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6 th Grade Fractions Chapter Questions

1. Explain how to add, subtract, multiply and divide fractions.

2. Explain why you multiply by the inverse when dividing.

3. What is the GCF and how do you determine it?

4. What is the LCM and how do you determine it?

NJ Center for Teaching and Learning ~ 1 ~ www.njctl.org

Chapter Problems

Greatest Common FactorClassworkFind the Greatest Common Factor of each set of numbers.

1) 72 and 64

2) 15 and 16

3) 14 and 49

4) 15 and 75

5) 66 and 147

6) 78 and 42

7) 75 and 18

8) 98 and 66

9) 27 and 72

10) 18 and 21

HomeworkFind the Greatest Common Factor of each set of numbers.

11) 30 and 45

12) 70 and 130

13) 98 and 30

14) 45 and 66

15) 77 and 21

16) 63 and 45

17) 36 and 63

18) 21 and 40

19) 6 and 51

20) 63 and 99

Least Common MultipleClassworkFind the Least Common Multiple of each set of numbers.

21) 9 and 21

22) 12 and 80

23) 6 and 10

24) 14 and 12

25) 15 and 36

26) 8 and 20

27) 9 and 6

28) 15 and 10

29) 8 and 14

30) 55 and 22

HomeworkFind the Least Common Multiple of each set of numbers.

31) 9 and 15

32) 4 and 7

33) 12 and 15

34) 10 and 9

35) 8 and 14

36) 11 and 13

37) 42 and 21

38) 4 and 6

39) 14 and 63

40) 22 and 8

GCF/LCM ApplicationsClasswork

41) Kiara baked 30 oatmeal cookies and 48 chocolate chip cookies to package in plastic containers for her friends at school. She wants to divide the cookies into identical containers so that each container has the same number of each kind of cookie.

a. If she wants each container to have the greatest number of cookies possible, how many plastic containers does she need?

b. How many of each cookie will she put in each container?

42) Beginning at 8:30 A.M., tours of the National Capitol and the White House begin at a tour agency. Tours for the National Capitol leave every 8 minutes. Tours for the White House leave every 10 minutes. How often do the tours leave at the same time?


43) Joe is making key chains with beads. He wants each key chain to have the same number of beads. He has 90 blue beads and 72 yellow beads.

a. What is the greatest number of key chains he can make that are exactly the same?b. How many of each color bead will be on each key chain?

44) A florist has 36 roses, 27 tulips, and 18 carnations she must use to create bouquets.a. What is the largest number of bouquets she can make without having any flowers left

over?b. How many of each flower will she put in each bouquet?

45) A radio station is giving away prizes to its callers. Depending on what number caller you are, you receive a different prize.

What number caller will be the first to receive all 3 prizes?

Homework46) Two neon lights are turned on at the same time. One blinks every 4 seconds and the other blinks

every 6 seconds. In 60 seconds, how many times will they blink at the same time?

47) Shannon is making identical balloon arrangements for a party. She has 32 maroon balloons, 24 white balloons, and 16 orange balloons. She wants each arrangement to have the same number of each color.

a. What is the greatest number of arrangements that she can make if every balloon is used?b. How many balloons of each color will be in each arrangement?

48) At a display booth at an amusement park, every visitor gets a gift bag. Some of the bags have items in them as shown in this table.

What number visitor will be the first to receive all 3 items in the gift bag?

49) There are 48 girls and 64 boys in the school choir. The choir teacher plans to arrange the students in equal rows. The same number of boys and the same number of girls will be in each row. What is the greatest number of rows the teacher can arrange?

50) Mike can buy red push pins in packages of 10 and yellow push pins in packages of 12. What is the least amount of packages of each color he must buy in order to have the same number of pins?


Prizes CallerHat Every 3rd callerT-shirt Every 5th callerBackpack Every 6th caller

Items BagsHat Every 2nd visitorT-shirt Every 7th visitorBackpack Every 10th visitor

DistributionClassworkUse the Distributive Property to rewrite each expression:

51) 45 + 75

52) 18 + 27

53) 77 + 91

54) 32 + 44

55) 46 + 69

56) 51 + 17

57) 24 + 66

58) 38 + 95

59) 85 + 95

60) 35 + 22

HomeworkUse the Distributive Property to rewrite each expression:

61) 20 + 44

62) 30 + 400

63) 63 + 72

64) 9 + 12

65) 33 + 45

66) 34 + 51

67) 65 + 91

68) 102 + 42

69) 104 + 78

70) 26 + 13

Adding FractionsClassworkSimplify to lowest terms:

71)12+ 12

72)14+ 24

73)312

+ 1412

74)57+ 37

75)1232

+ 1632

76) 1 13+3 23

77) 1112

+2 512

78) 3 57+2 37

79) 6 19+4 49

80) 3 332+11 15

32

81)12+ 13

82)13+ 25

83)310

+ 512

84)56+ 37

85)1218

+ 26

86) 1 12+2 13

87) 4 14+5 17

88) 9 312

+5 1120

89) 6 111+4 49

90) 3 324+1116

32

HomeworkSimplify to lowest terms:


91)14+ 34

92)26+ 36

93)618

+ 618

94)1112

+ 1512

95)416

+ 616

96) 316+2 36

97) 1 38+3 58

98) 5 118

+2 718

99) 2 413+3 1113

100) 7 1112+ 512

101)28+ 49

102)38+ 712

103)1112

+ 1522

104)20100

+ 30150

105) 1 14+2 35

106) 1 38+3 59

107) 4 27+4 25

108) 10 1730

+1 512

109) 7 1112

+ 516

Subtracting FractionsClasswork

110)52−32

111)57−27

112)78−38

113)1520

− 920

114) 2 34−1 1

4

115) 3 1422

−3 322

116) 7 56−4 3

6

117) 43 1314

−13 1114

118) 11 19−10 1

9

119)712

− 312

120)710

−35

121)34−23

122)1112

−29

123)1520

− 712

124)70120

−3090

125) 2 34−1 13

126) 5 25−2 17

127) 7 35−4 5

6


128) 43−13 110

129) 11 38−10 1

9

Homework

130)72−32

131)65−35

132)810

− 210

133)238

−118

134)84120

− 22120

135) 3 24−1 1

4

136) 6 1221

−5 521

137) 13 1524

−11 624

138) 15 35−6 25

139) 79 3350

−56 850

140)78−37

141)45−13

142)814

− 210

143)2340

−38

144)810

−2255

145) 3 25−1 14

146) 6 16−5 1221

147) 7 49−7 16

148) 41 1320

−30 615

149) 15−6 35

150) 79 3350

−56 720

Multiplying FractionsClasswork

151)14• 23

152)25• 56

153)310• 512

154)16• 39

155)1215• 612

156) 2 • 12

157) 8 • 35

158) 6 • 49

159) 2 • 516

160) 3 • 1532


161) 1 12• 2 12

162) 1 13•3

163) 8 •1 35

164) 9 12• 45

165) 3 310•2 311

Homework

166)26• 37

167)28• 49

168)38• 712

169)513• 710

170)1112• 1522

171) 3• 56

172) 2 • 58

173) 5 • 718

174) 10 • 1430

175) 7 • 512

176) 316• 2 25

177) 1 38•3

178) 2 45•3 47

179) 6 14• 45

180) 2 110•4 27

Dividing Fractions Classwork

181) Use the model below to demonstrate: 2÷ 12



183) Use the model below to demonstrate:4 12÷ 12

184)12÷ 13

185)25÷ 56

186)1218÷ 26

187)1215÷ 612

188) 6÷ 49

189) 2÷ 516

190) 3÷ 1532

191) 8÷ 35

192) 5 14÷ 18

193) 3 57÷2

194) 6 411÷4 49

195) 3 13÷4 15

Homework




198) Use the model below to demonstrate: 2 12÷ 12

199)38÷ 712

200)410÷ 27

201)312÷ 520

202) 26÷ 37

203) 2÷ 58

204) 5÷ 718

205) 10÷ 1430

206) 7÷ 512

207) 5 14÷2 13

208) 2 18÷3 34

209) 2 110÷ 38

210) 3 19÷ 56

Fraction Operations ApplicationClasswork

211) How much candy will each person get if 5 people share 6 ½ pounds of Swedish Fish?

212) How many

23 cup servings are in 1½ cups of cheese?

213) How long is a rectangle if its width is 2 310 feet and its area is

83750 square feet?

214) A recipe calls for

34 cup of brown sugar. If you want to make

14 of the recipe, how many

cups of brown sugar do you need?

215) For a party, you buy 8 34 lbs of salt water taffy. If 150 people are attending, how much

salt water taffy does each person get?

216) A cook has

35 ounce of pepper. A recipe for a steak marinade requires

115 ounce of


pepper. How many batches of marinade can the cook produce from

35 ounce of pepper?

217) Max wants to run 5 12 miles to train for track season. If the total length around the track

is

34 mile, how many laps does Max need to run around the track?

218) You are making hamburgers for a barbeque with your family and bought2 12 pounds of

ground beef. If you want to make

13 pound hamburgers, how many can you make from

2 12 pounds of ground beef?

219) Annie is baking cupcakes. The recipe calls for 13

cup of butter, 27

cup of sugar, and 23

cup of milk. How many cups of ingredients is that altogether?

220) Ben has 55 baseball cards. He will give 15 of his cards to his younger brother, Phil. How

many cards will Phil get?

221) Kelly has 45 cookies. She plans on bringing 23

of the cookies to school to share with her

class. How many cookies is she not bringing to school?

222) Jim needs 4 12 cups of bleach for every ten gallons of water for cleaning. How many

cups of bleach should he use if he is making 5 gallons?

223) If x4=5 is true, is

x5=4 also true? Why or why not?

224) Evaluate the expression 4d+ 23

if d = 5.


225) Sue has a picture that is 7 12

inches across and 8 inches long. She wants to put a border

that is 1 14

inches around the picture. What is the new perimeter of the picture, including

the border?

Homework

226) How many nuts will each person get if 9 people share 28 45 pounds of nuts?

227) How many 1 23 cup servings are in

15 14 cups of salsa?

228) How long is a rectangle if its width is 3 38 feet and its area is 27 square feet?

229) A recipe calls for 4 34 cups of flour. If you want to make

3 12 of the recipe, how many

cups of flour do you need?

230) For the first day of school, you buy 51 34 lbs of cookies. If you share with the 23 people in

homeroom, how many pounds of cookies do you give each person?

231) A cook has

47 ounce of baking powder. A recipe for chocolate chip cookies requires

128

ounce of baking powder. How many batches of cookies can the cook produce from

47

ounce of baking powder?

232) Anthony wants to run 8 12miles to train for track season. If the total length around the

track is

34 mile, how many laps does Anthony need to run around the track?

233) You are making a cake for a friend’s birthday and bought2 35 pounds of

butter. If each layer of the cake requires

13 pound of butter, how many layers can you


make from2 35 pounds of butter?

234) Pamela is baking muffins. She will put 34

cup of dried cranberries, 23

cup of sliced

almonds, 18

cup of raisins, and 1 14

cup of milk. How many cups of ingredients is that

altogether?

235) Brenda has 120 stickers. She will use 14

of them to decorate her folder. How many

stickers will she put on her folder?

236) Melanie works with 33 people. 13 of her coworkers are male. How many are female?

237) Krista uses 2 23

tablespoons of drink mix for every liter of fruit punch. How many

tablespoons does she need if she is making 5 liters for her class party?

238) If 7t=21 is true, is t=21 ∙7 also true? Why or why not?

239) Evaluate the expression 56+ v7

if v = 3.

240) Karla has a painting that is 20 inches across and 11 12 inches tall. She wants to put a 2 23

inch border around the painting. What is the area of the painting, including the border?

Fractions Multiple Choice Questions

1) Find the Greatest Common Factor of 24 and 72.a. 12b. 24c. 6d. 72

2) What is the Least Common Multiple of 3 and 18?a. 36b. 6c. 3d. 18


3) A cookie recipe calls for 234

cups of chocolate chips. If you want to make 14

of the recipe, how

many cups of chocolate chips should you use?a. 11 cups

b.1116cup

c. 3 cups

d. 1 38 cups

4) Use the distributive property to rewrite 16 + 64a. 16(1 + 4)b. 8(2 + 8)c. 4(4 + 16)d. 2(8 + 32)

5) 4 is the GCF of which two numbers?a. 8 and 16b. 16 and 32c. 8 and 12d. 24 and 36

6) 48 is the LCM of which two numbers?a. 16 and 48b. 12 and 4c. 6 and 8d. 2 and 24

7) How many 25

ounce servings are in 3 47

ounces?

a. 1 37

servings

b. 4 37 servings

c. 3 835

servings

d. 8 1314

servings

8) Use the distributive property to rewrite 12 + 74a. 6(2 + 13)b. 4(3 + 19)c. 2(6 + 37)d. 12(1 + 6)

9) 1 56

+ 3 79

a. 4 354


b. 5 1118

c. 4 34

d. 4 2918

10)58

• 49

a.518

b.2072

c. 11332

d.418

11)78

−35

a.43

b. 1 13

c.1140

d. 1940

12) 1 15 ÷ 34

a.910

b. 1320

c. 1415

d. 135

Fractions Short Constructed Response Questions

13)14+ 25 = ______ 14)

59−16 = ______


15) 6 58−3 4

5= ______

16) 413•3 45 = ______

17)67• 1011

=______

18)67÷ 38

= ______

19) 3 29÷1 23 = ______

20) Use the distributive property to rewrite

56 + 72 ______

21) What is the GCF of 15 and 54? ______

22) What is the LCM of 16 and 36? ______

Extended Constructed Response Questions

23) In order to buy wall paper, Abby needed to find the perimeter (total distance around the outside) of her bedroom. She measured each of the following lengths of her walls

East wall: 1038 ft North Wall: 12

716 ft West Wall: 10

38 ft South Wall: 8

516 ft

What is the perimeter of Abbey’s room?

Her sister Anna’s room is a square (four equal sides) of walls that are 1038

ft. Will Anna need to

buy more or less wallpaper than Abbey? Show all of your work to support your answers.

24) Nick wants to order enough food for his party. He knows medium pizzas come in slices of 6, and large pizzas come in slices of 8. He wants enough pizza for each of his friends to have 3 slices.

Write a fraction to show how many slices per large pizza each of his friends will eat.

If Nick wants to invite 10 friends over, how many large pizzas should he order? If he wants to order medium pizzas instead, how many will he need? A large pizza costs $12 and a medium pizza costs $9. Which type of pizza should Nick buy for

his party? Show all of your work to support your answers.

25) To find the volume of a swimming pool, you must multiply the length, width, and depth of the pool together. Michelle wants to find out how much water she needs to fill her pool.

She measured a length of 20 12

ft, a width of 12 23

ft, and a depth of 6 12

ft.

What is the volume of Michelle’s pool in cubic feet?


If she needs to buy 6 13

gallons of water for each cubic foot of space, how many gallons of water

will it take to fill her pool? Show all of your work to support your answers.

26) For a science project, Ms. States asked each of her students to measure how much gas they used driving to school each week. The students measured the amount of gas in

fractions of a tank. Mike used 25 of a tank, Jamie used

516 of a tank, Josh used

49 of a

tank, Adam used 37

of a tank, and Kate used 14

of a tank.

Rank the amount of gas used by each student, from least to greatest

If a tank of gas costs 24 12

dollars, how much money did Josh and Kate spend on gas combined?

Show all of your work to support your answers.

27) Miriam’s uncle donated 120 cans of juice and 90 packs of cheese crackers for the school field trip. Each student is to receive the same number of cans of juice and the same number of packs of crackers. What is the greatest number of students that can go on the field trip and share the food

equally with no food left over?

How many cans of juice and how many packs of crackers will each student receive? Explain.

28) Jeremy and his little sister, Deborah, are at a carnival. There are both a large and a small Ferris wheel. Jeremy gets on the large Ferris wheel at the same time his sister gets on the small Ferris wheel. The rides begin at the same time. The large wheel makes one revolution in 10 seconds and the small wheel makes one revolution in 7 seconds.

How many seconds will pass before Jeremy and Deborah are at the bottom at the same time

again?

How many times will each Ferris wheel go around before Jeremy and his sister are both on the

ground again?



Answer Key

1) 8

2) 1

3) 7

4) 15

5) 3

6) 6

7) 3

8) 2

9) 9

10) 3

11) 15

12) 10

13) 2

14) 3

15) 7

16) 9

17) 9

18) 1

19) 3

20) 9

21) 63

22) 240

23) 30

24) 84

25) 180

26) 40

27) 18

28) 30

29) 56

30) 110

31) 45

32) 28

33) 60

34) 90

35) 56

36) 143

37) 42

38) 12

39) 126

40) 88

41) a. 6 containersb. 5 oatmeal and 8

chocolate chip

42) Every 40 minutes

43) a. 18 key chainsb. 5 blue, 4 yellow

44)

a. 9 bouquetsb. 4 roses, 3 tulips, 2

carnations

45) 30th caller

46) 5 times

47) a. 8 arrangementsb. 4 maroon, 3

white, 2 orange

48) 70th visitor

49) 16 rows

50) 6 packages of red, 5 packages of yellow

51) 15(3 + 5)

52) 9(2 + 3)

53) 7(11 + 13)

54) 4(8 + 11)

55) 23(2 + 3)

56) 17(3 + 1)

57) 6(4 + 11)

58) 19(2 + 5)

59) 5(17 + 19)

60) 1(35 + 22)

61) 4(5 + 11)

62) 10(3 + 40)

63) 9(7 + 8)


64) 3(3 + 4)

65) 3(11 + 15)

66) 17(2 + 3)

67) 13(5 + 7)

68) 6(17 + 7)

69) 26(4 + 3)

70) 13(2 + 1)

71) 1

72)34

73) 1 512

74) 1 17

75)78

76) 5

77) 3 ½

78) 6 17

79) 10 59

80) 14 916

81)56

82)1115

83)4360

84) 1 1142

85) 1

86) 3 56

87) 9 1128

88) 14 45

89) 10 5399

90) 14 58

91) 1

92)56

93)23

94) 2 16

95)58

96) 5 23

97) 5

98) 7 49

99) 6 213

100) 8 13

101)2536

102)2324

103) 1 79132

104)25

105) 3 1720

106) 4 6772

107) 8 2435

108) 11 5960

109) 8 1148

110) 1

111)37

112) ½

113)310

114) 1 ½

115) ½


116) 3 13

117) 30 17

118) 1

119)13

120)110

121)112

122)2536

123)16

124)14

125) 1 512

126) 3 935

127) 2 2330

128) 29 910

129) 1 1972

130) 2

131)35

132)35

133) 112

134)3160

135) 2 14

136) 1 13

137) 2 38

138) 9 15

139) 23 12

140)2556

141)715

142)1335

143)15

144)25

145) 2 320

146)2542

147)518

148) 11 14

149) 8 25

150) 23 31100

151)16

152)13

153)18

154)118

155)25

156) 1

157) 4 45

158) 2 23

159)58

160) 1 1332

161) 3 34

162) 4


163) 12 45

164) 7 35

165) 7 12

166)17

167)19

168)732

169)726

170)58

171) 2 12

172) 1 14

173) 1 1718

174) 4 23

175) 2 1112

176) 7 35

177) 4 18

178) 10

179) 5

180) 9

181) 4

182) 1 14

183) 9

184) 1 12

185)1225

186) 2

187) 1 35

188) 13 12

189) 6 25

190) 6 25

191) 13 13

192) 42

193) 1 67

194) 1 1944

195)5063

196) 3 35

197)45

198) 5

199)914

200) 1 25

201) 1

202)79

203) 3 15

204) 12 67

205) 21 37

206) 16 45

207) 2 14

208)1730

209) 5 35

210) 3 1115

211) 1 310 lbs


212) 2 14 servings

213) 3 45 feet

214)316 cups

215)7120 lbs

216) 9 batches

217) 7 13 laps

218) 7 12 burgers

219) 1 27 cups

220) 11cards

221) 15 cookies

222) 2 14 cups

223) Yes, because

x=5 ∙4=20

224) 1 715

225) 41 inches

226) 3 15 lbs

227) 10 1320

servings

228) 8 feet

229) 16 58 cups

230) 2 14 lbs

231) 16 batches

232) 1113 laps

233) 7 45 layers

234) 2 1924 cups

235) 30 stickers

236) 22 workers

237) 13 13

tablespoons

238) It is false

because t= 721

∨13

239) 1 1142

426 49

Multiple Choice Questions

1) b

2) d

3) b

4) a

5) c

6) a

7) d

8) c

9) b

10) a

11) c

12) d

Short Constructed Response Questions

13)1320

14) 718

15) 23340


16) 16 715

17)6077

18) 227

19) 11415

20) 8(7 + 9)

21) 3

22) 144

Extended Constructed Response Questions

23) 10 38+12 7

16+10 3

8+8 516

= 10 616

+12 716

+10 616

+8 516

= 40 2416

= 41 12

feet

Anna's Room: 4 (10 38 )=41 x 838 =41 12

ft She needs to buy the same amount.

24)10x 38

=308

=3 34 so he should buy 4 large pizzas

10x 36

=306

=5 so he should buy 5 medium pizzas

12 x4=$ 48∧9 x5=$45 so he should buy medium pizzas

25) 20 12x12 2

3x6 12= 412x 383x 132

= 2025412

=1687 56

ft3

6 13x1687 5

6=193x 10127

6=10689 11

18 gallons

26)25=3280, 516

=2580, 49=2863, 37=2763, 14=2080

Least to greatest: 14, 516, 25, 37, 49

49+ 14=1636

+ 936

=2536

2536x 24 1

2=2536x 492

=122572

=17 172= $17.02


27) 30 students can go on the field trip

Each student will get 4 cans of juice and 3 packs of crackers.

30 is the GCF, so 4 x 30 = 120 (juice) and 3 x 30 = 90 (crackers)

28) It will be 70 seconds before they are both on the bottom again. The large Ferris Wheel will go

around 7 times, small will go 10 times.


Documents

NJCTLcontent.njctl.org/.../fractions-classwork-homework-201… · Web view2014/02/11 · Kiara baked 30 oatmeal cookies and 48 chocolate chip cookies to package in plastic containers