blue airliner is a 36% increase over the old model. The old plane

seated 374 passengers. How many passengers will the new model seat? 508 or 509 passengers

7. Last year, the population of Springfield grew from 1250 to 1300. If the population of the town grows by

the same percent this year, what will the new population be? 1352 8. Contributions to The Cougar Pep Band were 10% greater in 2014 than 2013. In 2013, contributions

were 15% greater than they were in 2012. If contributions in 2012 totaled $4355, what was the total in 2014? 5509 or $5510 in 2014

9. The selling price of a skateboard that had sold for $220 last year was increased by 15%. What is the

new price? $253


Module 1 Review Name: Period:

Note to Teachers: This is a rather long assignment, so you may want to consider breaking it up into two assignments, or just giving students an extra day to complete it. Read each set of directions carefully. You must show ALL of your work to earn credit. Be sure to write all fraction answers in simplest form. Good luck!

1. Six different decimals are shown: Which of the following fractions are equivalent to one of the six decimals? Select all that apply.

a.

b.

c.

d.

e.

f.

2. Miki goes jogging every morning. In which of the following situations does Miki jog a total distance of 5

miles for Monday and Tuesday combined? Select all that apply.

a. On Monday, Miki jogs 4 miles. On Tuesday, Miki jogs 25% of the distance she jogged on Monday.

b. On Monday, Miki jogs 2 miles. On Tuesday, Miki jogs 150% of the distance that she jogged on

Monday.

c. On Monday, Miki jogs

miles. On Tuesday, Miki jogs 1.5 miles more than on Monday.

d. On Monday, Miki jogs

miles. On Tuesday, Miki jogs 2.25 miles more than on Monday.

3. Marco’s Quality Sandals can make 840 sandals in an 8-hour period. Due to strict quality control

standards, the company must then discard an average of 2.5% of their sandals that contain manufacturing defects. a. How many sandals does Marco’s discard in an average 24-hour day? Show your work.

Marco discards 63 sandals in an average 24-hour day 840 x 3 = 2520 sandals; .025 x 2520 = 63 sandals

b. Marco’s received an order of 39,312 sandals from a large retail store. How many full 24-hour days will it take Marco’s to make the sandals with this discard rate? It will take 16 days for Marco to complete the order.

39312/(2520 – 63) = 16 days

4. A small furniture manufacturer sells their tables to a distributor. The distributor then sells the tables to a variety of furniture stores. The cost for the manufacturer to make their tables is $400. a. The manufacturer wishes to make a profit of at least $160 on each table. What minimum

percentage should the manufacturer use to mark up its price? A markup of at least 40%. 160/400 = 40%

b. The price markup for the distributor and furniture store is shown in the table below:

Markup

Distributor 15%

Furniture Store 35%

If the manufacturer makes $160 on every piece of furniture it sells, what is the final price of the furniture? The final price of the furniture is $869.40 560 x 0.15 = $84; 560 + 84 = $644 644 x .35 = $225.40; 644 + 225.40 = $869.40


5. James counts the hair colors of the 22 people in class, including himself. He finds that there are 4 people with blonde hair, 8 people with brown hair, and 10 people with black hair. What is the probability that a randomly chosen student in the class does not have red hair? Explain. There is 100% probability that a randomly chosen student does not have red hair, because all of the students in that class have some other color of hair and there are no students with red hair.

6. A spinner has four equally sized sections lettered A, B, C, and D. The table shows the results of

several spins. Find the experimental probability of spinning each letter as a fraction in simplest form, a decimal, and a percent.

A: ______

__________ B: __________

___________

C: _________

____ D: ___________

_____________

What is the theoretical probability for each of the spinner’s sections in number 6? How does the theoretical probability for each letter compare to the experimental probabilities?

The theoretical probability for each of the spinner’s sections is .25 or

. The theoretical probability is

higher for B and D, but lower for A and C than their experimental probabilities. 7. A soccer coach claimed that, on average, only 80% of the team comes to practice each day. The table

shows the number of students that came to practice for 8 days.

Days 1 2 3 4 5 6 7 8

Number of Students 18 15 18 17 17 19 20 20

If the team has 20 members, how many team members would come to practice daily to uphold the coach’s claim? Was the coach’s claim accurate? Explain your reasoning. For the 80% average to be true, there would need to be 16 players coming to practice on average each day. The data from the table indicates that the average for those 8 days is 18 players coming on average each day, which is 90% So, the coach is underestimating the average percentage of players who come to practice each day.

8. What is the probability of not rolling a 5 on a standard six-sided die? ( )

9. How many possible outcomes are there for rolling three standard six-sided dice? 6 x 6 x 6 = 216 possible outcomes

10. When rolling three six-sided standard dice, what is the probability of rolling a sum of two? Explain your

answer. The probability of rolling a sum of two on three dice is zero because the smallest sum that can be rolled is 3, since the smallest number on each die is 1.

Letter A B C D

Frequency 14 7 11 8


11. A jar contains 10 blue marbles, 2 yellow marbles, and 8 red marbles.

a. If you were to draw one marble from the jar, what is the theoretical probability, as a fraction, that you’d choose a yellow marble? What about blue? And red?

P(Yellow): _____

___ P(Blue): ______

____ P(Red): _____

_______

b. If Max picks a marble from the bag and returns it 80 times, predict how many times you would

expect him to pick a red marble. Explain your reasoning. No matter how many times he chooses a marble from the bag, as long as it is replaced, the probability of choosing a red marble remains the same. Out of 80 attempts, I’d predict he’d

pick a red marble 32 times, which is

of the 80 attempts.

c. What is the sum of the probabilities that you found in part a? Explain why this answer makes sense and what it represents.

The sum of the probabilities is

or 1 or 100%. This makes sense because you’re either

going to pick a yellow, blue, or red marble 100% of the time. There are no other color options.

12. In a different jar of colored marbles, there are blue, red, yellow, and green marbles. There is a 40%

possibility of randomly picking a blue marble, a 5% chance of choosing a red marble, and a 30% chance of randomly picking a yellow one. What is the probability of picking a green marble? The probability of picking a green marble is 25%.

13. Complete the table below. Fractions must be in simplest form.

Decimal Fraction in Simplest Form Percent

0.65

65%

1.05

105%

1.04

104%

Solve. Use a model to show your work. 14. What percent of 400 is 20? 5% 15. Find 45% of 12. 5.4 16. 20% of c is 24. What is c? 120 Find the percent of change from the first number to the second number. Remember to label your answer as an increase or decrease. 17. 60 to 36 40% decrease 18. 50 to 75 50% increase 19. A customer paid $12 in tax. His tax rate was 5%. Find the dollar amount of his purchase. $240 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12

5%tax

$240


20. A bicycle that usually sells for $240 is on sale for 15% off. Find the sale price.

12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12

21. Mark the location of

on the number line shown below.

22. Draw a model that represents the fraction .

For #23 – 24, read the word problem carefully and analyze the model. Determine the following: a. Does the model accurately represent the problem? b. If no, explain why it is incorrect, fix it, and solve the problem. c. If yes, use it to solve the problem. 23. 15% of the number of people who attended a concert arrived late. If 30 people arrived late, find the number of people who attended the concert.

24. At the Natural History Museum, 40% of the visitors are children. There are 36 children at the museum. How many visitors altogether are at the museum?

100% 15%

30 people

? people

100% 40%

? visitors

No, the model doesn’t accurately represent the Yes, the model accurately represents the problem. problem because the 30 people and the 15% The answer is 90 visitors. should be labeled on the same section. 100%

15% 200 people

5

7

15%off

$204

30 people

36 children

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