Yan Oi Tong Tin Ka Ping Secondary School
2021 Summer Pre-S1 Remedial Class
Name:
Chapter 1: Numbers and Four Operations of Integers
Date:
In these lessons, we will mainly:
(1) revise for simple mathematical concepts and basic computations; and
(2) introduce vocabulary frequently used in Mathematics.
Concept 1.1 (Numbers)
Vocabulary
Chinese Meaning
Meaning
(1) Natural number
All positive integers.
(2) Whole Number
All positive integers and ______.
(3) Even Numbers
All whole numbers which are
Example(s)
divisible by ______.
(4) Odd Numbers
All whole numbers which are not
divisible by ______.
Exercise 1.1
Questions
Answers
1. Write down all even numbers between 40 and 50.
2. Write down the first six whole numbers.
3. How many even numbers are there between 1 and 100?
Chapter 1 Notes
1
Concept 1.2 (Basic Numbers in English)
We need to know how to express numbers in English especially for conversation.
Express the following numbers in English.
Numbers
English
Numbers
1
11
2
12
3
13
4
14
5
15
6
16
7
17
8
18
9
19
10
20
30
70
40
80
50
90
60
100
Numbers
English
Numbers
1000
10000
Numbers
English
English
English
2847
5932
72492
46213
Chapter 1 Notes
2
Concept 1.3 (Four Basic Arithmetic Operations)
Operation
Chinese
Symbol
Example
Remark
Meaning
6 + 4 = 10
(1) Addition (n.)
____________ (v.)
10– 4 = 6
(2) Subtraction (n.)
____________ (v.)
5 × 9 = 45
(3) Multiplication (n.)
____________ (v.)
45 ÷ 9 = 5
(4) Division (n.)
47 ÷ 9 = 5 … 2
____________ (v.)
Concept 1.4 (Word phrases for Arithmetic Expressions)
Operation
Vocabulary Used
Expression Examples
𝑎+𝑏
(i)
a is added to b; Add a to b; a plus b
𝑎−𝑏
(ii)
Subtract b from a; a minus b
𝑎×𝑏
(iii)
a multiply to b; a times b
𝑎÷𝑏
(iv)
a is divided by b; Divide a by b
Chapter 1 Notes
3
Exercise 1.2
Express the word phrases in numerical expressions, then calculate the answers.
Word Phrases
e.g.
Add 3 to 6.
1.
52 is added to 28.
2.
Six is subtracted from nineteen.
3.
Eighty plus twelve and then multiply the sum to three.
4.
Divide 570 by 10 and then plus 9.
5.
The product of 19 and 274.
6.
Subtract five from the product of three and nineteen.
7.
Divide 735 by 5 and then add 16 to the quotient.
8.
Subtract 52 from the quotient of 666 divided by 6.
Numerical
Expressions
Answers
3+6
9
Exercise 1.3
Write a word phrase to describe each of the following.
e.g.
3+6
1.
5×7
2.
120 ÷ 8
3.
4 × 2 + 31
4.
9−7
5.
15 × (71 − 27)
6.
34 + (98 ÷ 7)
- Add 3 to 6. // 3 plus 6.
7.
8.
Chapter 1 Notes
4
Concept 1.5 (Order of Operations)
Rule 1: First multiplication or division, then addition or subtraction. (
Rule 2: Complete calculations in brackets first. (
)
)
Exercise 1.4
Calculate the followings.
1. 5 × (17 − 4)
2. (464 + 58) ÷ (222 ÷ 37)
3. 84 ÷ [3 × (72 − 68)]
4. 9 + (9 − 9) × 289 ÷ 328
5. 1200 ÷ 3 − (2208 ÷ 12) × 2 + 11
6. 24 ÷ {8 × [724 − (397 + 326)]}
Chapter 1 Notes
5
Exercise 1.6 (Word Problems)
To tackle with word problems, you are advised to understand the question first before calculating for the
numerical answer.
Question 1
Tom is 175 cm tall. Sam is 18 cm shorter than Tom. Find their total height.
Question 2
Jennifer made some cupcakes and puddings for Christmas party. The cost of making a cupcake is greater
than that of making a pudding by $4.
(a) If Jennifer made 12 cupcakes with $72, find the cost of making a pudding.
(b) Find the cost if Jennifer made 9 cupcakes and 17 puddings.
Chapter 1 Notes
6
Reflection: What have you learnt in this chapter?
Vocabulary learnt in this chapter:
Chapter 1 Notes
7