6th 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?

Chapter Problems

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Greatest Common Factor

Classwork

Find 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

Homework

Find 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 Multiple

Classwork

Find 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

Homework

Find 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

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GCF/LCM Applications

Classwork

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.

Prizes / Caller
Hat / Every 3rd caller
T-shirt / Every 5th caller
Backpack / Every 6th caller

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

Homework

46)  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.

Items / Bags
Hat / Every 2nd visitor
T-shirt / Every 7th visitor
Backpack / Every 10th visitor

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?

Distribution

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Classwork

Use 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

Homework

Use 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 Fractions

Classwork

Simplify to lowest terms:

71)  12+ 12

72)  14+ 24

73)  312+ 1412

74)  57+ 37

75)  1232+ 1632

76)  113+ 323

77)  1112+2 512

78)  357+2 37

79)  619+ 449

80)  3332+11 1532

81)  12+ 13

82)  13+ 25

83)  310+ 512

84)  56+ 37

85)  1218+ 26

86)  112+2 13

87)  414+5 17

88)  9312+5 1120

89)  6111+ 449

90)  3324+11 1632

Homework

Simplify to lowest terms:

91)  14+ 34

92)  26+ 36

93)  618+ 618

94)  1112+ 1512

95)  416+ 616

96)  316+2 36

97)  138+ 358

98)  5118+2 718

99)  2413+ 31113

100)  7 1112+ 512

101)  28+ 49

102)  38+ 712

103)  1112+ 1522

104)  20100+ 30150

105)  114+ 235

106)  138+ 359

107)  427+ 425

108)  101730+ 1512

109)  7 1112+ 516

Subtracting Fractions

Classwork

110)  52- 32

111)  57- 27

112)  78- 38

113)  1520- 920

114)  234- 114

115)  31422- 3322

116)  756- 436

117)  431314- 131114

118)  1119- 1019

119)  712- 312

120)  710- 35

121)  34- 23

122)  1112- 29

123)  1520- 712

124)  70120- 3090

125)  234- 113

126)  525- 217

127)  735- 456

128)  43- 13110

129)  1138- 1019

Homework

130)  72- 32

131)  65- 35

132)  810- 210

133)  238- 118

134)  84120- 22120

135)  324- 114

136)  61221- 5521

137)  131524- 11624

138)  1535- 625

139)  793350- 56850

140)  78- 37

141)  45- 13

142)  814- 210

143)  2340- 38

144)  810- 2255

145)  325- 114

146)  616- 51221

147)  749- 716

148)  411320- 30615

149)  15- 635

150)  793350- 56720

Multiplying Fractions

Classwork

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)  112•2 12

162)  113• 3

163)  8•1 35

164)  912• 45

165)  3310•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)  138• 3

178)  245• 347

179)  614• 45

180)  2110• 427

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Dividing Fractions

Classwork

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

182)  Use the model below to demonstrate: 56÷ 23

183)  Use the model below to demonstrate: 412÷ 12

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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)  514÷ 18

193)  357÷2

194)  6411÷ 449

195)  313÷4 15

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Homework

196)  Use the model below to demonstrate: 3÷ 56

197)  Use the model below to demonstrate: 23÷ 56

198)  Use the model below to demonstrate: 212÷ 12

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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)  514÷ 213

208)  218÷ 334

209)  2 110÷ 38

210)  319÷ 56

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Fraction Operations Application

Classwork

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

212)  How many cup servings are in 1½ cups of cheese?

213)  How long is a rectangle if its width is feet and its area is square feet?

214)  A recipe calls for cup of brown sugar. If you want to make of the recipe, how many

cups of brown sugar do you need?

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

salt water taffy does each person get?

216)  A cook has ounce of pepper. A recipe for a steak marinade requires ounce of

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

217)  Max wants to run miles to train for track season. If the total length around the track is mile, how many laps does Max need to run around the track?

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

ground beef. If you want to make pound hamburgers, how many can you make from

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 412 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 712 inches across and 8 inches long. She wants to put a border that is 114 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 pounds of nuts?

227)  How many cup servings are in cups of salsa?

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

229)  A recipe calls for cups of flour. If you want to make of the recipe, how many cups of flour do you need?

230)  For the first day of school, you buy 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 ounce of baking powder. A recipe for chocolate chip cookies requires

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

ounce of baking powder?

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

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

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

butter. If each layer of the cake requires pound of butter, how many layers can you

make from 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 114cup 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 223 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 1112 inches tall. She wants to put a 223 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.  12

b.  24

c.  6

d.  72

2)  What is the Least Common Multiple of 3 and 18?

a.  36

b.  6

c.  3

d.  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.  1116 cup

c.  3 cups

d.  1 38 cups

4)  Use the distributive property to rewrite 16 + 64

a.  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 16

b.  16 and 32

c.  8 and 12

d.  24 and 36

6)  48 is the LCM of which two numbers?

a.  16 and 48

b.  12 and 4

c.  6 and 8

d.  2 and 24

7)  How many 25 ounce servings are in 3 47 ounces?

a.  1 37 servings