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(c) 20 cm : 1 m  20 cm : 100 cm
20

100
1

5
1: 5
B uild-up Exercise 12A
(page 12.13)
10
20
1

2
1: 2
1. (a) 10 : 20 
5
15
1

3
1: 3
(b) 5 : 15 
18
12
3

2
3:2
(c) 18 : 12 
40
24
5

3
5:3
(d) 40 : 24 
0.2
0.6
2

6
1

3
1: 3
2. (a) 0.2 : 0.6 
1 1
(b) : 
2 4
1
2
1
4
2
 2 :1
42
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(d) 800 g : 0.5 kg  800 g : 500 g
800

500
8

5
8:5
3. (a) Area of the shaded regions : Area of the
unshaded regions
 4:4
 1:1
(b) Area of the shaded regions : Area of the
unshaded regions
 4:2
 2 :1
(c) Area of the shaded regions : Area of the
unshaded regions
 3:6
 1: 2
4. (a)
1: 2  x : 4
1 x

2 4
1
x
4  4
2
4
x 2
(b) 3 : 4  12 : y
3 12

4 y
3 y  12  4
48
y
3
 16
(c)
z : 10  9 : 5
z 9

10 5
z
9
 10   10
10
5
z  18
5. Number of salmon sushi : Number of California
rolls
 12 : 20
 3:5
8. (a) 10 : 6  ( x  1) : 3
10 x  1

6
3
10  3  6( x  1)
30  6 x  6
6 x  24
x 4
9 : 2  18 : ( y  3)
(b)
9
18

2 y3
9( y  3)  18  2
36
9
y34
y3
6. (a) Number of students wearing glasses :
Number of students of the whole class
 20 : 42
 10 : 21
(b) Number of students without wearing glasses
 42  20
 22
 Number of students without wearing
glasses : Number of students of the
whole class
 22 : 42
 11 : 21
(c) Number of students wearing glasses :
Number of students without wearing glasses
 20 : 22
 10 : 11
7. Number of candies got by her daughter
4
 28 
43
4
 28 
7
 16
Number of candies got by her son
3
 28 
7
 12
y 7
(c) ( z  5) : 4  7 : 2
z 5 7

4
2
7
z 5 4
2
z  5  14
z  19
3x  4 y
9. (a)
3x 4 y

y
y
3x 1 4 1
  
y 3 1 3
x 4

y 3

(b)
x: y  4:3
a b

2 3
a 1

2b 3
a 2

b 3
 a:b  2:3
43
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h  0.6k
(c)
(c) 
y:z 
h 0.6

k
1
3

5
 h : k  3:5

13. (a) 
5
5 1
5
 $2  30 
6
 $50
1
(b) Total value of $1 coins  $1  30 
6
 $5
(c) Total value of all coins in the bag
 $(50  5)
 $55
 Total value of $1 coins : Total value of
all coins in the bag

y : x  3: 2

x: y  2:3

x: y
 2:3
y:z 
(c) 
14. (a) 
x:
z  3:
 2 :1
1 : 10
x : y : z  2 : 1 : 10
 1: 2
y:z 
9:7
2  3 3:
1: 6 
23  9:
1: 6 
6
1: 6
a
1
b
b 1

c 2
 a : b  1:1
b : c  1: 2
 a : b : c  1:1: 2
(b) 
2:5
x : y : z  1: 2 : 5
44
 2008 Chung Tai Educational Press. All rights reserved.
a 1

b 2
 a : b  1: 2

18 30 12
:
(c) 18 : 30 : 12  :
6 6 6
3:5: 2
x: y
9 :7 
 b : c  1: 2
(page 12.14)
14 7 42
(b) 14 : 7 : 42  : :
7 7 7
 2 :1: 6
y:z 
9:7 
 6:9
x : y : z  9 :1: 6

x: y
 2  3: 3 3
x: y : z  6:9:7
y:z 

4
x : y : z  5:3: 4
 1 : 11
4 8 12
: :
4 4 4
1: 2 : 3

z  5:
 a : b  1:1
11. (a) 4 : 8 : 12 
(b) 
 5:3
 $5 : $55
B uild-up Exercise 12B

x: y
(b) 

4:3
x: y : z  9:4:3
x:
10. (a) Total value of $2 coins  $2  30 
12. (a) 
 9:4
x: y
b  3c
b
3
c
 b : c  3 :1
 3: 6
 a : b  1 : 2  1 3 : 2  3
b : c  3 :1 
3  2 : 1 2  6 : 2
 a : b : c  3: 6 : 2
(c) 
4a  5b
a 5

b 4
 a :b  5:4

5b  2c
b 2

c 5
 b:c  2:5
 5:4
 a :b  5:4  5: 4
b : c  2 : 5  2  2 : 5  2  4 : 10
 a : b : c  5 : 4 : 10
15. Number of gold coins : Number of silver coins :
Number of copper coins
 45 : 60 : 90
45 60 90
:
:
15 15 15
 3: 4:6

16. (a) Number of English books : Number of
Chinese books : Number of Japanese books
 6 : 10 : 2
6 10 2
: :
2 2 2
 3 : 5 :1
 Number of apples : Number of mangoes :
Number of pears
 6:4:5
5
645
5
 30 
15
 10
(b) Number of pears  30 
19. When the alloy is divided into 3  2  4  9
portions, the weight of copper equals to that of
3 portions, the weight of zinc equals to that of
2 portions and the weight of gold equals to that
of 4 portions.
3
 The weight of the alloy  72  g
9
9
 72  g
3
 216 g

(b) Number of English books : Number of
Chinese books : Number of Japanese books
 (6  2) : (10  2) : ( 2  4)
 8 : 12 : 6
8 12 6
: :
2 2 2
 4:6:3

17. Amount of the largest portion
3
 $6 000 
3  2 1
3
 $6 000 
6
 $3 000
18. (a) Number of apples : Number of mangoes
 3: 2
 3 2 : 2 2
 6:4
20. (a) The monthly salary of Gibson : The monthly
salary of Dicky  3 : 1
The monthly salary of Cathy : The monthly
5
salary of Dicky  : 1
2
 The monthly salary of Gibson : The
monthly salary of Cathy : The monthly
salary of Dicky
5
 3 : :1
2
5
 3  2 :  2 : 1 2
2
 6:5:2
(b) The monthly salary of Gibson
6
 $34 060 
652
6
 $34 060 
13
 $15 720
The monthly salary of Cathy  $34 060 
 $13 100
Number of mangoes : Number of pears
 4:5
45
 2008 Chung Tai Educational Press. All rights reserved.
5
13
The monthly salary of Dicky  $34 060 
2
13
 $5 240
B uild-up Exercise 12C
(page 12.16)
21. (a) 5 km/h

 (i)
(b) $5/unit

 (ii) $5 per square metre
(c) $5/m 2

 (iii) $5 per unit
(d) 5 m/s

 (iv) $5 per metre
(e) $5/dozen 
(f) $5/m
22. (a)

(b) The price of lemon tea in a pack of 6
$14.4

6 cartons
 $2.4/carton
(c) Lemon tea in a pack of 9 is more
economical.
$5 per dozen
 (v) 5 kilometres per hour
 (vi) 5 metres per second
Distance
Time
Speed
(a)
5 km
1h
5 km/h
(b)
250 km
5h
50 km/h
(c)
20 m
5s
4 m/s
(d)
125 m
20 s
6.25 m/s
26. (a) The typing speed of Suki 
540 words
15 min
 36 words/min
2 700 words
1.5 hours
2 700 words

1.5  60 min
 30 words/min
The typing speed of Carmen 
(b) Suki has a higher typing speed.
$45
5 bottles
 $9/bottle
23. (a) Selling price of the apple juice 
$9
1.5 L
 $6/L
(b) Selling price of the apple juice 
144 km
2h
 72 km/h
24. (a) Speed of the car 
144 km
2h
144  1 000 m

2  60  60 s
 20 m/s
(b) Speed of the car 
25. (a) The price of lemon tea in a pack of 9
$19.8

9 cartons
 $2.2/carton
46
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27. (a) The drawing tutorial fee of Louise
$420

3 lessons
 $140/lesson
(b) The drawing tutorial fee of Louise in July
 $140  14
 $1 960
60 km
1 .5 h
 40 km/h
28. (a) Speed of the bus 
(b) Time required for the bus to travel 100 km
100
hours

40
 2.5 hours
29. (a) Amount of HK dollars exchanged for 1 UK
pound
76 HK dollars

5 UK pounds
 15.2 HK dollars/UK pound
 Amount of HK dollars exchanged for
100 UK pounds
 15.2  100 HK dollars
 1 520 HK dollars
 Distance on the map
1

 Actual distance
20 000
1

 700 m
20 000
1

 700  100 cm
20 000
 3.5 cm
(b) Amount of HK dollars exchanged for
1 Canadian dollar
30.6 HK dollars

4 Canadian dollars
 7.65 HK dollars/Canadian dollar
 Amount of HK dollars exchanged for
100 Canadian dollars
 7.65  100 HK dollars
 765 HK dollars
(c) UK pounds has a higher exchange rate to
HK dollars.
33.
Actual height of the building
42 m

3.5 cm
1 cm
 4 200
Actual height of the building  4 200  3.5 cm
B uild-up Exercise 12D
30. (a) 5 cm : 10 m  5 cm : 10  100 cm
5

1 000
1

200
 1 : 200
(b) 20 mm : 4 000 cm  20 mm : 4 000  10 mm
20

40 000
1

2 000
 1 : 2 000
(c) 60 cm : 12 km  60 cm : 12  1 000  100 cm
60

1 200 000
1

20 000
 1 : 20 000
31. Scale of the map  5 cm : 10 km
5
10
 cm :
km
5
5
 1 cm : 2 km
32. 
 14 700 cm
(page 12.17)
Distance on the map
1 cm

Actual distance
200 m
1

20 000
 147 m
34.
35.
Distance on the map
1

800 m
10 000
1
 800 m
Distance on the map 
10 000
1

 800  100 cm
10 000
 8 cm
Actual distance 1 000 000

8 cm
1
Actual distance  1 000 000  8 cm
 8 000 000 cm
 80 km
36. (a)
Actual length of the room 200

3 cm
1
Actual length of the room  200  3 cm
 600 cm
6m
Actual width of the room 200

4 cm
1
Actual width of the room  200  4 cm
 800 cm
8m
 The actual dimensions of the room
are 6 m  8 m.
47
 2008 Chung Tai Educational Press. All rights reserved.
Actual area of rectangle AEFG  3  1 m 2
(b) Actual area of the room  6  8 m 2
 3 m2
 48 m 2
Actual length of rectangle ABCD
(1.5  1.15) cm
Actual length of rectangle ABCD
Actual length of the store room 200

37. (a)
1 cm
1
Actual length of the store room
 200  1 cm
 200 cm
2m
 530 cm
 5. 3 m
Actual width of rectangle ABCD
(0.5  2) cm
 300 cm
3m
 Actual area of the store room  2  3 m
1.5 cm
A
2
1.15 cm
G
D
2
F
2 cm
 26.5 m2
 Actual area of the master bedroom
 Actual area of rectangle ABCD
 Actual area of rectangle AEFG
 23.5 m 2
Master bedroom
B
200
1
Actual area of rectangle ABCD  5.3  5 m2
 (26.5  3) m 2
0.5 cm
E

Actual width of rectangle ABCD
 200  2.5 cm
 500 cm
5m
 200  1.5 cm
(b)
200
1
 200  2.65 cm
Actual width of the store room 200

1.5 cm
1
Actual width of the store room
6m

C
Actual length of rectangle AEFG 200

1.5 cm
1
Actual length of rectangle AEFG
 200  1.5 cm
 300 cm
3m
Actual width of rectangle AEFG 200

0.5 cm
1
Actual width of rectangle AEFG
 200  0.5 cm
 100 cm
1m
48
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