Fractions Operations Part I

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)*

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

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Homework

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

10)*

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

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13)

14)

15)

16)

17)

18)

Finding Common Denominators

Classwork

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

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19)

20)

21)

22)

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

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23)

24)

25)

26)

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

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27)

28)

29)

30)

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Homework

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

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31)

32)

33)

34)

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

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35)

36)

37)

38)

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

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39)

40)

41)

42)

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Comparing Fractional Numbers

Classwork

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

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43)

44)

45)

46)

47)

48)

49)

50)

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Circle which fraction is greatest:

51)

52)

Homework

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

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55)

56)

57)

58)

59)

60)

61)

62)

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Circle which fraction is greatest:

63)

64)

Adding Fractions with Unlike Denominators

Classwork

Add the following fractions. Simplify to lowest terms:

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65)

66)

67)

68)

69)

70)

71)

72)

73)

74)

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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:

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77)

78)

79)

80)

81)

82)

83)

84)

85)

86)

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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:

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89)

90)

91)

92)

93)

94)

95)

96)

97)

98)

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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:

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101)

102)

103)

104)

105)

106)

107)

108)

109)

110)

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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:

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113)

114)

115)

116)

117)1

118)

119)

120)

121)

122)

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123)Mary is preparing for a final exam. She studied hours on Saturday and hours on Sunday. How many hours did she study over the weekend?

124)During the pie eating contest, Jenna ate apple pie, and then she ate pumpkin pie. How much pie did Jenna eat altogether?

Homework

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

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125)

126)3

127)

128)

129)

130)

131)

132)

133)

134)

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

136)Reyna drank cups of water and 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:

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137)

138)

139)

140)

141)

142)

143)

144)

145)

146)

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147)Tiana bought gallons of paint, but she only used gallons of the paint. How much paint does she have left?

148)Mr. Ramirez’s dog is years old. His cat is years younger than the dog. How old is the cat?

Homework

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

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149)

150)

151)

152)

153)

154)

155)

156)

157)

158)

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159)Of his chocolate bars, Joey gave his sister . How much does he have left?

160)In her garden, the grandma planted rows of seeds. The groundhog came along and ate 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:

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Product
Sum
Difference
Quotient

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162)A fraction is expressed as:

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163)Which of the following fractions are equivalent to ?

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

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165)Which of the following fractions are equivalent to ?

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166)Which set of fractions is equivalent?

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167)How would you write in lowest terms?

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

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

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170)In mixed numbers, is written as

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171)In mixed numbers, is written as

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

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

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174)Which of the following fractions is the largest?

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175)Which of the following fractions is the largest?

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176)Which of the following fractions is the smallest?

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177)Which of the following fractions is the smallest?

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

178)

179)

180)

181)

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?

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 =

Extended Constructed Response Questions

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

East wall: 10 ftNorth Wall: 12 ftWest Wall: 10 ftSouth Wall: 8 ft

What is the perimeter of Abbey’s room?
Her sister Anna’s room is a square of walls that are 10 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.

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 ft, a width of 12 ft and a depth of 6 ft.

What is the volume of Michelle’s pool in cubic feet?
If she needs to buy 6 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 of a tank, Jamie used of a tank, Josh used of a tank, Adam used of a tank and Kate used 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

4)3 ½

5)3 3/4

6)8 2/5

7)7 7/11

8)45 3/5

9)52 2/3

10)

11)

12)

13)1 1/5

14)7 2/3

15)8 2/9

16)7 5/6

17)211 2/3

18)49 8/15

19)6

20)15

21)12

22)21

23)14

24)35

25)28

26)77

27)10

28)10

29)20

30)70

31)15

32)45

33)10

34)55

35)6

36)36

37)30

38)24

39)16

40)48

41)48

42)16

43)

44)

45)

46)

47)

48)

49)

50)

51)3/4

52)9/10

53)

54)

55)

56)

57)

58)

59)

60)

61)2/5

62)9/11

63)5/6

64)11/15

65)11/12

66)1 7/30

67)43/60

68)1 11/42

69)9/10

70)½

71)1

72)1 3/10

73)1 2/15 pizzas

74)37/40 of a mile

75)17/20

76)16/21

77)25/36

78)24/35

79)23/24

80)1 3/143

81)24/35

82)1 79/132

83)31/40

84)2/5

85)9/10 of the pie

86) 1 5/18 of a km

87)1/10

88)1/12

91)13/63

92)18/35

93)25/36

94)11/40

95)27/110

96)1/6

97)9/20

98)1/4

99)17/21 teaspoons

100)1/8 of a mile

101)25/56

102)9/35

103)7/15

104)547/679

105)13/35

106)11/50

107)1/5

108)4/15

109)2/5

110)5/16

111)5/28 of a teaspoon

112)21/45 of a mile

113)3 5/6

114)4 11/15

115)9 11/28

116)9 37/45

117)3 31/60

118)6 5/56

119)14 4/5

120)10 53/99

121)5 33/80

122)14 5/8

123)5 9/20 hours

124)12 27/40 pies

125)3 17/20

126)5 25/42

127)4 67/72

128)8 24/35

129)7 22/45

130)6 13/36

131)11 59/60

132)8 11/48

133)9 43/48

134)64 16/21

135)9 ½ years old

136)13 1/6 cups

137)1 5/12

138)3 9/35

139)5 11/40

140)31/42

141)2 23/30

142)29 9/10

143)1 19/72

144)4 3/20

145)2 11/85

146)11 1/4

147)1 1/21 gallons

148)2 ¾ years old

149)2 3/20

150)2 1/15

151)2 43/90

152)25/42

153)5/18

154)2 1/2

155)11 1/4

156)8 2/5

157)5 19/120

158)23 31/100

159)1 7/15 of chocolate bars

160)1 17/28 rows

161)d

162)c

163)d

164)c

165)a

166)b

167)c

168)a

169)c

170)a

171)b

172)b

173)a

174)c

175)a

176)b

177)a

178)d

179)a

180)b

181)d

182)1 7/12 teaspoons

182)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

190)41/42 feet

191)59/63

192)17/24

193)1 243/413

194)2 15/56

195)19/30

196)4/9

197)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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