Perc
enta
ge B
asic
s PERCENTAGEPERCENTAGEPERCENTAGEBASICSBASICSBASICS
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7HSERIES TOPIC
1Percentage Basics Solutions
Mathletics Passport © 3P Learning
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=
%71007=
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 Solutions
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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
6817
256
14042
195
2512
2511
2017
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
7HSERIES TOPIC
3Percentage Basics Solutions
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How does it work? Solutions Percentage Basics
Page 7 questions
Page 8 questions
Decimals and percentages
Combo time: Decimals, fractions and percentages
1
2
3
4
The percentage value is divided by 100, so the decimal point is moved 2 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 2 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 Solutions
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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 Solutions
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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 numeral
Mixed numeral Mixed numeral
Mixed numeral
Mixed numeral
Mixed numeral
Mixed numeral
Mixed numeral
6 Percentage Basics Solutions
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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 c
c
d
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 numeral
Mixed numeral
Mixed numeral
Mixed numeral
Mixed numeral
Mixed numeral
Mixed numeral
Mixed numeral
7HSERIES TOPIC
7Percentage Basics Solutions
Mathletics Passport © 3P Learning
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 Solutions
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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 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 Solutions
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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 numeral
Mixed numeral
10 Percentage Basics Solutions
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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 Solutions
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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 Solutions
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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.)
%
. %
.
4 994
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 Solutions
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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 Solutions
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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 Solutions
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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
#'
- =
=
=
^
^
h
h6 @
(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 Solutions
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7HSERIES TOPIC
Notes Percentage Basics
00 DECIM
ALS AND PERCEN
TAGES *
* *
...../...../20..
.. DECIM
ALS, FRACTIONS A
ND PERCENTA
GES *
...../...../20....
FRACTI
ONAL
AND DECIMALPE
RCENTAGES
...../...../
20....
**** ONE **** AMOUNT AS A PERCENTAGE
OF ANOTHER
...../...../2
0....
REC
URRING DECIMAL PERCE
NTAGES.....
.......
...../...../20....