Percentage Basics
PERCENTAGE
BASICS
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How does it work?
Solutions
Percentage Basics
Page 3 questions
Proper fractions to percentages
100 = 100%
100
1
a
9 = 9%
100
2
a
7% = 7
100
b
13% = 13
100
c
29% = 29
100
d
50% = 50 = 1
100
2
e
20% = 20 = 1
100
5
f
25% = 25 = 1
100
4
b
40 = 40%
100
c
75% = 75 = 3
100
4
h
14% = 14 = 7
100
50
78% = 78 = 39
100
50
k
45% = 45 = 9
100
20
a
6 = 6'2
200
200 ' 2
= 3
100
i
55% = 55 = 11
100
20
Simplest
Form
l
68% = 68 = 17
100
25
Simplest
Form
Simplest
Form
Simplest
Form
3
Simplest
Form
Simplest
Form
Simplest
Form
j
d
Simplest
Form
Simplest
Form
g
75 = 75%
100
b
= 3%
80 = 80 ' 4
400 ' 4
400
= 20
100
c
= 20%
150 = 150 ' 5
500
500 ' 5
= 30
100
= 30%
Page 4 questions
Proper fractions to percentages
3
d
7 = 7 # 10
10
10 # 10
= 70
100
e
= 70%
4
a
1 = 1 # 50
2
2 # 50
= 50
100
= 50%
5 = 5#2
50
50 # 2
= 10
100
f
= 10%
b
= 40%
3 = 3#4
25
25 # 4
= 12
100
c
10 = 10 # 10
10
10 # 10
= 100
100
= 100%
= 12%
Percentage Basics Solutions
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10 = 10 # 4
25
25 # 4
= 40
100
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How does it work?
Solutions
Percentage Basics
Page 4 questions
Proper fractions to percentages
4
d
3 = 3 # 25
4
4 # 25
= 75
100
3 = 3 # 20
5
5 # 20
= 60
100
e
= 75%
g
27 = 27 ' 3
300
300 ' 3
= 9
100
f
= 60%
198 = 198 ' 2
200 ' 2
200
= 99
100
= 9%
50 = 50 ' 25
2500
2500 ' 25
= 2
100
h
= 99%
355 = 355 ' 5
500 ' 5
500
= 71
100
i
= 2%
= 71%
Page 5 questions
Proper fractions to percentages
5
17
68
48%
9
15
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TOPIC
h
b
44%
S
h
S
Q
85%
U
d
O
E
42
140
b
z
a
R
S
O
L
I
D
U
S
d
h
m
a
z
b
x
Percentage Basics Solutions
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x
R
%
7
X
60
H
a
%
24
U
6
25
x
S
D
L
12
25
F
11
25
X
z
2
d
I
m
17
20
25%
m
30%
How does it work?
Solutions
Percentage Basics
Page 7 questions
Decimals and percentages
1
2
The percentage value is divided by 100, so the decimal point is moved 2 places to the left.
a
b
35 ' 100 = 0 . 3 5 .
= 0.35
d
4
32 ' 100 = 0 . 3 2 .
= 0.75
e
4 ' 100 = 0 . 0 4 .
= 0.32
f
1 ' 100 = 0 . 0 1 .
9 ' 100 = 0 . 0 9 .
= 0.01
= 0.04
3
c
75 ' 100 = 0 . 7 5 .
= 0.09
The decimal is multiplied by 100, so the decimal point is moved 2 places to the right.
a
b
0.55 # 100 = 0 . 5 5 .
= 55%
d
c
0.23 # 100 = 0 . 2 3 .
0.7 # 100 = 0 . 7 0 .
= 23%
e
0.8 # 100 = 0 . 8 0 .
= 70%
f
0.01 # 100 = 0 . 0 1 .
= 80%
0.04 # 100 = 0 . 0 4 .
= 4%
= 1%
Page 8 questions
Combo time: Decimals, fractions and percentages
Fra
cti
on
1
10
1
2
4
5
3
5
7
10
9
50
3
4
al
0.25
0.1
0.5
0.8
0.6
0.7
0.18
0.75
en
tag
e
25%
10%
50%
80%
60%
70%
18%
75%
De
1
4
cim
Pe
rc
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Solutions
Percentage Basics
Page 9 questions
Combo time: Decimals, fractions and percentages
2
a
b
: 40 ' 100 = 0 . 4 0 .
: 90 ' 100 = 0 . 9 0 .
= 0.4
= 0.9
: 40 = 2
100
5
c
: 90 = 9
100
10
d
: 0.42 # 100 = 0 . 4 2 .
: 0.15 # 100 = 0 . 1 5 .
= 15%
= 42%
: 42 = 21
100
50
e
3
a
:
: 15 = 3
100
20
90 ' 2 = 45
100
200 ' 2
f
:
7 ' 2 = 14
100
50 ' 2
= 0.45
Decimal
= 0.14
Decimal
= 45%
Percentage
= 14%
Percentage
: 0.08 # 100 = 0 . 0 8 .
b
: 1 # 5 = 5 = 0.05
100
20 # 5
c
: 36 ' 100 = 0. 3 6 .
= 8%
:
d
= 0.36
8 = 2
100
25
: 6 # 4 = 24 = 0.24
100
25 # 4
:
e
: 36 = 9
100
25
5 = 5%
100
: 84 ' 3 = 28
300 ' 3
100
f
:
60 ' 15 = 4 = 1
1500 ' 15
100
25
= 0.28
4
: 24 = 24%
100
: 28 = 28%
100
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= 0.04
:
4 = 4%
100
How does it work?
Solutions
Percentage Basics
Page 11 questions
Fractional and decimal percentages
1
a
2 = 0.5 = 0.5%
400
100
1%
2
=
Decimal
c
4 = 0.8 = 0.8%
500
100
a
15 = 7.5 = 7.5%
200
100
Decimal
c
13 = 2.6 = 2.6%
500
100
Decimal
e
4%
5
=
71 %
2
=
Decimal
3 = 0.4 = 0.4%
750
100
23 %
5
=
41 %
4
b
10 = 2.5 = 2.5%
400
100
92%
5
2%
5
=
Proper
fraction
d
Mixed numeral
30 = 3.75 = 3.75%
800
100
26 = 5.2 = 5.2%
500
100
Mixed numeral
=
75 = 18.75 = 18.75%
400
100
Mixed numeral
51 %
5
Mixed numeral
Decimal
h
33%
4
=
Decimal
f
21 %
2
=
Decimal
Mixed numeral
=
Proper
fraction
Decimal
Mixed numeral
17 = 4.25 = 4.25%
400
100
47 = 9.4 = 9.4%
500
100
d
Mixed numeral
=
3%
4
=
Decimal
Proper
fraction
Decimal
g
3 = 0.75 = 0.75%
400
100
Proper
fraction
Decimal
2
b
=
18 3 %
4
Mixed numeral
Decimal
Page 12 questions
Fractional and decimal percentages
3
4
a
0.105
b
0.3705
c
0.0245
d
0.0604
e
0.0075
f
0.000 15
a
2.5%
b
6.25%
c
11.85%
e
45.05%
e
7.05%
f
0.96%
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How does it work?
Solutions
Percentage Basics
Page 12 questions
Fractional and decimal percentages
5
c
0.255 =
25.5%
Decimal
c
0.1025 =
0.045 =
10.25%
4.6%
Decimal
g
0.218 =
21.8%
Decimal
6
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d
0.085 =
=
10 1 %
4
d
50.75 =
43 %
5
f
0.084 =
Mixed numeral
=
21 4 %
5
Mixed numeral
50.75%
8.4%
Decimal
h
0.555 =
Mixed numeral
55.5%
Decimal
Percentage Basics Solutions
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81 %
2
=
=
Decimal
Mixed numeral
=
8.5%
Decimal
Mixed numeral
Decimal
e
25 1 %
2
=
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50 3 %
4
Mixed numeral
82 %
5
=
Mixed numeral
=
55 1 %
2
Mixed numeral
Where does it work?
Solutions
Percentage Basics
Page 14 questions
Percentage of an amount
1
a
25% of 20 = 25
100
b
# 20
30% of 30 = 30
100
=9
=5
c
2
a
40% of 65 = 40 ' 100 # 65
10
100
# 60
d
75
100
# 28
= 0.45 # 40
= 26
= 18
= 600
100
b
50
100
# 18
= 2100
100
40
100
# 24
= 960
100
= 900
100
c
25
100
# 16
=9
e
60
100
# 20
= 21
g
45% of 40 = 45 ' 100 # 40
= 0.4 # 65
=6
d
# 30
= 1200
100
=4
f
= 12
h
= 9.6
20
100
# 39
= 400
100
80
100
# 30
= 2400
100
= 24
= 780
100
= 7.8
Page 15 questions
Percentage of an amount
3
a
^20 ' 100h # 40 = 8
b
^30 ' 100h # 20 = 6
c
^50 ' 100h # 32 = 16
d
^35 ' 100h # 80 = 28
e
^25 ' 100h # 44 = 11
f
^75 ' 100h # 18 = 13.5
g
^21 ' 100h # 30 = 6.3
h
^19 ' 100h # 25 = 4.75
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Where does it work?
Solutions
Percentage Basics
Page 15 questions
Percentage of an amount
4
a
^40 ' 100h # 45 = 18
40
100
or
# 45
= 1800 = 18
100
` 18 of the people were dressed as angels.
b
^15 ' 100h # 200 = 30
15
100
or
# 200
= 3000 = 30
100
` Qian's music collection fills 30 GB of storage space.
Page 16 questions
Percentage of an amount
5
a
18% = the word 'love', ` 100% - 18% = 82% of the words are not the word 'love'.
^82 ' 100h # 150 = 123
82
100
or
# 150
= 12 300 = 123
100
` 123 of the 150 words in Justin's poem are not the word 'love'
b
58% = prefer bananas, ` 100% - 58% = 42% prefer apples.
^42 ' 100h # 800 = 336
or
42
100
# 800
= 33 600 = 336
100
` 336 of the 800 fruit eating animals at the zoo preferred the taste of apples.
6
a
35% + 14% + 6% = 55%, 100% - 55% = 45% of the mixture is milk
^45 ' 100h # 430 = 193.5
or
45
100
# 430
= 19 350 = 193.5
100
` there is 193.5 mL in the pancake mixture.
b
20% of 245 = ^20 ' 100h # 245
= 49 g
` (245 - 49) = 196 g left on the heaviest side
` total amount weights on the scales = 2 # 196 = 392 g
8
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Solutions
Percentage Basics
Page 18 questions
Percentages greater than 100%
1
a
25 = 25 # 5 =
20
20 # 5
125
100
= 125%
2
3
30 = 30 # 4 =
25
25 # 4
e
9 = 9 # 20 =
5
5 # 20
a
11
2
=
3
2
120
100
150
100
=
Improper
fraction
Fraction
9
5
180
100
c
14
5
e
2 12
25
a
120% =
=
=
=
62
25
= 120%
180
100
120
100
Improper
fraction
= 180%
= 150%
= 180%
= 248%
= 1 20
100
= 11
5
Mixed
numeral
110% =
110
100
= 1 10
100
= 1 1
10
e
355% =
355
100
= 3 55
100
= 3 11
20
Percentage
720 = 720 ' 3 =
300
300 ' 3
240
100
= 240%
f
576 = 576 ' 2 =
200
200 ' 2
288
100
= 288%
b
21
4
=
9
4
225
100
=
Improper
fraction
= 225%
Fraction
Percentage
d
3 13
10
=
43
10
=
430
100
= 430%
f
1 17
20
=
37
20
=
185
100
= 185%
b
270% =
270
100
Improper
fraction
= 2 70
100
= 2 7
10
Simplified
Mixed
numeral
d
475% =
475
100
= 4 75
100
= 43
4
f
192% =
192
100
= 1 92
100
= 1 23
25
Percentage Basics Solutions
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= 160%
d
Simplified
c
160
100
Equivalent
fraction
Percentage
248
100
=
320 = 320 ' 2 =
200
200 ' 2
Percentage
Equivalent
fraction
c
b
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Solutions
Percentage Basics
Page 19 questions
Percentages greater than 100%
4
5
a
124% = 124 ' 100 = 1.24
b
2.35 = 2.35 # 100% = 235%
c
213% = 213 ' 100 = 2.13
d
1.68 = 1.68 # 100% = 168%
e
490% = 490 ' 100 = 4.90
f
9.07 = 9.07 # 100% = 907%
g
300% = 300 ' 100 = 3.00
h
4.5 = 4.5 # 100% = 450%
Combo time:
a
212.5 ' 100 = 2.125
b
105.75 ' 100 = 1.0575
c
165 1 = 165.5
2
d
286 1 = 286.25
4
` 165.5 ' 100 = 1.655
` 286.25 ' 100 = 2.8625
e
3.105 # 100 = 310.5%
f
1.0535 # 100 = 105.35%
g
2.125 # 100 = 212.5%
h
1.902 # 100 = 190.2
` 212.5% = 212 1 %
2
i
` 190.2% = 190 1 %
5
j
3.004 # 100 = 300.4%
2.0075 # 100 = 200.75%
` 200.75% = 200 3 %
4
` 300.4% = 300 2 %
5
Page 21 questions
Recurring decimal percentages
1
10
a
55.5o % = 55 5 %
9
b
122.2o % = 122 2 %
9
c
64.4o % = 64 4 %
9
d
o o % = 23 23 %
23.23
99
e
o o% = 8 8 %
8.08
99
f
o o = 10 12 % = 10 4 %
10.12%
99
33
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Solutions
Percentage Basics
Page 21 questions
Recurring decimal percentages
2
a
0.002o # 100 = 0.2o %
b
0.007o # 100 = 0.7o %
= 2%
9
d
0.064o # 100 = 6.4o %
0.3o # 100 = 33.3o %
e
0.08o # 100 = 8.8o %
a
h
0.98o # 100 = 98.8o %
f
0.1o # 100 = 11.1o %
= 11 1 %
9
i
0.26o # 100 = 26.6o %
= 98 8 %
9
o
2 4 % = 2.4%
9
= 26 2 %
3
o
4 16 % = 4 8 % = 4.8%
18
9
b
` 4.8o ' 100 = 0.048o
` 2.4o ' 100 = 0.024o
c
= 25 %
9
= 88%
9
= 33 1 %
3
3
0.025o # 100 = 2.5o %
= 7%
9
= 64%
9
g
c
o
1 2 % = 1 6 % = 1.6%
3
9
` 1.6o ' 100 = 0.016o
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Solutions
Percentage Basics
Page 23 questions
One amount as a percentage of another
1
a
5 out of 20 = 5
20
= 25
100
b
10 out of 25 = 10
25
= 40
100
= 40%
= 25%
c
128 out of 200 = 128
200
= 64
100
d
450 out of 500 = 450
500
= 90
100
= 64%
2
a
c
= 90%
12 out of 32 = 12
32
b
21 out of 24 = 21
24
= 6^25 ' 32h # 100 @%
= 6^21 ' 24h # 100 @%
= 37.5%
= 87.5%
= 37 1 %
2
= 87 1 %
2
25 out of 30 = 25
30
d
= 6^25 ' 30h # 100 @%
10.1 out of 40 = 6^10.1 ' 40h # 100 @%
= 25.25%
= 25 1 %
4
o
= 83.3%
= 83 1 %
3
3
a
4 out of 9 = 4
9
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13 out of 33 = 13
33
= 6^4 ' 9h # 100 @%
= 6^13 ' 33h # 100 @%
= 44.4o %
o o%
= 39.39
= 44.44
12
b
(to 2.d.p.)
= 39.39
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^ to 2 d.p.h
What else can you do?
Solutions
Percentage Basics
Page 23 questions
One amount as a percentage of another
3
c
8.9 out of 11 = 6^8.9 ' 11h # 100 @%
d
22.8 out of 34 = 6^22.8 ' 34h # 100 @%
o o%
= 80.90
= 67.058 823 53%
= 80.91% (to 2 d.p.)
= 67.06% ^ to 2 d.p.h
Page 24 questions
One amount as a percentage of another
4
= 6^48 ' 50h # 100 @%
= 96%
` Grace spelled 96% of the words correctly in the test.
5
= 6^16 ' 25h # 100 @%
= 64%
` 64% of luke's passes were good.
6
Two of the covers have a striped pattern and there are eight different covers altogether.
= 6^2 ' 8h # 100 @%
= 25%
` 25% of covers available have a striped pattern.
7
Green is one of the seven different main dispersed light colours.
= 6^1 ' 7h # 100 @%
= 14.285 714 29%
= 14.29% (to 2 d.p.)
The colour green makes up 14.29% of the dispersed white light.
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Percentage Basics
Page 25 questions
One amount as a percentage of another
8
= 6^0.82 ' 3.6h # 100 @%
= 22.7o %
= 22.8% (to 1 d.p.)
` 22.8% of the cordial is syrup flavour.
9
= 6^14 ' 39h # 100 @%
= 35.897 435 9...%
= 35.9% (to 1 d.p.)
` One song contains 35.9% of all the different chords the band plays in one show.
10
= 6^12.6 ' 16h # 100 @%
= 78.75%
= 78 3 %
4
` Nicola has already used 78 3 % of the memory stick storage space.
4
11
Of the fifteen hexagons, eight of them are shaded black.
= 6^8 ' 15h # 100 @%
= 53.3o %
= 53 1 %
3
` 53 1 % of the hexagons are shaded black.
3
12
There are four pink wrapped chocolates, and eighteen wrapped chocolates altogether.
= 6^4 ' 18h # 100 @%
= 22.2o %
= 22 2 %
9
` 22 2 % of the chocolates have pink foil.
9
14
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Percentage Basics
Page 26 questions
One amount as a percentage of another
13
6^22 ' 25h # 100 @% = 88%
` 88% of the students had completed their homework.
14
If 35 voted 'yes', then 67 - 35 = 32 voted 'no'.
= 6^32 ' 67h # 100 @%
= 47.761194 03
= 47.8% (to 1 d.p.)
` 47.8% of the people at the meeting voted 'no'.
15
= 6^4 + 3 + 5h ' ^4 + 3 + 5 + 2h # 100 @% = 88%
= 6612 ' 14 @ # 100 @% = 85.7% (to 1 d.p.)
` 85.7% of the movies were not romantic comedies.
16
^41 500 - 19 173h = 22 327
6^22 327 ' 41 500h # 100 @% = 53.8%
= 53 4 %
5
` 53 4 % of the supporters left the game disappointed.
5
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Notes
16
Percentage Basics
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