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$: NJCTLcontent.njctl.org/courses/math/5th-grade-math/fraction... · Web view2014/12/10 · NJ Center for Teaching and Learning ~ 1 ~ *Problem derived from Engage NY NJ Center for Teaching$
5th Grade PMI

Fractions Operations Part I

Fractions as a form of division

Classwork

Draw a picture to show the division. Express your answer as a fraction.

1) * 6÷4

2) * A baker poured 4 pounds of oats equally into 3 bags. What is the weight of each

bag?

3) * A principal evenly distributes 6 reams of copy paper to 8 fifth-grade teachers. How

much paper does each teacher receive?

Divide and Check – Give the answer as a mixed number

4)72

5)154

6)425

7)8411

8)2285

9)63212

Homework

NJ Center for Teaching and Learning ~ 1 ~ *Problem derived from Engage NY www.njctl.org

Draw a picture to show the division. Express your answer as a fraction.

10)* 4 ÷6

11)* A baker poured 3 pounds of oats equally into 4 bags. What is the weight of each

bag?

12)* A principal evenly distributes 8 reams of copy paper to 6 fifth-grade teachers. How

much paper does each teacher receive?

Divide and Check – Give the answer as a mixed number

13)65

14)233

15)749

16)9412

17)6353

18)74315

Finding Common Denominators

Classwork

Find the Least Common Denominator between 13 and each of the following fractions:


19)12

20)45

21)34

22)37


23)12

24)45

25)34

26)111


27)12

28)45

29)34

30)37

Homework


31)23

32)49

33)110

34)311


35)12

36)29

37)45

38)712



39)34

40)23

41)512

42)18

Comparing Fractional Numbers

Classwork

Fill in with the correct symbol ( >, <, or = ).

43)1814

44)3738

45)2325

46)7856

47)3725

48)5947

49)19217384

50)611715

Circle which fraction is greatest:

51)35, 23, 34

52)45, 79, 910

Homework

Fill in with the correct symbol ( >, <, or = ).

55) 3435

56) 4579

57) 31416

58) 25411


59) 522311

60) 7132239

61) 313

417

62) 1715

Circle which fraction is greatest:

63) 38, 25, 14

64) 57, 79, 911

Adding Fractions with Unlike Denominators

Classwork

Add the following fractions. Simplify to lowest terms:

65)12+ 13

66)13+ 25

67)14+ 23

68)25+ 56

69)310

+ 512

70)56+ 37

71)310

+ 1220

72)16+ 39

73)1218

+ 26

74)1215

+ 612

75) Samantha ate 4/5 of her pizza and tony ate 1/3 of the pizza. How much pizza did the two eat together?

76) Francine ran 4/5 of a mile, stopped for a break, and ran 1/8 of a mile. How many miles did Francine run altogether?


Homework

Add the following fractions. Simplify to lowest terms:

77)14+ 35

78)26+ 37

79)28+ 49

80)25+ 27

81)38+ 712

82)513

+ 711

83)410

+ 27

84)1112

+ 1522

85)410

+ 616

86)20100

+ 30150

87) Aunt Margaret ate 1/2 of the Thanksgiving pie, and Uncle Mark ate 2/5 of the pie. How much of the pie did they eat together?

88) In 30 seconds, Michael swam 5/6 of a kilometer, and then he swam another 4/9 of a kilometer. How much of a kilometer did he swim in that time?

Subtracting Fractions with Unlike Denominators

Classwork

Subtract the following fractions. Simplify the difference to lowest terms:

89)710

−35

90)34−23

91)79−47

92)57−15

93)1112

−29

94)78−35

95)611

− 310

96)1520

− 712

97)1112

− 715

98)70120

−3090


99) A recipe needs 3/4 teaspoon black pepper and 1/7 teaspoon salt. How much more black pepper does the recipe need than salt?

100) Jonathan lives 3/8 mile from the Museum of Natural History. Sylvia lives 1/4 mile from the same museum. How much closer is Sylvia from the museum?

Homework

Subtract the following fractions. Simplify the difference to lowest terms:

101)78−37

102)67−35

103)45−13

104)67− 597

105)814

− 210

106)2325

− 710

107)2340

−38

108)1720

− 712

109)810

−2255

110)90160

− 30120

111) A recipe needs 3/7 teaspoon of vanilla bean extract and 1/4 teaspoon of cocoa powder. How much more vanilla bean extract does the recipe call for than cocoa powder?

112) Richard lives 1/9 of a mile away from Times Square. Maria lives 4/5 of a mile away from Times Square. How many miles closer is Richard than Maria?

Adding Mixed Numbers with Unlike Denominators

Classwork

Add the following mixed numbers. Simplify the sum to lowest terms:


113) 1 12+2 13

114) 1 13+3 25

115) 4 14+5 17

116) 8 29+1 35

117) 1110

+2 512

118) 3 57+2 38

119) 9 312

+5 1120

120) 6 111

+4 49

121) 2 110

+3 516

122) 3 324

+111632

123) Mary is preparing for a final exam. She studied 314 hours on Saturday and 2

15

hours on Sunday. How many hours did she study over the weekend?

124) During the pie eating contest, Jenna ate 978 apple pie, and then she ate 2

45

pumpkin pie. How much pie did Jenna eat altogether?

Homework

Add the following mixed numbers. Simplify the sum to lowest terms:

125) 1 14+2 35

126) 316+2 37

127) 1 38+3 59

128) 4 27+4 25

129) 5 110

+2 718

130) 2 49+3 1112

131) 10 1730

+1 512

132) 7 1112

+ 516

133) 3 116

+6 56

134) 21 35105

+43 3070

135) The dog is 712 years old. The cat is 2 years older than the dog. How old is the

cat?


136) Reyna drank 823 cups of water and 4

12 cups of milk today. How much fluid did

Reyna have to drink today?

Subtracting Mixed Numbers with Unlike Denominators

Classwork

Subtract the following mixed numbers. Simplify the difference to lowest terms:

137) 2 34−1 13

138) 5 25−2 17

139) 6 78−1 35

140) 3 1412

−3 37

141) 7 35−4 5

6

142) 43−13 110

143) 11 38−10 1

9

144) 12 34−8 3

5

145) 5 610

−3 817

146) 27 1112

−16 23

147) Tiana bought 237 gallons of paint, but she only used 1

25 gallons of the paint. How

much paint does she have left?

148) Mr. Ramirez’s dog is 512 years old. His cat is 2

34 years younger than the dog.

How old is the cat?

Homework

Subtract the following mixed numbers. Simplify the difference to lowest terms:

149) 3 25−1 14 150) 4 2

5−2 1

3


151) 5 710

−3 29

152) 6 16−5 1221

153) 7 49−7 16

154) 13 1520

−11 624

155) 41 1320

−30 615

156) 15−6 35

157) 7 58−2 715

158) 79 3350

−56 720

159) Of his 223 chocolate bars, Joey gave his sister 1

15 . How much does he have left?

160) In her garden, the grandma planted 349 rows of seeds. The groundhog came

along and ate 112 rows of the seeds. How many rows of seeds are left?

Fractions Unit Multiple Choice Questions

161) A fraction is an expression that indicates the ________ of two quantities:

a. Productb. Sum

c. Differenced. Quotient

162) A fraction is expressed as:

a.instigatordenominator

b.denominatornumerator

c.numeratordenominator

d.numeratorinstigator

163) Which of the following fractions are equivalent to 23?

NJ Center for Teaching and Learning ~ 10 ~ *Problem derived from Engage NY

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a.26

b.13

c.49

d.46

164) Which of the following fractions are NOT equivalent to 34?

a.912

b.68

c.57

d.1520

165) Which of the following fractions are equivalent to 3550?

a.710

b.35

c.3040

5035


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166) Which set of fractions is equivalent?

a.26= 410

b.36=12

c.46= 810

167)56=65How would you write

1030 in lowest terms?

a.26

b.515

c.310

d.13

168) Which of the following fractions is in its lowest term?

a.34

b.26

c.510

d.1216

169) Which of the following fractions is in its lowest term?

a.610

b.1418

c.1516

d.2530

170) In mixed numbers, 225 is written as

a. 4 25

b. 5 25

c. 20 25

d. 22 15

171) In mixed numbers, 133 is written as


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a. 1 33

b. 4 13

c. 4 23

d. 13 13

172) Which of the following shows 5 12 as an improper fraction?

a.512

b.112

c.152

d.110

173) Which of the following shows 2 58 as an improper fraction?

a.218

b.128

c.78

d.516

174) Which of the following fractions is the largest?

a.23

b.34

c.45

d.510

175) Which of the following fractions is the largest?

a.58

b.49

c.716

d.2145

176) Which of the following fractions is the smallest?


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a.18

b.115

c.220

d.330

177) Which of the following fractions is the smallest?

a.45

b.910

c.78

d.56

Select the simplest form answer to each of the following expressions:

178)35+ 35

a.35

b.65

c.310

d.610

179)23+ 25

a.1615

b.45

c.48

d.168

180) 2 16+1 13


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a. 313

b. 312

c. 319

d. 326

181) 4 45−2 1

2

a. 112

b. 212

c. 233

d. 2310

Short Constructed Response Questions

182) The apple pie recipe calls for 3/4 cup of cinnamon and 5/6 cup of powdered sugar. How much spice will the recipe call for all together?

183) Tina ate 5/14 of the cookie cake, and Margaret ate 3/7 of the cookie cake. How much of the cookie cake did the two eat together?

184) Aliesa ran 2 1/5 mile, and Jackie ran 5 3/8 of a mile. How much farther did Jackie run?

185) Billy fed his dog 2/7 of a can of dog food everyday. After his vet said the dog was under weight, Billy started adding 2/15 can of dog food to his normal portion. How much dog food is eaten now?

186) While cleaning the laundry room, Taylor realized she only has 1/20 of laundry detergent left when last week she had 3/5. How much detergent did Taylor use in a week?


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187) While on vacation, the Dover family spent 1/9 of their budget on souvenirs and 2/5 of their budget on food. How much of their budget has the family spent already?

188) Buzz Lightyear traveled 4/5 of a lightyear in 5 minutes. He traveled another 1 5/9 lightyears after resting. How many lightyears did Buzz fly altogether?

189) Freddy and Shranya went apple picking. Freddy picked 8 1/6 of a barrel of gala apples, and Shranya picked 14 7/8 of a barrel. How many more barrels did Shranya pick than Freddy?

190) Sam and Dean ate 8/9 of a gallon of ice cream. Sam ate 1/2 of the ice cream. How much did Dean eat?

191) Lori measured 4 1/6 feet at the doctors. Her brother measured 5 1/7 feet. How many feet taller is Lori’s brother than Lori?

192) 5/7 + 2/9 =

193) 1/3 + 3/8 =

194) 4/7 + 1 3/17 =

195) 2 1/7 + 1/8 =

196) 4/5 - 1/6 =

197) 17/18 - 1/2 =

198) 3 3/5 - 1 1/6 =

199) 8 20/23 - 2 12/17 =


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Extended Constructed Response Questions

200) In order to buy wall paper, Abbey needed to find the perimeter of her bedroom. She measured each of the following lengths of her walls.

East wall: 1038 ft North Wall: 12 716 ftWest Wall: 1038 ft South Wall: 8 516 ft

What is the perimeter of Abbey’s room?

Her sister Anna’s room is a square 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.

201) Nick wants to order enough food for his party. He knows small pizzas come in slices of 6, and medium 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 medium pizza each of his friends will eat.

If Nick wants to invite 10 friends over, how many medium pizzas should he order?

If he wants to order small pizzas instead, how many will he need? A medium pizza costs $12 and a small pizza costs $9. Which type of pizza

should Nick buy for his party? Show all of your work to support your answers.


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202) 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.

203)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. Show all of your work to support your answers. Rank the amount of gas used by each student from least to greatest. What is the total fraction of a gas tank that Mike and Josh used?


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Answer Key

1)

2)

3)

4) 3 ½5) 3 3/4 6) 8 2/57) 7 7/118) 45 3/59) 52 2/3 10)

11)

12)


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13)1 1/514)7 2/315)8 2/916)7 5/617)211 2/318)49 8/1519)620)1521)1222)2123)1424)3525)2826)77 27)1028)1029)2030)7031)1532)4533)1034)55 35)636)3637)3038)2439)1640)4841)4842)1643)<44)>45)>46)>47)>48)>49)>50)>

51)3/4 52)9/10 53)>54)>55)>56)>57)<58)<59)<60)<61)2/562)9/1163)5/664)11/1565)11/1266)1 7/3067)43/6068)1 11/4269)9/1070)½71)172)1 3/1073)1 2/15 pizzas74)37/40 of a mile 75)17/2076)16/2177)25/3678)24/3579)23/2480)1 3/14381)24/3582)1 79/13283)31/4084)2/585)9/10 of the pie86) 1 5/18 of a km87)1/1088)1/1291) 13/6392) 18/3593) 25/3694) 11/4095) 27/11096) 1/697) 9/2098) 1/4


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99) 17/21 teaspoons100) 1/8 of a mile101) 25/56102) 9/35103) 7/15104) 547/679105) 13/35106) 11/50107) 1/5108) 4/15109) 2/5110) 5/16111) 5/28 of a teaspoon112) 21/45 of a mile113) 3 5/6 114) 4 11/15115) 9 11/28116) 9 37/45117) 3 31/60118) 6 5/56119) 14 4/5120) 10 53/99121) 5 33/80122) 14 5/8123) 5 9/20 hours124) 12 27/40 pies 125) 3 17/20126) 5 25/42127) 4 67/72128) 8 24/35129) 7 22/45130) 6 13/36131) 11 59/60132) 8 11/48133) 9 43/48134) 64 16/21135) 9 ½ years old136) 13 1/6 cups137) 1 5/12138) 3 9/35 139) 5 11/40140) 31/42141) 2 23/30142) 29 9/10143) 1 19/72144) 4 3/20

145) 2 11/85146) 11 1/4147) 1 1/21 gallons148) 2 ¾ years old149) 2 3/20150) 2 1/15151) 2 43/90152) 25/42153) 5/18154) 2 1/2155) 11 1/4156) 8 2/5157) 5 19/120158) 23 31/100159) 1 7/15 of chocolate bars160) 1 17/28 rows161) d 162) c163) d164) c165) a166) b167) c168) a169) c170) a171) b172) b173) a174) c175) a176) b177) a178) d179) a180) b181) d182)1 7/12 teaspoons182) 11/14 cookie pie 183) 3 7/40 miles 184) 4/105 of a can 185) 11/20 detergent 186) 23/45 of the budget 187) 2 16/45 lightyears 188) 6 17/24 barrels 189) 7/18 gallon


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190) 41/42 feet 191) 59/63192) 17/24 193) 1 243/413194) 2 15/56195) 19/30196) 4/9197) 2 13/30 198) 6 64/391 199) Abbey’s room perimeter = 41 1/2

feet

Anna’s room perimeter = 41 1/2 feet

The same amount of wallpaper.200) 3/8 4 large pizzas 5 medium pizzas medium pizzas 201) volume = 1687 5/6 cubic feet 10,689 11/18 gallons of water 202) Kate, Jamie, Mike, Adam, Josh

38/45 of a gas tank


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