Upload
tranxuyen
View
222
Download
3
Embed Size (px)
Citation preview
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
Mathletics Passport © 3P Learning
5HSERIES TOPIC
How does it work? FractionsSolutions
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
3Fractions Solutions
Mathletics Passport © 3P Learning
How does it work? FractionsSolutions
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
4 Fractions Solutions
Mathletics Passport © 3P Learning
5HSERIES TOPIC
How does it work? FractionsSolutions
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
5Fractions Solutions
Mathletics Passport © 3P Learning
How does it work? FractionsSolutions
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
6 Fractions Solutions
Mathletics Passport © 3P Learning
5HSERIES TOPIC
How does it work? FractionsSolutions
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
7Fractions Solutions
Mathletics Passport © 3P Learning
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
8 Fractions Solutions
Mathletics Passport © 3P Learning
5HSERIES TOPIC
Where does it work? FractionsSolutions
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
9Fractions Solutions
Mathletics Passport © 3P Learning
Where does it work? FractionsSolutions
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
10 Fractions Solutions
Mathletics Passport © 3P Learning
5HSERIES TOPIC
Where does it work? FractionsSolutions
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
Adding and subtracting fractions with a different denominator
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
Adding and subtracting fractions with a different denominator
LCM = 21 LCM = 402
5HSERIES TOPIC
11Fractions Solutions
Mathletics Passport © 3P Learning
Where does it work? FractionsSolutions
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
Adding and subtracting fractions with a different denominator
a b221 2
21+ = 1 1
43
43+ =4
LCM = 12 LCM = 24
Page 20 questions
Adding and subtracting fractions with a different denominator
3
12 Fractions Solutions
Mathletics Passport © 3P Learning
5HSERIES TOPIC
Where does it work? FractionsSolutions
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
13Fractions Solutions
Mathletics Passport © 3P Learning
Where does it work? FractionsSolutions
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
Multiplying and dividing fractions
14 Fractions Solutions
Mathletics Passport © 3P Learning
5HSERIES TOPIC
Where does it work? FractionsSolutions
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
Multiplying and dividing fractions
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
15Fractions Solutions
Mathletics Passport © 3P Learning
Where does it work? FractionsSolutions
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)
16 Fractions Solutions
Mathletics Passport © 3P Learning
5HSERIES TOPIC
Where does it work? FractionsSolutions
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
17Fractions Solutions
Mathletics Passport © 3P Learning
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
#
18 Fractions Solutions
Mathletics Passport © 3P Learning
5HSERIES TOPIC
What else can you do? FractionsSolutions
4
5
6
3 c d
7
Page 31 questions
Fractions of an amount
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
19Fractions Solutions
Mathletics Passport © 3P Learning
What else can you do? FractionsSolutions
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
Fractions of an amount
8
`
20 Fractions Solutions
Mathletics Passport © 3P Learning
5HSERIES TOPIC
What else can you do? FractionsSolutions
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
21Fractions Solutions
Mathletics Passport © 3P Learning
What else can you do? FractionsSolutions
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.
22 Fractions Solutions
Mathletics Passport © 3P Learning
5HSERIES TOPIC
What else can you do? FractionsSolutions
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.