6th Grade Fractions Chapter Questions
- Explain how to add, subtract, multiply and divide fractions.
- Explain why you multiply by the inverse when dividing.
- What is the GCF and how do you determine it?
- 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 / CallerHat / 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 / BagsHat / 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