14
Introduction
Bridge Programme P6 to S1 is written according to the latest secondary mathematic curriculum. It
is aimed to help primary 6 students get consolidated on some primary mathematics concepts in the
summer holiday, so that they can get well prepared before studying Mathematics in S1.
In this book, 8 revision units are chosen from the primary Mathematic Curriculum with the
following key features.
Key Features The basic mathematic concepts are illustrated with Examples. Students can get a full review
on the primary mathematic knowledges.
The Examples and Solutions are written in the format as secondary school to help students get
familiar in learning mathematics in secondary school.
English pronunciations of useful vocabulary and sentences are provided on our website to
give genuine support for students adapting to a new learning language medium.
Relevant mathematical terms are tabulated in Key Terms / Phrases or underlined for easy
reference and memory reinforcement.
Knowing More focus on some topics which can help students have a better preparation for the
secondary school lessons.
Useful Sentences are available to allow students adequate exposure to different question types.
Different types of questions are included in Exercises. The Chinese translations of difficult
vocabulary are given in footnotes to facilitate student’s understanding.
Numerical answers to questions are provided.
How to use?
This book can be distributed to Primary 6 students in the summer holiday for self-study. Students
are suggested to complete this book before their first Mathematics lesson in S1.
CONTENTS 1. Arithmetic Operations .......................................... 1
A Four Basic Arithmetic Operations .............................. 1
B Multiples and Factors ............................................... 3
Key Terms / Phrases ..................................................... 5
Useful Sentences ........................................................ 5
Exercise 1 ..................................................................... 5
2. Decimals and Fractions ....................................... 8
A Conversion between Decimals and Fractions............. 8
B Basic Operations of Decimals and Fractions .............. 10
Key Terms / Phrases ..................................................... 13
Useful Sentences ........................................................ 13
Exercise 2 ..................................................................... 13
3. Approximations
4. Basic Algebra and Simple Equations .............. 17
A Introduction to Algebra ............................................. 17
B Simple Equations ..................................................... 18
C Application of Equations ........................................... 19
Key Terms / Phrases ..................................................... 21
Useful Sentences ........................................................ 21
Exercise 4 .................................................................... 22
5. Percentages
6. Shape and Space
7. Perimeters, Areas and Volumes
8. Data Handling .......................................................... 25
A Different Statistical Diagrams ...................................... 25
B Applications of Statistical Diagrams ............................ 26
Key Terms / Phrases ..................................................... 28
Useful Sentences ........................................................ 28
Exercise 8 ..................................................................... 29
Answers ............................................................................ 32
Knowing More
Recurring decimals
Knowing More
Prime Factors
Index Notation
Bridge Programme P6 to S1 Junior Secondary Mathematics in Action
8 © Pearson Education Asia Limited 2020
2 Decimals and Fractions
A. Conversion between Decimals and Fractions
16.295 is a decimal, which can be read as sixteen point two nine five.
Fractions can be classified into following three types:
Proper fraction Improper fraction Mixed fraction
The numerator is smaller than
the denominator.
The numerator is greater than
or equal to the denominator.
An improper fraction which is
written as a sum of a natural
number and a proper fraction.
Read as : three-fifths /
three over five
Read as : seven quarters /
seven over four
Read as : six and two-thirds /
six and two over three
Example 1
Convert 0.45 into a fraction.
450.45
100
9
20
=
=
Reduce the fraction to its simplest form.
numerator
3 5
7 4
integral part
6 2 3
Improper fractions can be converted into mixed fractions and vice versa.
e.g. 7 3
14 4
=
denominator
fractional part
16.295 thousandths
tenths
decimal point
hundredths
units
tens
9
20
Bridge Programme P6 to S1 Junior Secondary Mathematics in Action
9 © Pearson Education Asia Limited 2020
Example 2
Convert 3
5 and
7
25 into decimals.
Method 1: Expand the fractions 3 3 2
5 5 2
6
10
0.6
=
=
=
7 7 4
25 25 4
28
100
0.28
=
=
=
Method 2: Use division .. 3
3 55
0.6
=
=
77 25
25
0.28
=
=
Example 3
Arrange the following numbers in descending order.
1 3
1 , 1 , 1.1254 8
Method 1: Convert the numbers into fractions 1 1 2 2
1 1 14 4 2 8
= =
125 11.125 1 1
1000 8= =
∵ 3 2 1
1 1 18 8 8
∴ 3 1
1 1 1.1258 4
Method 2: Convert the numbers into decimals
1 11 1 1 0.25 1.25
4 4
3 31 1 1 0.375 1.375
8 8
= + = + =
= + = + =
∵ 1.375 1.25 1.125
∴ 3 1
1 1 1.1258 4
Compare the numerators.
5 3.0
0.6
3 0
25 7.00
0.28
5 0
2 00 2 00
Bridge Programme P6 to S1 Junior Secondary Mathematics in Action
10 © Pearson Education Asia Limited 2020
B. Basic Operations of Decimals and Fractions
The following table shows some basic arithmetic operations of decimals.
Addition Subtraction
e.g. 2.08 3.42
5.5
+
=
e.g. 5.4 2.25
3.15
−
=
Multiplication Division
e.g. 8.12 3.4
27.608
=
e.g.
3.5 0.4
(3.5 10) (0.4 10)
35 4
8.75
=
=
=
Example 4
Evaluate 2.5 3.6 1.5 .
2.5 3.6 1.5 9 1.5
(9 10) (1.5 10)
90 15
6
=
=
=
=
The following table shows some basic arithmetic operations of fractions.
Addition Subtraction
e.g. 1 1 2 1
3 6 6 6
3
6
1
2
+ = +
=
=
e.g. 2 1 6 1
3 2 3 25 15 15 15
51
15
11
3
− = −
=
=
Multiplication Division
e.g.
1 1 10 1
33 15 3 15
2
9
=
=
e.g. 5 2 5 9
27 9 27 2
5
6
=
=
.2.08
+ 3.42
5.50
.5.40
– 2.25
3.15
8.12
× 3.4
24 360
+ 3 248
27.608
Multiply both the divisor and the dividend by 10 so that the divisor
becomes a whole number.
. 2.5
× 3.6
. 7 50
+ . 1 50
9.00
.1
2
3 3
1
. 8.75 0.4 3.5.00 3 2 3 0 2 8 20 20
Bridge Programme P6 to S1 Junior Secondary Mathematics in Action
11 © Pearson Education Asia Limited 2020
Example 5
Evaluate 1 3 5
2 34 4 6
+ .
1 3 5 1 15 62 3 2
4 4 6 4 4 5
1 92
4 2
1 12 4
4 2
1 22 4
4 4
36
4
+ = +
= +
= +
= +
=
Example 6
Harry bought a 3
kg4
chocolate cake and ate 3
5 of it. Find the weight of the remaining chocolate
cake.
Weight of the remaining chocolate cake
3 31 kg
4 5
3 2 kg
4 5
3 kg
10
= −
=
=
Express 3
34
as an improper fraction.
Perform multiplication and division before addition and subtraction.
Express the fractions in a common denominator.
If the multiplication and division of fractions involve mixed fractions, we
should first change the mixed fractions into improper fractions.
Bridge Programme P6 to S1 Junior Secondary Mathematics in Action
12 © Pearson Education Asia Limited 2020
Example 7
The selling price of a pen is $6.3 and the selling price of a pencil is $3.7. What is the total selling
price of half a dozen pens and 1
13
dozen pencils?
Total selling price
1 1$ 6.3 12 3.7 12 1
2 3
4$ 6.3 6 3.7 12
3
$(6.3 6 3.7 16)
$(37.8 59.2)
$97
= +
= +
= +
= +
=
In a decimal, if a digit or a pattern of digits after the decimal point repeats continuously, the decimal is called a
recurring decimal. For example: 0.555…, 0.409 09 …, 0.629 629… are recurring decimals.
In a recurring decimal, the repeated part is called the recurring period. It is indicated by the recurring
point(s).
For example:
0.555 555... 0.5•
= 0.409 090... 0.409• •
= 0.629 629... 0.629• •
=
We can use recurring decimals to represent fractions as follows:
1 8 11
0.333... 0.3, 0.7272... 0.72, 0.407 407... 0.4073 11 27
• • • • •
= = = = = =
Knowing More
Recurring point(s)
Recurring period
Recurring decimals
Bridge Programme P6 to S1 Junior Secondary Mathematics in Action
13 © Pearson Education Asia Limited 2020
decimal 小數 thousandths 千分位 mixed fraction 帶分數
decimal point 小數點 fraction 分數 divisor 除數
units 個位 numerator 分子 dividend 被除數
tens 十位 denominator 分母 recurring decimals 循環小數
tenths 十分位 proper fraction 真分數
hundredths 百分位 improper fraction 假分數
What fraction of the time is spent on studying? 花在學習上的時間佔幾分之幾？
What fraction of 7
8 is
1
2?
1
2 是
7
8 的幾分之幾？
Convert the following mixed fraction into an
improper fraction. 把以下帶分數寫成假分數。
4.085 is read as three point zero seven five. 4.085 讀作四點零八五。
Which digit in 35.62 is in hundredths place? 在 35.62 這個數中，哪一個數字是在百分位？
Exercise 2
1. Consider the number 65.013. Determine whether each of the following is true for the number.
Put a ‘’ or a ‘’ in each of the boxes.
(a) ‘1’ is in the hundredths place. (b) ‘1’ in the number represents 10.
(c) ‘6’ in the number represents 60 000. (d) ‘0’ is in the tenths place.
(e) ‘5’ in the number represents 50. (f) It is equal to 13
65100
.
2. Reduce the following fractions into their simplest forms.
(a) 24
80 (b)
120
135 (c)
126
42
Useful Sentences
Key Terms / Phrases
Pronunciation
Bridge Programme P6 to S1 Junior Secondary Mathematics in Action
14 © Pearson Education Asia Limited 2020
3. Convert the following decimals into fractions.
(a) 0.55 (b) 3.75 (c) 15.625
4. Convert the following fractions into decimals.
(a) 98
200 (b)
13
8 (c)
27
25
5. Compare the values of each of the following pairs of fractions. Put a ‘>’ or ‘<’ in each of the boxes.
(a) 4 6
5 7
(b) 11 14
8 11
(c) 5 7
13 17
6. Arrange each of the following sets of numbers in ascending order.
(a) 6.7, 8.03, 0.969, 10.34
(b) 3.6, 3.06, 36, 30.6
7. Arrange each of the following sets of numbers in descending order.
(a) 2
3,
5
6,
7
12,
1
2
(b) 0.5, 1
8,
11
16, 1.15,
11
4, 0.12
Evaluate the following. (8 − 19)
8. 5.4 3.2 2.6− + 9. 19.8 0.33
10. 12.6 0.7 2.25 4 − 11. (6.6 0.3 1.5) 4 −
12. 11 5 7
30 6 10+ − 13.
7 6 10
30 7 12
14. 19 1
1 32 145 7
15. 2 11
3 25 35
−
16. 7 1 1 2
110 2 6 3
− 17. 2 11 5 5
3 12 6 8
− +
18. 3
2.5 3 (2 0.75)4
+ 19. 7 1
0.25 2 112 16
−
Bridge Programme P6 to S1 Junior Secondary Mathematics in Action
15 © Pearson Education Asia Limited 2020
ascending order 由小至大排列
Find the result of each of the following. (20 − 22)
20. 6.5 L orange juice is divided into 26 cups equally. How much orange juice
is there in each cup in L?
21. Wendy is 35 years old and Jacky is 15 years old. What fraction of Wendy’s
age is Jacky’s age?
22. A bag of coconuts weighs 10.5 kg. If we sell 5 bags of coconuts for $756,
how much does one kilogram of coconuts cost?
Solve the following problems. Show your working steps clearly. (23 – 26)
23. Each box of apples costs $35.8. It costs $4.3 more than each box of oranges. Nelson pays $250 for
5 boxes of oranges. How much change should he get?
24. A bag of peanuts weighing 4
25
kg costs $30. Mary buys a bag of peanuts that weighs 2
43
kg.
How much should she pay?
Bridge Programme P6 to S1 Junior Secondary Mathematics in Action
16 © Pearson Education Asia Limited 2020
coconut 椰子
25. Red roses cost $50.4 per dozen, yellow roses cost $81.6 per dozen.
How much do 5 red roses and 8 yellow roses cost?
26. Linda uses 1
7 of a bag of flour to make some bread and
3
5 of the
rest of it to make some biscuits. What fraction of the flour is left?
Bridge Programme P6 to S1 Junior Secondary Mathematics in Action
32 © Pearson Education Asia Limited 2020
Answers
Exercise 1 Arithmetic Operations
1. 12 + 70 = 82 2. 2000 – 106 = 1894
3. 97 – 48 + 23 = 72 4. 30 × 5 – 38 = 112
5. (12 + 4) × 8 = 128 6. (35 + 17) ÷ 13 = 4
7. (30 – 14) + 20 = 36 8. 28 ÷ 4 + 16 × 4 = 71
9. 50 – 45 ÷ 9 = 45 10. 10
11. 70 12. 3317
13. 160 14. 177
15. 36 16. 41
17. 34 18. False
19. False 20. True
21. True
22. (a) 56 (b) 72
(c) 150 (d) 120
23. (a) 6 (b) 4
(c) 27 (d) 6
24. 87 25. $15
26. $36 27. 2 kg
28. $152 29. $80
30. 16
31. 1:45 p.m., 5:30 p.m., 9:15 p.m.
Exercise 2 Decimals and Fractions
1. (a) (b) (c)
(d) (e) (f)
2. (a) 3
10 (b)
8
9 (c) 3
3. (a) 11
20 (b)
33
4 (c)
515
8
4. (a) 0.49 (b) 3.125 (c) 1.08
5. (a) < (b) > (c) <
6. (a) 0.969 < 6.7 < 8.03 < 10.34
(b) 3.06 < 3.6 < 30.6 < 36
7. (a) 5 2 7 1
6 3 12 2
(b) 1 1 1
1 1.15 1 0.5 0.124 16 8
8. 4.8 9. 60
10. 9 11. 1.92
12. 1
2 13.
1
6
14. 7
180 15.
101
81
16. 16
45 17.
49
72
18. 5
16
19. 1
3
20. 0.25 L 21. 3
7
22. $14.4 23. $92.5
24. $50 25. $75.4
26. 12
35
Exercise 4 Basic Algebra and
.Simple Equations
1. Alegebraic
expression Equation
(a) 5 4b+
(b) 7 3 17c+ =
(c) 23 8 1d d+ =
(d) 2 100x −
(e) 2
6 73
m n− =
2. a + 10 3. b – 7
4. 5c 5. 4
d
6. a + 5.5 7. b – 10
Bridge Programme P6 to S1 Junior Secondary Mathematics in Action
2 © Pearson Education Asia Limited 2020
8. 3y 9. 50
k
10. 25m2 11. 7
12. 173 13. 19
14. 60 15. 9
16. 5 17. 5
18. 35 19. 7
20. 3.9 21. 1.5
22. 4.61 23. x + 25 = 59
24. y + 1 = 15 25. p – 7 = 12
26. 130z = 3380 27. 100 – 4d = 16
28. 2[12 + (12 – a)] = 42
29. 35 30. 65
31. $5.4 32. 32
33. $3120
Exercise 8 Data Handling
1. (a) broken-line graph (b) broken-line graph
(c) bar chart (d) bar chart
(e) broken-line graph
2.
3. (a) Monday, 240 mm (b) Saturday, 540 mm
(c) 2140 mm
4. (a) $220 000 (b) September
(c) March and April
5. (a) Cooking (b) 17
(c) Book store A, 46
