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www.mathletics.com
PercentageBasics
Solutions
Percentage BasicsSERIES
H
Curriculum Ready
Copyright © 2009 3P Learning. All rights reserved.
First edition printed 2009 in Australia.
A catalogue record for this book is available from 3P Learning Ltd.
ISBN 978-1-921861-43-7
Ownership of content The materials in this resource, including without limitation all information, text, graphics, advertisements, names, logos and trade marks (Content) are protected by copyright, trade mark and other intellectual property laws unless expressly indicated otherwise.
You must not modify, copy, reproduce, republish or distribute this Content in any way except as expressly provided for in these General Conditions or with our express prior written consent.
Copyright Copyright in this resource is owned or licensed by us. Other than for the purposes of, and subject to the conditions prescribed under, the Copyright Act 1968 (Cth) and similar legislation which applies in your location, and except as expressly authorised by these General Conditions, you may not in any form or by any means: adapt, reproduce, store, distribute, print, display, perform, publish or create derivative works from any part of this resource; or commercialise any information, products or services obtained from any part of this resource.
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Published 3P Learning Ltd
For more copies of this book, contact us at: www.3plearning.com/contact/
Designed 3P Learning Ltd
Although every precaution has been taken in the preparation of this book, the publisher and authors assume no responsibility for errors or omissions. Neither is any liability assumed for damages resulting from the use of this information contained herein.
7HSERIES TOPIC
1Percentage Basics SolutionsMathletics © 3P Learning Ltd
How does it work? Solutions Percentage Basics
Page 3 questions
Page 4 questions
Proper fractions to percentages
Proper fractions to percentages
1
2
3
3
4
a
a
a
d
d
g
j
b
b
e
e
h
k
c
c
f
f
i
l
b c d
Simplest Form
Simplest Form
Simplest Form
Simplest Form
Simplest Form
Simplest Form
Simplest Form
Simplest Form
Simplest Form
%1009 9= %
10040 40= %
10075 75= %
100100 100=
%7100
7=
50%10050
21= =
%7510075
43= =
78%10078
5039= =
%
2006
2006
1003
3
22''=
=
=
%
107
107
10070
70
1010#
#=
=
= %
505
505
10010
10
22#
#=
=
= %
2510
2510
10040
40
44#
#=
=
=
40080
%
44
40080
10020
20
''=
=
=
500
%
5500150 150
10030
30
5''=
=
=
%4510045
209= = %68
10068
2517= =
14%10014
507= = 55%
10055
2011= =
%2010020
51= = %25
10025
41= =
%1310013= %29
10029=
a b c2 501 50
%
21
10050
50
#
#=
=
=
253
12
%
253
44
100
12
#
#=
=
=
1010
%
1010
1010
100100
100
#
#=
=
=
2 Percentage Basics SolutionsMathletics © 3P Learning Ltd
7HSERIES TOPIC
How does it work? Solutions Percentage Basics
Page 4 questions
Page 5 questions
Proper fractions to percentages
Proper fractions to percentages
4
5
d
g
e
h
f
i
4 253 25
%
43
10075
75
#
#=
=
=
200 2
%
200198 198 2
10099
99
''=
=
=
5
%
53
203 20
10060
60
#
#=
=
=
%
250050
2500 2550 25
1002
2
''=
=
=
%
30027
300 327 3
1009
9
''=
=
=
500 5
%
500355 355 5
10071
71
''=
=
=
d h m a z b x
4 %8
4 %4
3 %0
6%0
8 %5
%24
2%5
L
m
O
h
S
xI
a
Ub
D
z
S
d
FX
X
E
Q
R
R
S
U
d
h
m
a
z
b
x
S O L I D U S
1687
256
21404
159
2512
2511
2107
7HSERIES TOPIC
3Percentage Basics SolutionsMathletics © 3P Learning Ltd
How does it work? Solutions Percentage Basics
Page 7 questions
Page 8 questions
Decimals and percentages
Combo time: Decimals, fractions and percentages
1
1
2
3
4
The percentage value is divided by 100, so the decimal point is moved places to the left.
. .
.
35 100 0 3 5
0 35
' =
=
0.55 100 0 . 5 5 .
%55
# =
=
4 100 0 . 0 4 .
.0 04
' =
=
0.8 100 . .
%
0 8 0
80
# =
=
. .
.
75 100 0 7 5
0 75
' =
=
. . .
%
0 23 100 0 2 3
23
# =
=
1 100 0 . 01 .
.0 01
' =
=
0.01 100 0 . 01 .
%1
# =
=
32 100 0 . 3 2 .
.0 32
' =
=
0.7 100 0 . 7 0 .
%70
# =
=
9 100 0 . 0 9 .
.0 09
' =
=
0.04 100 0 . 0 4 .
%4
# =
=
a
a
d
d
b
b
e
e
c
c
f
f
The decimal is multiplied by 100, so the decimal point is moved places to the right.
Decimal
Fraction
Percentage
41
101
0.25
25% 10% %60
0.5 0.18
54
21
107
53
43
509
0.1 0.8
80%50% 70% 18% 75%
0.6 0.7 0.75
4 Percentage Basics SolutionsMathletics © 3P Learning Ltd
7HSERIES TOPIC
How does it work? Solutions Percentage Basics
Page 9 questions
Combo time: Decimals, fractions and percentages
2
3
a
a
d
d
e f
b
b
e
c
c
f
40 100 0 . 4 0 .
.0 4
: ' =
=
0.08 100 0 . 0 8 .
%8
#: =
=
25 46 4 0.24
10024
#
#: = =
0.15 100 0 . .
%
15
15
#: =
=
0.45
%
200 290 2
10045
45
:''
=
=
=
0.
%
50 27 2
10014
14
14
:''
=
=
=
10040
52: =
1008
252: =
%10024 24: =
10015
203: =
. .
.
90 100 0 9 0
0 9
: ' =
=
20 51 5 0.05
1005
#
#: = =
.
300 384 3
10028
0 28
:'' =
=
0.42 100 0 . 4 2 .
%42
: # =
=
36 100 0. 3 6 .
.0 36
: ' =
=
0.04
1500 1560 15
1004
251:
'' = =
=
10090
109: =
%1005 5: =
%10028 28: =
42100 50
21: =
10036
259: =
%1004 4: =
Decimal Decimal
Percentage Percentage
7HSERIES TOPIC
5Percentage Basics SolutionsMathletics © 3P Learning Ltd
How does it work? Solutions Percentage Basics
Page 11 questions
Page 12 questions
Fractional and decimal percentages
Fractional and decimal percentages
1
2
4
3
a
a
e
d
b
b
e
e
c
c
f
f
a
c
b
d
. 0.5% %4002
1000 5
21= = =
. 0.8% %5004
1000 8
54= = =
. 0.75% %4003
1000 75
43= = =
. 0.4% %7503
1000 4
52= = =
Decimal
Decimal
Decimal
Decimal
Proper fraction
Proper fraction
Proper fraction
Proper fraction
a
e
c
g
b
f
d
h
. . % %50013
1002 6 2 6 2
53= = =
. . % %50047
1009 4 9 4 9
52= = =
. . % %20015
1007 5 7 5 7
21= = =
. . % %40017
1004 25 4 25 4
41= = =
. . % %40010
1002 5 2 5 2
21= = =
. . % %50026
1005 2 5 2 5
51= = =
. . % %80030
1003 75 3 75 3
43= = =
. . % %40075
10018 75 18 75 18
43= = =
Decimal
Decimal
Decimal
Decimal
Decimal
Decimal
Decimal
Decimal
2.5%
0.105
45.05%
0.0604
6.25%
0.3705
7.05%
0.0075
11.85%
0.0245
0.96%
0.000 15
Mixed number
Mixed number Mixed number
Mixed number
Mixed number
Mixed number
Mixed number
Mixed number
6 Percentage Basics SolutionsMathletics © 3P Learning Ltd
7HSERIES TOPIC
How does it work? Solutions Percentage Basics
e
g
f
h
. . % %0 045 4 6 453= =
0.218 21.8% 21 %54= =
. 8. % 8 %0 084 452= =
. . % 5 %0 555 55 5 521= =
Decimal
Decimal
Decimal
Decimal
Page 12 questions
Fractional and decimal percentages
5 a
c
b
d
. . % %0 255 25 5 2521= =
0.1025 10.25% 10 %41= =
. . % %0 085 8 5 821= =
. . % %50 75 50 75 5043= =
Decimal
Decimal
Decimal
Decimal
Mixed number
Mixed number
Mixed number
Mixed number
Mixed number
Mixed number
Mixed number
Mixed number
7HSERIES TOPIC
7Percentage Basics SolutionsMathletics © 3P Learning Ltd
Where does it work? Solutions Percentage Basics
1
2
a
a
e
c
c
g
b
b
f
d
d
h
of25% 20 2010025
5
#=
=
6010010
100600
6
# =
=
10060 20
1001200
12
# =
=
of%
.
40 65 40 100 65
0 4 65
26
#
#
'=
=
=
1610025
100400
4
# =
=
.
10040 24
100960
9 6
# =
=
of%30 3010030 30
9
#=
=
1810050
100900
9
# =
=
10080 30
1002400
24
# =
=
of45% 40 45 100
0.45 40
40
18
#
#
'=
=
=
2810075
1002100
21
# =
=
.
10020 39
100780
7 8
# =
=
Page 14 questions
Percentage of an amount
3 40 820 100 #' =^ h
35 100 80 28#' =^ h
.21 100 30 6 3#' =^ h .19 100 25 4 75#' =^ h
30 100 20 6#' =^ h
25 100 44 11#' =^ h
650 100 32 1#' =^ h
.75 100 18 13 5#' =^ h
Page 15 questions
Percentage of an amount
a
e
c
g
b
fd
h
8 Percentage Basics SolutionsMathletics © 3P Learning Ltd
7HSERIES TOPIC
Where does it work? Solutions Percentage Basics
4
5
6
of
g
%20 245 20 100 245
49
#'=
=
^ h
Page 15 questions
Page 16 questions
Percentage of an amount
Percentage of an amount
a
a
a
b
b
b
40 100 45 18#' =^ h
15 100 200 30#' =^ h
45 1810040
1001800
# = =
10015 200
1003000 30# = =
or
or
82 100 150 123#' =^ h 150 12310082
10012 300
# = =or
42 100 800 336#' =^ h 800 33610042
10033 600
# = =or
` 18 of the people were dressed as angels.
` Qian's music collection fills 30 GB of storage space.
` 123 of the 150 words in Justin's poem are not the word 'love'
` 336 of the 800 fruit eating animals at the zoo preferred the taste of apples.
` total amount of weights on the scales g2 196 392#= =
18% = the word 'love', ` 100% - 18% = 82% of the words are not the word 'love'.
58% = prefer bananas, ` 100% - 58% = 42% prefer apples.
.45 100 430 193 5#' =^ h 0 193.510045 43
10019 350
# = =or
` there is 193.5 mL in the pancake mixture.
` (245 - 49) = 196 g left on the heaviest side
35% + 14% + 6% = 55%, 100% - 55% = 45% of the mixture is milk
7HSERIES TOPIC
9Percentage Basics SolutionsMathletics © 3P Learning Ltd
Where does it work? Solutions Percentage Basics
1
2
3
Page 18 questions
Percentages greater than 100%
a
a
a
c
e
c
c
e
e
b
b
b
d
f
d
d
f
f
20 525 5 125%
2025
100125
#
#= = =
15 %121
23
100150 0= = =
120% 1 1100120
10020
51= = =
1 0% 1 11100110
10010
101= = =
%355100355 3
10055 3
2011= = =
%270100270 2
10070 2
107= = =
%475100475 4
10075 4
43= = =
%192100192 1
10092 1
2523= = =
1 1 0%54
59
100180 8= = =
%22512
2562
100248 248= = =
%241
49
100225 225= = =
%31013
1043
100430 430= = =
1 1 5%2017
2037
100185 8= = =
120%2530
25 430 4
100120
#
#= = =
180%59
5 209 20
100180
#
#= = =
200 2160%
200320 320 2
100160
''= = =
0%300720
300 3720 3
100240 24
''= = =
%200576
200 2576 2
100288 288
''= = =
Equivalent fraction
Fraction FractionImproper fraction
Improper fraction
Improper fraction
Improper fraction
Equivalent fraction
Percentage
Percentage
Simplified Simplified
Percentage
Percentage
Mixed number
Mixed number
10 Percentage Basics SolutionsMathletics © 3P Learning Ltd
7HSERIES TOPIC
Where does it work? Solutions Percentage Basics
Page 19 questions
Page 21 questions
Percentages greater than 100%
4
5
1
a
a
c
g
i
a
d
b
e
c
f
e
b
d
h
j
f
c
e
g
b
d
f
h
% .124 124 100 1 24'= =
. 100 .212 5 2 125' =
165 165.5
. .
21
165 5 100 1 655` '
=
=
2.125 100 212.5%
. % %212 5 21221
#
`
=
=
3.004 100 . %
. % %
300 4
300 4 30052
#
`
=
=
3.105 100 310.5%# =
.
. .
28641 286 25
286 25 100 2 8625` '
=
=
1.902 100 190.2
. % %190 2 19051
#
`
=
=
2.0075 100 . %
. % %
200 75
200 75 20043
#
`
=
=
1.0535 100 105.35%# =
. .105 75 100 1 0575' =
% 100 .213 213 2 13'= =
% 100 .490 490 4 90'= =
% 100 .300 300 3 00'= =
2.35 2.3 100% 235%5 #= =
. . 100% %1 68 1 68 168#= =
. . 100% %9 07 9 07 907#= =
. . 100% %4 5 4 5 450#= =
Combo time:
. % %55 5 5595=o
. % %23 23 239923=o o
. % %122 2 12292=o
. % %8 08 8998=o o
. % %64 4 6494=o
10.12% 10 % 10 %9912
334= =o o
Recurring decimal percentages
7HSERIES TOPIC
11Percentage Basics SolutionsMathletics © 3P Learning Ltd
Where does it work? Solutions Percentage Basics
Page 21 questions
2
3
a
a
d
g
b
b
e
h
c
c
f
i
. . %
%
0 002 100 0 2
92
# =
=
o o
2 % 2.4%
. .
94
2 4 100 0 024` '
=
=
o
o o
. . %
%
0 064 100 6 4
694
# =
=
o o
. . %
%
0 3 100 33 3
3331
# =
=
o o
. . %
%
0 007 100 0 7
97
# =
=
o o
4 % 4 % 4.8%
. .
1816
98
4 8 100 0 048` '
= =
=
o
o o
. . %
%
0 08 100 8 8
898
# =
=
o o
. . %
%
0 98 100 98 8
9898
# =
=
o o
. . %
%
0 025 100 2 5
295
# =
=
o o
1 % 1 % 1.6%
. .
32
96
1 6 100 0 016` '
= =
=
o
o o
. . %
%
0 1 100 11 1
1191
# =
=
o o
. . %
%
0 26 100 26 6
2632
# =
=
o o
Recurring decimal percentages
12 Percentage Basics SolutionsMathletics © 3P Learning Ltd
7HSERIES TOPIC
What else can you do? Solutions Percentage Basics
Page 23 questions
One amount as a percentage of another
1
2
3
a
a
a
c
b
b
b
d
c d
out of5 20
%
205
10025
25
=
=
=
out of
100 %
37.5%
%
12 323212
25 32
3721
#'
=
=
=
=
^ h6 @
out of
(to d.p.)
%
. %
.
4 9 94
4 9 100
44 4
44 44 2
' #
=
=
=
=
o
^ h6 @
out of25 30
100 %
83.3%
%
3025
25 30
8331
#'
=
=
=
=
o
^ h6 @
out of
%
128 200200128
10064
64
=
=
=
out of
%
450 500500450
10090
90
=
=
=
out of
%
10 252510
10040
40
=
=
=
out of
100 %
87.5%
%
21 242421
21 24
8721
#'
=
=
=
=
^ h6 @
out of
to d.p.
%
. %
.
13 333313
13 33 100
39 39
39 39 2
' #
=
=
=
=
o o
^
^
h
h
6 @
out of. . 100 %
. %
%
10 1 40 10 1 40
25 25
2541
#'=
=
=
^ h6 @
7HSERIES TOPIC
13Percentage Basics SolutionsMathletics © 3P Learning Ltd
What else can you do? Solutions Percentage Basics
Page 23 questions
Page 24 questions
One amount as a percentage of another
One amount as a percentage of another
3
4
5
6
7
c dout of
(to d.p.)
. . %
. %
. %
8 9 11 8 9 11 100
80 90
80 91 2
#'=
=
=
o o
^ h6 @ out of
to d.p.
. . %
. %
. %
22 8 34 22 8 34 100
67 058 823 53
67 06 2
#'=
=
=
^
^
h
h
6 @
100 %
%
48 50
96
#'=
=
^ h6 @
%
%
16 25 100
64
#'=
=
^ h6 @
%
%
2 8 100
25
#'=
=
^ h6 @
(to d.p.)
%
. %
. %
1 7 100
14 285 714 29
14 29 2
#'=
=
=
^ h6 @
` Grace spelled 96% of the words correctly in the test.
` 64% of Luke's passes were good.
` 25% of covers available have a striped pattern.
Two of the covers have a striped pattern and there are eight different covers altogether.
Green is one of the seven different main dispersed light colours.
The colour green makes up 14.29% of the dispersed white light.
14 Percentage Basics SolutionsMathletics © 3P Learning Ltd
7HSERIES TOPIC
What else can you do? Solutions Percentage Basics
Page 25 questions
One amount as a percentage of another
8
9
10
11
12
(to d.p.)
. . %
. %
. %
0 82 3 6 100
22 7
22 8 1
#'=
=
=
o
^ h6 @
(to d.p.)
%
. ...%
. %
14 39 100
35 897 435 9
35 9 1
#'=
=
=
^ h6 @
. %
78.75%
%
12 6 16 100
7843
#'=
=
=
^ h6 @
%
. %
%
8 15 100
53 3
5331
#'=
=
=
o
^ h6 @
%
. %
%
4 18 100
22 2
2292
#'=
=
=
o
^ h6 @
` One song contains 35.9% of all the different chords the band plays in one show.
` Nicola has already used %7843 of the memory stick storage space.
` %5331 of the hexagons are shaded black.
` %2292 of the chocolates have pink foil.
Of the fifteen hexagons, eight of them are shaded black.
There are four pink wrapped chocolates, and eighteen wrapped chocolates altogether.
` 22.8% of the cordial is syrup flavour.
7HSERIES TOPIC
15Percentage Basics SolutionsMathletics © 3P Learning Ltd
What else can you do? Solutions Percentage Basics
Page 26 questions
One amount as a percentage of another
13
14
15
16
% 88%22 25 100#' =^ h6 @
(to d.p.)
%
.
47.8% 1
32 67 100
47 761194 03
#'=
=
=
^ h6 @
100 % . %
%
41500 19173 22 327
22 327 41500 53 8
5354
#'
- =
=
=
^^
hh6 @
(to d.p.)
% %
% . %
4 3 5 4 3 5 2 100 88
12 14 100 85 7 1
#
#
'
'
= + + + + + =
= =
^ ^h h6
66
@
@ @
` 88% of the students had completed their homework.
` 47.8% of the people at the meeting voted 'no'.
` 85.7% of the movies were not romantic comedies.
` %5354 of the supporters left the game disappointed.
If 35 voted 'yes', then 67 - 35 = 32 voted 'no'.
16 Percentage Basics SolutionsMathletics © 3P Learning Ltd
7HSERIES TOPIC
Notes Percentage Basics
www.mathletics.com
Percentage BasicsSERIES
H