fractions - navigate mathnavigatemath.weebly.com/.../g7_fractions_solutions.pdf · · 2014-07-09h...

$: Fractions - Navigate Mathnavigatemath.weebly.com/.../g7_fractions_solutions.pdf · · 2014-07-09H 5 SERIES TOPIC Fractions Solutions 1 ... Improper fractions and mixed numbers 1$
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Fractions

FractionsSolutions

5HSERIES TOPIC

1Fractions Solutions

Mathletics Passport © 3P Learning

How does it work? FractionsSolutions

Page 3 questions

Proper fractions

e f g h

b c da e125

88

b c da e

1611

104

73

259

103

107

41

65

2

3

31

85

43

199

189

21=

1811

53

95

1 a b c d

4

Page 4 questions

Proper fractions

(ii)

(i)a

There are many possible ways to shade. Here is just one way for each of them.

There are many possible ways to shade. Here is just one way for each of them.

(i)

(ii)

b

2 Fractions Solutions


5HSERIES TOPIC


Page 6 questions

Equivalent proper fractions

1 a b

2 a b

c d

3 a b

4

5

32

64

2416= = 2

163

126

42= = =

41

55

205

#

#=

108

22

54

'' =

53

33

159

#

#=

2412

66

42

'' =

2016

44

54

'' =

328

88

41

'' =

2114

77

32

'' =

2416

88

32

'' =a b

2114 and

2416 are equivalent fractions as they both simplify fully to give

32 .

d

(ii)

(i)d

Page 4 questions

Proper fractions

(ii)

(i)c4

5HSERIES TOPIC




3510

54

128

43

156

246

21

108

155

51

1612

3015

83

53

31

32

306

148

41

72

7227

52

106

74

Page 7 questions

Equivalent proper fractions

S I M P L E S T F O R M

6



5HSERIES TOPIC


b

2 a

3 a

4

a

5 a

b

a

512 2

52= 4

314

32= c

223 11

21=

b1915

35

32= = 1

1421

23

21= = c 1

1618

89

81= =

b1 121

21

23

=

=

2 243

43

411

=

=

c 4 454

54

524

=

=

b4 4

4

122

61

61

625

=

=

=

2 2

2

246

41

41

49

=

=

=

c 25 25

25

7224

31

31

376

=

=

=

c d

e f

Page 9 questions

Improper fractions and mixed numbers

1 232

352

341

182 1

41=

242 2

21= 3

43

#

+

#

+

#

+

#

+

#

+

#

+

b

2 a

3 a

4

a

5 a

b

a

512 2

52= 4

314

32= c

223 11

21=

b1915

35

32= = 1

1421

23

21= = c 1

1618

89

81= =

b1 121

21

23

=

=

2 243

43

411

=

=

c 4 454

54

524

=

=

b4 4

4

122

61

61

625

=

=

=

2 2

2

246

41

41

49

=

=

=

c 25 25

25

7224

31

31

376

=

=

=

c d

e f

1 232

352

341

182 1

41=

242 2

21= 3

43

#

+

#

+

#

+

#

+

#

+

#

+

5HSERIES TOPIC




1

2

3

4 a

5

41

1542

514 2

54= =

1027 2

107=

a b c

10a b c

10 10

33

158

b c

a211 5

21=

522 4

52=b c

6 a b c31863

27

21= =

25110

522 4

52= =

21 43 5

32 54 6

128

32=

52

127

Page 11 questions

Fractions on the number line

54

31

83

a

10 1010

141

45=2

32

38= 5

53

528=b c

or

10



5HSERIES TOPIC


1

2

3

4 a

5

6

a

a

a

a

a

b c d23

117

619

154

b c d1610

35

32= =

b c d15 5=

b c231

37

73

=

b c

b c4810

245

524

454

=

=

Page 13 questions

Reciprocal fractions

148

74= 12

1823 1

21= =

2510

52=

19 9=

21

41

352

517

175

=

11210

1222

2212

116

=

=

195

914

149

=

3102

1032

3210

165

=

=

2219

2151

717

177

=

=

6612

112

211

521

=

=

11515

233

323

732

=

=

reciprocal reciprocal

reciprocal

reciprocal

reciprocal

reciprocal

reciprocal reciprocal reciprocal

5HSERIES TOPIC



Where does it work? FractionsSolutions

1

2

3

a

a

a

b

b

b

49

716

, ,53

2012

21

2010

2011

2010

2011

2012

21

2011

53

44

1010

#

#

#

#

1 1

1 1

, ,129

32

128

65 2

1210

128

129

1210

32

129

65

44

2#

#

#

#

1 1

1 1

,314

415

821and

,52

156

31

155

155

156

31

52

33

55

#

#

#

#

1

1

,75

44

43

2821

2820

2820

2821

75

43

77

#

#

#

#

1

1

Page 15 questions

Comparing fractions

and

,49

2863

716

2864

2863

2864

241 2

72

77

44

#

#

#

#

1

1

, ,314

24112

415

2490

8 321 3

2463

2463

2490

24112

821

415

314

285 3

43 4

32

88

66

#

#

#

#

#

#

1 1

1 1

1 1

` `

LCM = 15 LCM = 28

LCM = 20 LCM = 12

LCM = 28 LCM = 24



5HSERIES TOPIC


2

3

4

a b c2

1 425

221

+ =

=

58 2

56

151

- =

=

32 5

37

231

+ =

=

d e f4

10 149

241

- =

=

711 4

715

271

+ =

=

215 8

27

321

- =

=

a b c4

11 546

23

121

- =

=

=

613 19

632

316

531

+ =

=

=

2

89 13

822

86

243

+ =

=

=

a b c9

4 1 297+ + =

320 10 4

36

2

- - =

=

21 1 1

21+ - =

d e f5

1 4 253+ - =

78 4 6

710

173

- + =

=

613 11 9

615

25

221

+ - =

=

=

Page 17 questions

Adding and subtracting fractions with the same denominator

1 a b c3

1 132+ =

53 1

52- =

95 2

97+ =

d e f11

8 6112- =

1511 4

157- = 8

3 588

1

+ =

=

5HSERIES TOPIC




1

2

a b

a b

c

31

22

31

21

21

62

63

62 3

65

33

#

#

#

#+ = +

= +

= +

=

21

33

65

21

65

65

63

65 3

62

31

#

#- = -

= -

= -

=

=

61

22

61

43

43

122

129

122 9

1211

33

#

#

#

#+ = +

= +

= +

=

d

LCM = 6

31

61

31

61

62

61

63

21

22

#

#+ = +

= +

=

=

75

51

75

51

3525

357

3518

55

77

#

#

#

#- = -

= -

=

LCM = 35

Page 19 questions

Adding and subtracting fractions with a different denominator

52

41

44

55

52

41

208

205

208 5

203

#

#

#

#- = -

= -

= -

=

LCM = 6 LCM = 6

LCM = 20 LCM = 12



5HSERIES TOPIC


3 a b

c

54

22

21

54

21

105

108

105 8

1013

1103

55

#

#

#

#+ =

= +

= +

=

=

813

55

813

53

53

4065

4024

4065 24

4041

1401

88

#

#

#

#- = -

= -

= -

=

=

21

41

44

22

21

83

41

83

84

83

82

84 3 2

85

#

#

#

#+ - = + -

= + -

= + -

=

d

103

43

22

55

53

103

43

53

2012

206

2015

2012 6 15

203

44

#

#

#

#

#

#+ - = + -

= + -

= + -

=

Page 20 questions


LCM = 8 LCM = 20

LCM = 10 LCM = 40

e f

76

33

76

32

32

2118

2114

2118 14

214

77

#

#

#

#- = -

= -

= -

=

53

88

53

83

83

4024

4015

4024 15

4039

55

#

#

#

#+ = +

= +

= +

=

Page 19 questions


LCM = 21 LCM = 402

5HSERIES TOPIC




e f

32

41

65

32

41

65

128

123

1210

128 3 10

1215

45

141

44

33

22

#

#

#

#

#

#- + = - +

= - +

= - +

=

=

=

127

32

2411

127

31

2411

2414

248

2411

2414 8 11

2417

22

88

11

#

#

#

#

#

#- + = - +

= - +

= - +

=

c 132

33

32

31

- = -

=

d

e f

183

88

83

85

- = -

=

253

510

53

57

152

- = -

=

=

441

416

41

415

343

- = -

=

=

g h335

39

35

34

131

- = -

=

=

525

210

25

25

221

- = -

=

=

Page 21 questions


a b221 2

21+ = 1 1

43

43+ =4

LCM = 12 LCM = 24

Page 20 questions


3



5HSERIES TOPIC


1 a b

c d

e f

5

=

simplified

54

54of

52

83of =

32

74of` =

`

51

43of` =

4

3

7

5

5

=`

5

8

=of of =`

9

==`

4

43

97

6

4

43

65

simplifiedsimplified

Page 23 questions

Multiplying and dividing fractions

3

20

8

21

16

25

6

40

3

20

21

36

7

12

15

24

5

8

5HSERIES TOPIC




2 a b

c d

e f

g h

i j

k l

a b

c

2 31 1

61

#

#=

5 43 1

203

#

#=

3 32 2

94

#

#= d

e f31

23

31

32

3 31 2

92

#

#

#

' =

=

=

112

41

112

14

11 12 4

118

#

#

#

' =

=

=

53 3

5 259

#

#=

g h

i

65 4

65

41

6 45 1

245

#

#

#

' =

=

=

43 8

43

81

4 83 1

323

#

#

#

' =

=

=

1 510 4

540

8

#

#=

=

j

k l1253

112

35

1 312 5

360

20

#

#

#

' =

=

=

=

2132

12

213

1 22 13

226

13

#

#

#

' =

=

=

=

1 824 3

872

9

#

#=

=

Page 24 questions




5HSERIES TOPIC


3 a b

c

8 82 2

644

161

#

#=

=

4 23 3

89

181

#

#=

=

83

54

8 53 4

4012

103

##

#=

=

=

d

e f109

85

10 89 5

8045

169

##

#=

=

=

4 3 23 2 1

246

41

# #

# #=

=

32

53

3 52 3

156

52

##

#=

=

=

g h5 6 32 3 1

906

151

# #

# #=

=

21

41

21

2 41 1

21

81

21

81

12

82

41

##

#

#

' '

'

=

=

=

=

=

4 32

64 of

Page 25 questions


is exactly the same as

32

64

32

32

32

812

32

128

32

32

#

#

#

#

'

=

=

=

=

32

64

` of32

812'

or41

41

412

#= =` j

161=

5HSERIES TOPIC




1

2

a b

c

2 4

49

314

83

33

41

32

49

314

1227

1256

12

61211

44

#

#

#

#

+

+ = +

= +

=

=

49

57

55

44

241 1

52

49

57

2045

2028

2017

#

#

#

#

-

- = -

= -

=

5 2

528

25

22

53

21

528

25

1056

1025

1031

3101

55

#

#

#

#

-

- = -

= -

=

=

d 3 1

619

4

55

61

51

619

56

56

3095

3036

30131

3011

66

#

#

#

#

+

+ = +

= +

=

=

a b

c

4 152

14

57

1 54 7

528

553

#

##

#=

=

=

473 2

731

12

7 131 2

762

876

#

##

#=

=

=

143 3

21

47

27

4 27 7

849

681

#

##

#=

=

=

d 531 1

54

316

59

3 516 9

15144

953

#

##

#=

=

=

Page 27 questions

Operations with mixed numbers

(LCM = 12) (LCM = 20)

(LCM = 10) (LCM = 30)



5HSERIES TOPIC


Page 28 questions

Combining all the operations

3 a b3 221

13

25

13

52

1 53 2

56

151

#

#

#

'

' =

=

=

=

132 3

35

13

35

31

3 35 1

95

#

#

#

'

' =

=

=

252 1

21

512

23

512

32

5 312 2

1524

58

153

#

#

#

'

' =

=

=

=

=

521 1

32

211

35

211

53

2 511 3

1033

3103

#

#

#

'

' =

=

=

=

c d

Page 27 questions

Operations with mixed numbers

32 243 1

83 3

32

411

811

311

32121

311

32121

311

96363

96352

96715

79643

33

3232

#

#

#

#

#

#

+

= +

= +

= +

= +

=

=

46 354 16

29

623

316

29

236

316

4654

316

138864

613836

6236

#

# #

#

#

#

'

=

=

=

=

=

=

1099

77

71

533

23

71

5 233 3

71

1099

71

7010

70693

70703

10703

1010

#

#

#

#

#

#

#

+

= +

= +

= +

= +

=

=

1

(LCM = 70) (LCM = 96)

5HSERIES TOPIC



What else can you do? FractionsSolutions

1

2

a b

c

51 20

51

120

520

4

# =

=

d

a b

c d

of43 32

43

132

496

24

# =

=

of

32 24

32

124

348

16

# =

=

of65 42

65

142

6210

35

# =

=

of

221 4

221

14

25

14

220

10

# #=

=

=

of 154 15

154

115

59

115

5135

27

# #=

=

=

of

372 14

372

14

723

114

7322

46

# #=

=

=

of 432 36

432

136

314

136

3504

168

# #=

=

=

of

Page 30 questions

Fractions of an amount

3 a bday43

124

472

18

#=

=

=

103

12000

106000

600

#=

=

=

hours

hours

hours

kilograms grams

grams

grams

143

# 2103

#



5HSERIES TOPIC


4

5

6

3 c d

7

Page 31 questions


hours65

1120

6600

100

#=

=

=

51

13000

53000

600

#=

=

=

minutes

minutes

minutes

kilometres metres

metres

metres

51

160

560

12

# =

=

There were 12 players in the brass section.

$

51

1900

5900

180

# =

=

Krista received $180.

72

128

756

8

28 8 20

# =

=

- =

20 of the towels were not bought by Hank.

118

133

11264

24

33 24 9

# =

=

- =

9 grams of the lead was made of non-graphite materials.

this is the number of towels bought by Hank

this is the amount of graphite in the lead

265

# 351

#

`

`

`

`

5HSERIES TOPIC




81 of the total letters used = 21

21

18 168# =

74 of the total audience = 280 people

of the total audience = 280 people 4'

There are 168 letters in total used in the question.

07=

71

9

people

490= people

77` of total audience = 70 people 7#

490` people were there to watch Jolly Rob perform.

10 65 of total time waiting = 30 minutes

of total time waiting = 30 minutes 5'

6=

61

minutes

36= minutes

66` of total time waiting = 6 minutes 6#

` Juan waited a further 6 minutes.

The bus arrived at 3:06 pm.`

Page 32 questions


8

`



5HSERIES TOPIC


1

2

3

a b

c d

205

41=

4

5

e f

g h

e f

g h

Page 34 questions

Two amounts as a fraction

112216 8=

4035

87=

242

121=

305

61=

20025

81=

3600300

121=

9223

41=

800240

103=

10016

254=

2727

276

2721

97

- =

=

500 175 125125

800125

325

+ +=

=

103 of the school are Year 7 students.`

254 of the rolls were 5.`

97 of the arrows missed the bullseye.`

325 of the recipe is butter.`

5HSERIES TOPIC




the number of questions answered correctly

1

Page 36 questions

Word problems with fractions

85 56

85

156

8280

# #=

=

2

The table got 21 questions incorrect.

132 1 60

32

100

#=

=

hours minutes

minutes

6041 steps 100# minutes 6025= steps

CoTin would expect to walk 6025 steps every 132 hours.`

331

61

41

124

122

123

129

43

+ + = + +

=

=

Fraction of potato plants is 44

43

41- = `

Number of potato plants:41

180

480

20

# =

=

4

35

56 35 21

`

=

- =

32

124

348

16

# =

=

Number of students with brown eyes:

number of students with brown eyes

Number of boys with brown eyes:83

116

848

6

16 6 10

# =

=

- =

(Number of boys with brown eyes.)

number of girls with brown eyes

` There are 20 potato plants in the garden.

` 10 girls had brown eyes.



5HSERIES TOPIC


5 Year 7 year group

Year 8 year group

Year 9 year group

Year 10 year group

Total number of students from Years 7 to 10 256 128 96 48

528

= + + +

=

6 Shared profiles: 53 90

53

190

5270

54

#=

=

=

Page 37 questions

Word problems with fractions

256

21 256 128

21 128 96

21 96 48

#

#

#

=

= =

= =

= =

54

54 6 324

61

#

=

=

`

`

of total profiles in the class

There are 324 different profiles linked to students from this class.

7 Photos taken by Meagan:

Number of photos moved:

New number of background photos taken by Meagan:

Number of photos on Meagan’s touchpad:

Fraction of photos not taken by Meagan:

75

156

7280

40

# =

=

85

140

8200

25

# =

=

40 25 15- =

56 25 31- =

3131

3115

3116- =

of

`3116 of the photos were not taken by Meagan.

` There are 528 students in Years 7 to 10.

5HSERIES TOPIC



Fractions Notes



5HSERIES TOPIC

Fractions Notes

www.mathletics.com

Fractions

fractions - navigate mathnavigatemath.weebly.com/.../g7_fractions_solutions.pdf · · 2014-07-09h...

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