christmas break work

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1. a. For each of the fraction strips below, write a fraction that expresses howmuch of the strip is shaded.

i. ii.

iii. iv.

v. vi.

b. For each of the six fraction strips above, write a fraction that expresses howmuch of the strip is not shaded.

c. What is the relationship between the fraction you wrote for the shadedpart and the fraction you wrote for the unshaded part for each of the sixfraction strips? Explain your reasoning.

2. The drawing shows the controls on a small, portable stereo system. Use the drawing to answer each of the following questions. Record all of your answers as fractions.

a. What fraction of the total volume is the stereo playing?

b. What fraction of the total bass output is the stereo playing?

c. What fraction of the total treble output is the stereo playing?

d. If the volume of the stereo is turned down to half the current volume, whatfraction of the total volume will be the new volume? Explain yourreasoning.

e. If the bass control on the stereo is adjusted up so that the stereo is playingat double the bass output it is playing at now, what fraction of the total bassoutput will be the new bass output? Explain your reasoning.

3. A bag contains 24 marbles (Note: You may want to use 24 cubes, chips,marbles, or other objects to help you solve this problem.)

a. If 16 of the marbles are removed from the bag to play a game, whatfraction of the marbles are left in the bag?

b. Of the 16 marbles taken from the bag, one-fourth are put back in the bag.Now how many marbles are in the bag? Explain your reasoning.

Name ____________________________________________ Date ____________ Class ____________

Additional PracticeBits and Pieces I

Investigation 1

18

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4. Joey’s father stops at the gas station to buy gas. The car has a 16-gallon tank,

and the fuel gauge says there is of a tank of gas.

a. How many gallons of gas are in the tank?

b. If Joey’s father buys 6 gallons of gas, what fraction of the tank will the car’sfuel gauge read?

c. What fraction of the gas tank is empty after Joey’s father puts 6 gallons ofgas in the tank?

5. For parts (a)–(b), use fraction strips or some other method to name the pointwith a fraction.

a.

b.

6. For parts (a)–(c), copy the grids on your paper. Shade each grid to representthe given fraction.

a. Represent the fraction on each grid.

b. Represent the fraction on each grid.

c. Represent the fraction on each grid.

7. Tony is driving from Alma, Michigan to Elizabeth City, North Carolina. Thedrive covers a total distance of 1,100 miles. Tony’s car can travel 400 miles on afull tank of gas. How many tanks of gas will Tony’s car need for the entire trip?Explain your reasoning.

16

37

45

38

Name ____________________________________________ Date ____________ Class ____________

Additional Practice (continued)

Bits and Pieces I

Investigation 1

10

10

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1. For each pair of fractions, insert a less-than symbol (<), greater-than symbol(>), or an equals symbol (�) between the fractions to make the true statement.

a. b. c.

d. e. f.

2. a. For each pair of fractions, insert a less-than symbol (<), greater-thansymbol (>), or an equals symbol (�) between the fractions to make thetrue statement.

i. ii. iii.

b. Describe a way to compare two fractions when the numerators are thesame.

3. a. For each pair of fractions, insert a less-than symbol (<), greater-thansymbol (>), or an equals symbol (�) between the fractions to make thetrue statement.

i. ii. iii.

b. Describe a way to compare two fractions when the denominators are thesame.

4. For each group of fractions, rewrite the fractions in order from least togreatest.

a. , , , b. , , ,

c. , , , , d. , , , ,

5. For each of the six fraction strips below, write two fractions that express theportion of the strip that is shaded.

a. b.

c. d.

e. f.

6. Find a fraction between each pair of fractions given.

a. and b. and c. and 2818

14

13

57

47

316

12

38

34

1116

16

19

13

15

12

17

1116

14

244

26

34

12

23

311

511

79

49

45

25

38

34

45

46

25

23

37

58

810

34

23

45

13

512

25

13

510

12

Name ____________________________________________ Date ____________ Class ____________


Investigation 2

20


7. Copy each number line below and estimate where the number 1 would be.Explain the strategy you used for each number line.

a.

b.

c.

8. For each shape below, write a fraction to express the portion of the entireshape that is shaded.

a. b. c. d.

9. Copy and complete the following table:

10. Lisa has two oranges that are the same size but each one is divideddifferently. One orange has been divided into five equal-size sections and theother orange has been divided into ten equal-size sections.

a. If Brian eats three pieces of the orange with five sections, what fraction ofthe orange will he get?

b. Lisa gave John the orange with ten sections. John wants to eat the sameamount as Brian. How many pieces of his orange will John have to eat?Explain.

c. Lisa bought a new orange that she wants to share equally among threepeople. This orange has been divided into five equal-size sections. Explainhow Lisa should cut the orange so three people can share it.

Name ____________________________________________ Date ____________ Class ____________


Bits and Pieces I

Investigation 2

0 14

0 23

0 112

Fraction

Mixed Number

74

323 25

6 712

353

194

21

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Name the fractions modeled and determine if they are equivalent.

1. 2. 3.

Compare each pair of fractions. Use <, >, or �.

4. 5. 6. 7.

8. 9. 10. 11.

12. 13. 14. 15.

Order from least to greatest.

16. , , 17. , , 18. , ,

19. , , 20. , , 21. , ,

22. , , 23. , , 24. , ,

25. A pattern requires a seam of at least in. Rachel sewed a seem in. wide.

Did she sew the seam wide enough? Explain.

12

58

12

78

1516

712

23

59

78

12

34

1516

1112

910

12

56

38

23

59

78

38

25

14

78

56

12

16

13

14

12

716

1120

12

38

25

79

49

812

1015

12

815

23

712

610

45

1115

715

48

612

12

45

310

78

Name ____________________________________________ Date ____________ Class ____________

Skill: Comparing FractionsBits and Pieces I

Investigation 2

22


Write each mixed number as an improper fraction.

1. 1 2. 2 3. 7 4. 8

5. 3 6. 4 7. 5 8. 1

9. 3 10. 4 11. 2 12. 2

Write each improper fraction as a mixed number in simplest form.

13. 14. 15. 16.

17. 18. 19. 20.

21. 22. 23. 24.

25. Find the improper fraction with a denominator of 6 that is equivalent to .

26. Find the improper fraction with a denominator of 12 that is equivalent to .1014

512

174

3521

2618

2712

208

98

76

1110

73

52

83

152

715

35

78

1112

910

56

14

34

23

13

34

78

Name ____________________________________________ Date ____________ Class ____________

Skill: Mixed Numbers and Improper FractionsBits and Pieces I

Investigation 2

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1. In the diagram, the hundredths grid is the whole. Use the grid to answer each of the following questions and write each answer in both decimal and fraction form.

a. What portion of the grid is shaded gray?

b. What portion of the grid is striped?

c. What portion of the grid is checkered?

d. What portion of the grid is blank?

2. For each pair of numbers, insert a less-than symbol (<), a greater-than symbol(>), or an equals symbol (�) between the numbers to make a true statement.

a. 0.305 0.35 b. 0.123 0.1002

c. 0.25 0.25000 d. 0.25 0.025

e. 3.45 3.045 f. 12.03 12.30

3. For each pair of numbers, insert a less-than symbol (<), greater-than symbol(>), or an equals symbol (�) between the numbers to make a true statement.

a. 2.5 2 b. 0.65 c. 0.8

d. 0.625 e. 0.3 f. 2.1 1

g. h. 0.5 i. 9 8

4. Copy each number line below. In each case, two of the marks are labeled.Label the unlabeled marks with decimal numbers.

a.

b.

c.

d.

810

36

1111

1112

910

37

58

47

23

25

Name ____________________________________________ Date ____________ Class ____________


Investigation 3

0.3 0.6

0.11 0.13

0.03 0.12

0.5 0.75

24


5. Name three fractions that are equivalent to each decimal below. Explainyour reasoning. Draw a picture if it helps you explain your thinking.

a. 0.60 b. 1.7 c. 0.05 d. 2.3 e. 0.15 f. 0.625

6. Name a decimal that is equivalent to each fraction below. Explain yourreasoning. Draw a picture if it helps you explain your thinking.

a. b. c. d. e. f.

7. Sarah can jog at a steady pace of 4.75 miles per hour, and Tony can jog at asteady pace of 4.25 miles per hour.

a. How many miles can Sarah jog in 30 minutes? Explain your reasoning.

b. How many miles can Tony jog in 30 minutes?

c. If Sarah and Tony jog for 45 minutes, how much farther will Sarah go thanTony? Explain your reasoning.

8. Each small square on the grid represents .

a. What whole number is represented by the whole grid?

b. What decimal is represented by the shaded region of the grid?

9. Each small square on the grid represents 0.25.

a. What whole number is represented by the whole grid?

b. What fraction is represented by the shaded region of the grid?

10. Paul claims that the fraction is a good estimate for the decimal 0.3.

a. Do you agree or disagree with Paul’s claim? Explain your reasoning.

b. Is Paul’s estimate less than, greater than, or equal to 0.3? Explain yourreasoning.

13

15

1824

11120

38

74

315

12

Name ____________________________________________ Date ____________ Class ____________


Bits and Pieces I

Investigation 3

26


Insert <, >, or � in each box to make a true statement.

1. 0.62 0.618 2. 9.8 9.80 3. 1.006 1.02 4. 41.3 41.03

5. 2.01 2.011 6. 1.400 1.40 7. 5.079 5.08 8. 12.96 12.967

9. 15.8 15.800 10. 7.98 7.89 11. 8.02 8.020 12. 5.693 5.299

Order each set of decimals on a number line.

13. 0.2, 0.6, 0.5 14. 0.26, 0.3, 0.5, 0.59, 0.7

15. Three points are graphed on the number line below. Write statementscomparing 0.3 to 0.5 and 0.5 to 0.7.

16. Models for three decimals are shown below.

a. Write decimal names that each shaded part represents.

b. Rewrite the decimals in order from least to greatest.

Name ____________________________________________ Date ____________ Class ____________

Skill: Comparing and Ordering DecimalsBits and Pieces I

Investigation 3

0 1.0 0 1.0

0 1.00.3 0.5 0.7

27

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1. For each of the grids given below, express the shaded region of the grid as afraction, a decimal, and a percent.

a. b. c.

d. e. f.

2. Angie and Jim conducted a survey of their sixth-grade classmates in theirmathematics class. They found out the following information:

• 70% of the students in the class do homework three or more nights eachweek.

• Of the students who do homework three or more nights each week, half dohomework five nights each week.

a. What percentage of the students in the class do homework two nights orless each week? Explain your reasoning.

b. What fraction of the students in the class do homework five nights eachweek? Explain your reasoning.

c. What percentage of students in the class do homework three or four nightsa week? Explain your reasoning.

d. From the information provided, can you tell how many students are in theclass? Explain why or why not.

3. In a class of 24 sixth-graders, 25% walk to school, ride bicycles to school,

take the bus to school, and the remainder of the class are driven to school by

their parents or guardians.

a. How many students in the class walk to school? Explain your reasoning.

b. How many students in the class ride bicycles to school? Explain yourreasoning.

c. How many students in the class take the bus to school?

d. What fraction of the class are driven to school by their parent or guardian?Explain your reasoning.

e. What percentage of the students in the class walk, ride bicycles or the bus,or are driven to at school by a parent or guardian? Explain your reasoning.

13

18

Name ____________________________________________ Date ____________ Class ____________


Investigation 4

28


4. Express the shaded region of each drawing as a fraction, a decimal, and as apercent.

a. b.

c. d.

5. In one competition, the archery team had to shoot at targets from threedifferent distances: 10 m, 20 m, and 30 m. The number of hits and the numberof shots for each distance are given below. Write their score for each round asa fraction, a decimal, and a percent.

a. at 10 m: 42 hits out of 50 shots

b. at 20 m: 37 hits out of 50 shots

c. at 30 m: 18 hits out of 50 shots

6. Fill in the missing parts of the table.

Name ____________________________________________ Date ____________ Class ____________


Bits and Pieces I

Investigation 4

Fraction Decimal

0.88

0.625

Percent

35%

38

114

275%

30


Write each percent as a decimal and as a fraction.

1. 46% 2. 17% 3. 90% 4. 5%

Write each decimal as a percent and as a fraction.

5. 0.02 6. 0.45 7. 0.4 8. 0.92

Write each fraction as a decimal and as a percent.

9. 10. 11. 12.

13. Write each fraction or decimal as a percent. Write the percent (without thepercent sign) in the puzzle.

ACROSS DOWN

1. 1.

2. 2. 0.25

3. 0.55 3.

5. 0.23 4.

6. 5. 0.24

7. 0.17 6.

9. 0.4 7. 0.1

10. 8. 425

925

310

720

320

12

15

1320

35

1720

1325

710

35

Name ____________________________________________ Date ____________ Class ____________

Skill: Percents, Fractions, and DecimalsBits and Pieces I

Investigation 4

1. 2.

3.

4.

5. 6.

7. 8.

9. 10.

Name ___________________________________________________ Date ______________

© Math Worksheet Center

Independent Practice 1: Decimal Word Problems

1 Eric studied for 17.5 hours over a period of 4.5 days. On average, how much did he study each day?

2 If licorice cost $6.59 a pound, how much would it cost to buy a quarter pound of licorice? (Hint: Convert the mixed fraction to an improper fraction or decimal and multiply by the quantity required.)

3

If your weekly salary is $415.00, how much do you take home each week after deductions are made for federal income tax of $82.13, state tax of $9.74, social security and Medicare tax of $31.75, and retirement plan deduction of $41.50.

4 Carpeting costs $7.99 a yard. If Jan buys 12.4 yards, how much will it cost her? (Round it to two decimal places)

5 Kim's scores in the diving competition were 7.2, 6.975, 8.0, and 6.96. What is her total score?

6 If you had a half a dollar, three quarters, eight dimes, six nickels, and nine pennies, how much money would you have all together? (Hint: Add 0.50, 0.75, 0.80, 0.30 and 0.09)

7 Sally scored 9.007 in gymnastics. Jack scored 8.949. How much higher was Sally's score than Jack's?

8 All the people of a neighborhood pooled together and won the lottery. They won $10,000,000 and each person got a 0.02 share. How much money did each person receive?

9 If 58 out of 100 students in a school are boys. Write decimal expression for the part of the school that consists of boys.

10 A computer processes information in nanoseconds. A nanosecond is one billionth of a second. Write this number as decimal.

11

Five swimmers are entered into competition. Four of the swimmers have had their turns. Their scores are 9.8s, 9.75 s, 9.79 s and 9.81 s. What score must the last swimmer get in order to win the competition?

12 To make miniature ice cream truck, you need tires with a diameter between 1.465 cm and 1.472 cm. Will a tire that is 1.4691 cm in diameter work?

13 Ellen wanted to buy the following items: A DVD holder for $19.95, headphones for $41.25 and personal stereo for $30.65. How much money does Ellen need?

14 What is combined thickness of these shims: 0.008, 0.125, 0.15, 0.185 and 0.005 cm?

15 Melissa purchased $39.46 in groceries at a store. The cashier gave her $1.46 in change from $50 bill. How much change should Melissa get from Cashier?

16 If a 10 foot piece of electrical tape has 0.037 feet cut from it. What is the new length of tape?

17 A director replayed 231 of the 1000 scenes filmed for a movie. Write a decimal to represent the part of movie the director replayed.

18 The times for three runners in a 100 yard dash are 9.85 s, 9.6 s and 9.625 s. What is the winning time?

19 A cylinder is normally 3.4375 cm in diameter. If it is remade to be 0.095 cm larger, what is the new size of the cylinder?

20 Brandon is training for 200 meter dash. His best running time so far was 31.25 seconds. If Brandon wants to run the dash in 27 seconds, how much time must he cut in order to reach his goal?

Name ___________________________________________________ Date ______________


Independent Practice 1: Fraction Word Problems

1 Jane had a whole pie. She cut it into 8 pieces. She ate one piece and gave Karen and Candy 2 pieces. What is the fraction of the pie that is left?

2 Molly baked a dozen cookies. She ate 2. She gave Missy 2, Cindy 2, and Shelly 2. What is the fraction for the number of pieces that are left?

3 Tom had 12 baseball cards. He gave Steve 3 cards, Billy 3 cards, and Bob 3 cards. What is the fraction of cards that he gave away?

4

Juliet had 35 blank computer disks that she wanted to share with her friends, Cindy and Jessie. She wanted to divide the disk among the three of them so that each one would have an equal amount. What is the fraction of disks that she would have left over?

5

Carol had a birthday party. She had a cake that she could cut in 12 equal sizes. She wanted to invite 20 friends over for her birthday party. How many sheet cakes would she need if she friend received two pieces of cake? Would there be any cake left over? If so, what would the fraction be?

6

Paula had 2 pitchers of fruit punch for her birthday party. She could fill 24 cups using 1 pitcher. Would she have enough fruit punch so that each of her 20 friends could have a refill? If so, would she have any left? What fraction would she have left?

7

Careen had a large bag of candy that contained 169 pieces. She wanted to divide the candy into equal amounts with her friends, Susan and Megan. What fraction of candy would she have left after dividing the candy?

8 Christ bought two bags of Christmas candy for $4.00. She gave the cashier $10.00. How much would she get back? What is the fraction of her money that she spent?

9 Ben had 96 pictures. He gave his friends, Megan and Christy, 2/3 of his pictures, and he kept 1/3. How many pictures did Ben give away?

10

Dick had $135 that he collected from doing lawn work. His friends, Tom and Jim, helped with the lawn work, too. He needed to divide the amount equally. Would he have anything left over? If he did, what fraction would be left?

11 Jessie bought 8/9 of a pound of chocolates and ate 1/3 of a pound. How much was left?

12 Tim bought a board that was 7/8 of a yard long. He cut off 1/2 of a yard. How much was left?

13 Sammy rode his bike 2/5 of a mile and walked another 3/4 of a mile. How far did he travel?

14 Polly walked 3/4 of a mile before lunch and 1/2 of a mile after lunch. How far did she walk in all?

15 Donne bought 3/4 of a pound of jellybeans and 5/8 pound of gummy bears. How much did the candy weighin total?

16 The track is 3/5 of a mile long. If Tyrone jogged around it twice, how far did he run?

17 Which apple weighs more, one that weighs 2/3 of a pound or one that weighs 5/6 of a pound?

18 Stany ordered two pizzas cut into eighths. If he ate 5/8 of a pizza, how much was left?

19 Sandy bought 2¾ yards of red fabric and 1¼ of blue. How much cloth did she buy in all?

20 An equilateral triangle measures 3½ inches on one side. What is the perimeter of the triangle?

Name ___________________________________________________ Date ______________


Independent Practice 1: Least Common Multiple

1. Find the least common multiple of 15 and 60.




5. Find the least common multiple of 24, 48 and 58.
















Name ___________________________________________________ Date ______________


Independent Practice 2: Least Common Multiple





















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