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Name Date Period

PLAN Review Packet

Decimals and Percents: Review

Places: 6512.38749 =

6 is in the thousands place. Value of the digit 6 is six thousand.

7 is in the thousandths place. Value of the digit 7 is seven thousandths.

_____ is in the tens place. Value of the digit ___ is ___________.

_____ is in the tenths place. Value of the digit ____ is __________.

Comparing Decimals: Compare 0.34203 and 0.34198

(1) start at the greatest place value, 0 = 0

(2) compare digits left to right, 3 = 3

(3) continue until digits differ, 4 = 4

(4) compare the different digits, 2 > 1

(5) the greater digit signifies the greater decimal. 0.34203 _____ 0.34198

Rounding Decimals Round 0.34198 to the thousandths

1) locate the place you are rounding to 0.34198

2) look at the digit to the right of that place 0.34198

3) if the digit is less than 5, round down

if the digit is greater than 5, round up rounded to 0.342

Percent Definition

Percent means out of one hundred. 15 % means 15 out of 100

1.5 % means 1.5 out of 100

Decimals to Percents to Fractions

To write a decimal as a percent: (1) move the decimal point two places to the right

(2) write the percent sign

0.78 = 78 % 0.0524 = _________ % 28.634 = _____________

To write a percent as a decimal: (1) move the decimal point two places to the left

(2) write zeros if necessary

36 % = 0.36 7 % = 0. 386.29 % =

To write a fraction as a percent: (1) divide the numerator by the denominator = decimal

(2) follow the procedure to turn decimal into a fraction

¼ = 0.25 = 25 % ¾ = 0.75 = _________ %

To write a percent as a fraction: (1) write the percent with 100 as the denominator

(2) simplify the fraction if possible

56 % = 56/100 = 14/25 84 % = ______/100__ = ______/______

Decimals and Percents: Practice

Write < or > in the blank.

1. 0.32 _____ 0.289

2. 1.91 _____ 9.1

3. 20.347 _____ 20.351

4. 408.246 _____389.978

5. 16.4 _____ 16.43 _____16.432

6. 0.56893 _____ 0.56981 _____ 0.5699

Write the value of each digit in the numeral 45.2031

7. 1 ____________________

8. 2 ____________________

9. 3 ____________________

10. 4 ____________________

11. 5 ____________________

12. 0 ____________________

Round 3,245.60537 to the

13. thousandths place ____________________

14. thousands place ____________________

15. hundredths place ____________________

16. tenths place ____________________

Complete the table. The three numbers across each row should be equal.

|Fraction |Decimal |Percent |

|17. |18. |18 % |

|19. |0.036 |20. |

|5/8 |21. |22. |

|23. |24. |0.84 % |

25. Jennifer ran 3/8 of a mile. What percent of a mile did she run?

26. Eric works out 5 days out of the week and he jogs on 4 of those days. On what percent of the workout days does he jog?

Decimals and Percents PLAN—Type Problems

27. The following shows a list of people and their times for a 100-meter dash.

| Name |Time |

|Nathan |11.63 seconds |

|Andy |11.15 seconds |

|Julia |11.16 seconds |

|Thomis |11.21 seconds |

|Ann |11.28 seconds |

Who had the fastest time?

a. Nathan

b. Andy

c. Julia

d. Thomis

e. Ann

28. What is the sum of the digits found in the tenths place and in the ten-thousandths place of 10,324,961.76?

a. 5

b. 7

c. 10

d. 15

e. 16

29. The symbol < can be used to fill in the blank to make which choice true?

a. 345.982 ____ 345.992

b. 356.792 ____ 356.782

c. 272.81 ____ 272.18

d. 3.9182 ____ 3.9082

e. 576.91 ____ 567.91

30. Leticia works in the personnel department at a company. Two out of every five people she interviews are female. What percent of the people that Leticia interviews are female?

a. 20%

b. 30%

c. 40%

d. 50%

e. 60%

31. There are 8 chairs around one dining room table. Three of the chairs have arm-rests. There are 8 chairs around another table, and 7 of them have arm-rests. What percent of the 16 chairs have arm-rests?

a. 47.5%

b. 50%

c. 55%

d. 62.5%

e. 70%

32. On one math test Beth got 84% of the questions correct. On another test she got 6 of 15 answers correct. What is the difference between the fraction of questions Beth answered correctly on the two tests?

a. 2/5

b. 11/25

c. 13/25

d. 3/5

e. 32/75

33. Rachel wants to buy a calculator. A calculator normally sells for $80, but it is on sale for 40% off. Which expression correctly represents how to find the sale price?

a. 80*40

b. 80 – 80*(0.60)

c. 80*60

d. 80 – 80*(0.40)

e. 80*(0.40)

34. A book normally costs $50. The book is on sale for 35% off. What is the sale price of the book?

a. $17.50

b. $27.50

c. $32.50

d. $37.50

e. $45.00

Word Problem Strategies: Review

First, read the problem and highlight (or underline) key numbers and words or phrases

|Key Words or Phrases clue you into the appropriate operation to use |

|WORDS |OPERATION |EXAMPLE |

|Altogether |add |(add) Jess picked up 43 marbles, 73 sea shells and 105 pins. How many things did he pick up |

|Total |or |altogether? (Or, what is the total number of things he picked? |

|More than |multiply | |

|Multiple of | |(multiply) Fran bought seven lottery tickets every day for five days. How many tickets did |

|Increased (by) | |she buy altogether? (or, what is the total number of tickets she bought? |

|Plus | | |

|Left |subtract |How much money is left? |

|Remaining | | |

| | |How much money is remaining? |

|More |subtract |How many more people live in New Jersey than in Colorado? |

|Difference | | |

|Less than | |What is the difference between the number of people that live in New Jersey and Colorado? |

| | | |

| | |The population of New Jersey is how much less than the population of Colorado? |

|Increase |subtract |How much did the price increase from last year? |

|Go up | | |

|Grow | |NOTE: This key word may surprise you. You might think that “increase would mean to add. But|

| | |it doesn’t. To find an increase, you have to subtract the old, lower size for amount. The |

| | |same goes for “go up” and “grow.” |

|Decrease |subtract |How much did the price decrease from last year? |

|Go down | | |

|Reduce | |NOTE: You may think that if “increase” means subtraction, then “decrease” would mean |

| | |addition. But it doesn’t. To find a decrease, you use exactly the same subtraction |

| | |operation as for increase. The same goes for “go down” and “reduce.” |

|Of |multiply |(fraction) How many miles is 3/5 of the distance? |

|(particularly when used| | |

|with fractions and | |(percent) What is 43% of the original $600? |

|percents) | | |

|Each |divide |How many did each one get? |

|per |divide |What is the price per gallon? |

Then, identify what the problem is asking you to find.

Ask yourself: what is the problem asking you to find?

Next, choose a method to solve the problem (define variables and set up expression, draw picture or diagram, etc.) and solve.

Ask yourself: how do I solve the problem?

Next, set up an expression that uses the numbers and key words/phrases

Or draw a picture/diagram/etc. to explain the problem

Then, solve the problem using the expression or picture

Finally, write out your answer in a complete sentence within the context of the problem (make sure to include units).

Word Problem Strategies: Practice

Write what operation each of the following problems is suggesting and which key word clued you in.

1. How much did each one cost?

a. Operation _____________________

b. Key Word/Phrase __________________________________

2. The team gained 75 yards less by rushing this week than it did last week. The team gained 315 yards last week. How much did the team gain this week?

a. Operation _____________________

b. Key Word/Phrase __________________________________

3. It took ¾ of the summer vacation to build the addition to the kitchen. How much time was that?

a. Operation _____________________

b. Key Word/Phrase __________________________________

4. Sixty percent of the senior class did not come to the first dance. How many people came to the dance?

a. Operation _____________________

b. Key Word/Phrase __________________________________

Fill out the problem strategy forms to solve the following word problems

5. Julie measured a plant in the spring. It was 32 cm high. When she measured it in the fall it was 78 cm high. How much did the plant grow?

a. Highlight or underline the key numbers and words/phrases

b. What does the problem want us to find?

c. Set up the problem and solve

d. Explain solution in complete sentence

6. Michael was overjoyed. His uncle’s will says that he left him 2/5 of his property. The property consists of 250 acres of vacant land. How much land will Michael receive from his uncle’s estate?

a. Highlight or underline the key numbers and words/phrases

b. What does the problem want us to find?

c. Set up the problem and solve

d. Explain solution in complete sentence

7. Last year Juan paid $450 for a new TV. This year the same TV sells for 8% less. How much did the price decrease from last year? (a) Follow the steps of the problem solving strategy to complete a-d

b.

c.

d.

Word Problems – PLAN Type Problems

Follow the problem solving strategy to solve the following problems

8. Anita places one dollar in coins in her jacket pocket on Monday. Each day of the week Anita takes some of the coins and donates them to a charity box in her school’s lunchroom. Listed below are the amounts Anita donates each day.

|Day |Amount |

|Monday |$0.10 |

|Tuesday |$0.09 |

|Wednesday |$0.15 |

|Thursday |$0.07 |

|Friday |$0.20 |

How much money remains in Anita’s jack pocket at the end of the week?

a. $0.39

b. $0.41

c. $0.46

d. $0.51

e. $0.55

9. When Frank went to the store on Monday he bought 4/5 of a pound of grapes. How many ponds of grapes did Frank eat on Monday if he has 2/3 of a pound of grapes left on Tuesday?

a. 3/13

b. 2/15

c. 4/11

d. 6/17

e. 7/12

10. Jim bench-presses 225 pounds and does arm curls with a weight 1/3 the amount he bench-presses. What weight does he arm-curl?

a. 65 pounds

b. 70 pounds

c. 75 pounds

d. 80 pounds

e. 85 pounds

11. One bird chirps every 6 seconds and another bird chirps every 15 seconds. If the two birds just chirped, how many seconds will it be before the two birds next chirp at the same time?

a. 15

b. 21

c. 24

d. 30

e. 90

12. Mrs. White’s gross monthly income in $1,800. If 15% is withheld for income taxies, 7% for Social Security, and 2% for insurance, what is her net monthly income (after deducting these expenses)?

a. $432

b. $630

c. $1,210

d. $1,368

e. $1,530

13. Abby got 21 questions right on a recent algebra test. She scored 84% on the test. How many questions were on the exam?

a. 18

b. 23

c. 25

d. 28

e. 35

14. The height of the Willis Tower in Chicago is 160 ft more than twice the height of the Lake Point Tower. If W = height of the Willis Tower, and L = height of the Lake Point Tower, which of the following expressions would correctly find the height of the Lake Point Tower?

a. (L -160)/2 = W

b. W/2 +160 = L

c. W/2 -160 = L

d. L/2 +160 = W

e. (W -160)/2 = L

Problems Involving a Diagram or Table: Review

Working with Diagrams, Pictures, and Graphs, Tables, and Charts

1) Analyze the data/picture

a. Don’t jump to the question

b. Read all of the labels (title, headings, key)

c. Look at the numbers in the table, scale, and axes

d. Look at the shape of the data

2) Read the question

a. Look for important numbers and key phrases

b. Ask yourself: what is the problem asking us to find?

3) Ask yourself: What data do I need to solve the problem?

a. Now that you know what to you need to find, look for the data that will help you solve the problem

b. Use those data points to solve the problem

4) During the PLAN test - Approximate when possible

a. Let the answer choices be your guide

Problems Involving a Diagram or Table: Example

1. What do you notice about this diagram (labels, numbers, shape, etc.)?

Title: Jackets sold at Mike’s Sporting Goods

Shapes: circle = men’s jacket sales (sales dropped 1994/1995

increased 1996)

Square = women’s jacket sales (sales increased ‘94 then

stayed the same)

Triangle = children’s jacket sales (sales increased til 1993,

decreased til ’95, increased in ’96)

Labels: y-axis = number of jackets sold in 1000s

x-axis = year

2. Read the question: What is the problem asking us to find?

In which year were twice as many women’s jackets sold as children’s jackets?

The problem is asking us to find the year in which the number of women’s jackets equals twice the amount as children’s jackets.

3. What data will I need to solve the problem? Then solve the problem.

I will only need to look at the data involving the number of women’s and children’s jackets.

Should only look at data points where the number of women’s jackets sold is MORE than the number of children’s jackets sold.

Solution: 1994

4. Compare solution to answers and approximate when possible.

Answers available are (A) 1990, (B) 1991, (C) 1992, (D) 1993, (E) 1994

The answer is E

Problems Involving a Diagram or Table: Practice

1. Follow the steps in interpret the diagram to solve the problem.

a. What do you notice about this diagram (labels, numbers, shape, etc.)?

b. Read the question: What is the problem asking us to find?

How many cats were seen at the veterinary clinic last week?

c. What data will I need to solve the problem? Then solve the problem.

d. Compare solution to answers and approximate when possible.

Answers available: (A) 25, (B) 26, (C) 65, (D) 104, (E) 130

2. Follow the steps in interpret the diagram to solve the problem.

a. What do you notice about this diagram (labels, numbers, shape, etc.)?

b. Read the question: What is the problem asking us to find?

During an August heat wave, Wendy kept track of the high temperature every day for a week. She graphed her results on a line graph. To the nearest degree, what was the average high temperature that week?

c. What data will I need to solve the problem? Then solve the problem.

d. Compare solution to answers and approximate when possible.

Answers available: (A) 95 degrees, (B) 96 degrees, (C) 97 degrees, (D) 98 degrees, (E) 100 degrees

Problems Involving a Diagram or Table: PLAN-Type Problems

3. Alex likes to eat salads for lunch. Alex makes his salads with lettuce, tomatoes, onions, mushrooms, and peppers. Alex uses 2 times as many mushrooms as peppers, the same amount of onions as peppers, 3 times as many tomatoes as peppers, and 4 times as much lettuce as peppers. Which of the following circle graphs best fits this information?

a. b.

c. d.

e.

4. The bar graph below shows the scores on a recent math test. What percentage of the class scored in the 80’s or higher?

a. 8 %

b. 25 %

c. 41 2/3 %

d. 66 2/3 %

e. 91 2/3 %

5. A large mail order business sells hundreds of thousands of items. The line graph shows the sales levels of three of these items (Item A, Item B, and Item C) from November 19 to November 25. On which date was the sales level of Item A approximately half the sales level of Item C?

a. November 19

b. November 20

c. November 22

d. November 23

e. November 25

6. The pattern below shows how toothpicks can be used to make squares. Which of the following describes the total number of toothpicks used to make n squares in the arrangement illustrated below?

a. The total number of toothpicks is always equal to 13 toothpicks, regardless of the number of squares.

b. The total number of toothpicks is always twice the number of squares.

c. The total number of toothpicks is always 1 more than 3 times the number of squares.

d. The total number of toothpicks is always 4 times the number of squares.

e. There is no consistent relationship between this total and the number of squares.

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