Percentage Basics Solutions GBR

www.mathletics.com

Percentage Basics

PercentageBasics

Solutions

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

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7HSERIES TOPIC

1Percentage Basics SolutionsMathletics Passport © 3P Learning

How does it work? Solutions Percentage Basics

questions

Page 4 questions

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 Passport © 3P Learning

7HSERIES TOPIC


questions

Page 5 questions



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



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 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


7HSERIES TOPIC


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



Page 11 questions

Page 12 questions

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


7HSERIES TOPIC


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


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


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


a

e

c

g

b

fd

h


7HSERIES TOPIC


4

5

6

of

g

%20 245 20 100 245

49

#'=

=

^ h

Page 15 questions

Page 16 questions



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



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


7HSERIES TOPIC


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



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


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



Page 23 questions

Page 24 questions



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.


7HSERIES TOPIC


Page 25 questions


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



Page 26 questions


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'.


7HSERIES TOPIC

Notes Percentage Basics

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Percentage Basics

Percentage Basics Solutions GBR

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