Grade 7 Book 1 Unit 1 and 2

SARASAS AFFILIATED SCHOOLS
Mathematics Grade 7

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Foreword:
By Dr. Chamrat Nongmak

When talking about bilingual education in private elementary and secondary schools in Thailand, discussion
invariably tends to focus on Sarasas Affiliated Schools, a large group of private schools that was formerly owned and
administered by the late Mr. Peboon Yongkamol. Mr. Peboon, a well-known and respected educator, was a leading
pioneer of the bilingual education concept here in Thailand. These schools provide a benchmark and a showcase for
bilingual education in Thailand. Many school proprietors, directors, and managers make it a point to visit Sarasas
Affiliated Schools seeking advice and guidance from a successful leader in the field of bilingual education.

Sarasas programs for teaching students both in English and in Thai have been carefully planned and developed
step by step. One of the toughest challenges Sarasas has had to face has been finding the necessary texts and materials
for teaching Thai subjects in English. This is because a bilingual school, like any other Thai school, needs government
approval to operate and must teach the curriculum mandated by the Ministry of Education. Unfortunately, the
materials needed for teaching Thai subjects in English are not readily available. Publishers do little to support this need
because the concept is still fairly new and the demand is small. This has forced Sarasas to create its own texts and
materials.

Sarasas has been more fortunate though, than most other schools struggling to develop their own bilingual
program. It already has bilingual education experience, a qualified staff and the resources necessary to produce its
own high-quality textbooks and materials. The staff, of course, is the most important ingredient. Sarasas’ large, well-
seasoned staff of highly competent, well qualified and dedicated teaching professionals, both Thai and native speakers
of English, gives it a unique advantage over others attempting to produce these much-needed materials.

Even so, it has not been an easy task. The materials have been produced through the careful process of
research and development. Revision or total change is done when those materials are proven to be inadequate. The
people involved in developing these textbooks or workbooks are classroom teachers. They are the ones who will have
to teach with the same materials they have helped to create. Knowing this gives them a greater incentive to do it right.

The teams of classroom teachers responsible for classroom material development operate under the close
supervision of the Sarasas Board of Executives.

One of the roles of the board is to assure proper quality control by collecting and carefully evaluating the
actual work done by students using the new materials. They make certain that the students are able to understand the
material and use them effectively. One of the things they check for, is whether the level of English used in the books is
appropriate for the students’ level of English. The board also makes certain that the content of the material is in
accordance with the approved syllabus. The Mathematics book has been developed through this process.

This book is not only useful for teachers but also for parents and guardians. Its purpose is to encourage and
support students in their quest for knowledge and understanding of Mathematics, as well as stimulate their interest
and improve their skills. Each unit provides an introduction to the material, a list of new words the student will
encounter, problem solving examples to help the student better understand how to do the work, oral exercises, and a
review of what was learned.

This new Maths material will provide students with a greater international perspective and understanding of
Mathematics and Mathematics terminology which will benefit them greatly in later life. This said, I would like to take
this opportunity to thank those responsible for developing this material and offer my sincere congratulations for a job
well done.

Chamrat Nongmak, PhD.

Former Deputy Permanent Secretary
The Ministry of Education

PREFACE

This Mathematics textbook has been developed for bilingual learners based
on the B.E. 2560 (A.D. 2017) revised version of Thailand’s Basic Education Core
Curriculum B.E. 2551 (A.D. 2008). The content of this book follows the Basic
Mathematics for Grade 7 Book written by The Institute of Academic Development.

This textbook aims to enhance students’ abilities needed in the 21st century.
These include analytical skills, problem solving skills, creativity and collaboration
skills.

At the beginning of each unit of this textbook, a useful vocabulary list is
provided to learners. Examples demonstrate to students how to apply the
information they have learnt to solve related problems. Exercises and activities
follow that allow for immediate practice. At the end of each unit, a summary of the
key learning concepts along with a revision exercise is provided to help students
consolidate what they have learnt.

Author,
Sarasas Affiliated Schools

March 2022

TABLE OF CONTENTS

Unit 1: Integers 18

1 1. Integers…………………………………… 2 Week 1 to 4
1.1 Positive Integers
Unit 2: 1.2 Ordering Integers 7
11
2. Properties of Integers………………
3. Addition of Integers………………… 16
19
3.4 Using a Number Line 621
3.5 Using Absolute Value 23
4. Subtraction of Integers…………… 24
5. Multiplication of Integers……….. 112447
6. Division of Integers………………….
Summary………………………………
Revision Exercise…………………..

Fractions and Decimals

11.. FFrraaccttiioonnss………………………………… 28 Week 5 to 8
1.11.1DefiDneitfiionnition
1.12.2EquEivqauleivnatleFnrat cFtriaocntsions
1.13.3ComCpoamripnagriFnrgacFtriaocntsions

22.. AAddddiittiioonnaannddSSuubbttrraaccttiioonnooff
FrFarcatciotinosns……………………………. 32
2.21.1AddAitdiodnitioofnForaf cFtriaocntsions
2.22.2SubStruabcttriaocntioofnForaf cFtriaocntsions

33..MMulutilptilpiclaictaiotinonanadndDiDviivsiiosinonofof
FFrraaccttiioonnss……………………………….. 37
3.31.1MultiMpliuclatitpiolincaotfioFnraocftiFornasctions
3.32.2DiviDsiiovnisioofnForaf cFtriaocntsions

44.. DDeeccimimaalsls……………………………….. 41
4.41.1PlacPelaVcaeluVealoufeDoefcDimecailms als
4.42.2ComCpoamripnagriDnegcDimecailms als
4.43.3RouRnoduinngdianDg eacDimecailms als

55.. AAddddiittiioonnaannddSSuubbttrraaccttiioonnooff
DDeeccimimaalsls………………………………… 46
5.51.1AddAitdiodnitioofnDoefcDimecailms als
5.52.2SubSturabcttriaocntioofnDoefcDimecailms als

6.6M. MultuipltliipclaictiaotnioannadnDdiDviisviiosnioonfof Week 9
DeDciemcaimlsa…ls………………………………. 51
66..11 MMuultlitpiplicliactaitoionnoof fDDeceicmimalasls
66..22 DDiviivsiisoionnoof fDDeceicmimalasls
SSuummmmaarryy…………………………….. 58
RReevviissiioonnEExxeerrcciissee…………………. 59

Unit 3: Exponents 62

1. Exponents……………………………… 63 Week 11 to 13
1.1 Definition
Unit 4: 1.2 Finding the value of
Exponential Numbers
1.3 Writing numbers in Exponential
Form

2. Laws of Exponents………………… 67
2.1 Product Law
2.2 Quotient Law
2.3 Power Law
2.4 Negative Exponent
2.5 Zero Law

3. Scientific Notation………………… 72
Summary……………………………. 75
Revision Exercise………………… 76

Linear Equation in One Variable 79

1. Linear Equation with One Week 14
Variable………………………………. 80
1.1 Definition
1.2 Mathematical Sentence and
Truth Value

2. Properties of Equality……………. 84
2.1 Addition Property of
Equality
2.2 Subtraction Property of
Equality
2.3 Multiplication Property of
Equality

2.4 Division Property of Equality Week 15 to 16
2.5 Solving Equations using the
Week 17 to 19
Properties
3. Application of Linear

Equation……………………………… 92
3.1 Number Problems
3.2 Age Problems
3.3 Geometry Problems
3.4 Speed and Time Problems
3.5 Investment Problems
3.6 Work Problems
Summary…………………………….. 116
Revision Exercise………………… 117

Unit 5: Ratios, Proportions, and Percentages 121

1. Ratios……………………………………. 122
1.1 Equivalent Ratio

2. Proportions…………………………… 128
3. Percentages…………………………… 134

3.1 Writing a Ratio as a
Percentage

3.2 Writing a Percentage as a
Ratio

3.3 Percent calculation
4. Application of Ratios, Proportions

and Percentages………………… 142
Summary……………………………. 147
Revision Exercise………………… 148







Integers

Mathematical Terms

Neutral ท่ีเปน็ กลาง

Absolute Value คา่ สมั บรู ณ์ Number line เสน้ จำนวน
Ascending การเพม่ิ ขน้ึ
Descending การลดลง Order ระเบยี บ, ลำดบั
Divisor ตัวหาร Quotient ผลหาร
Increase เพมิ่ ขึ้น, มีมากข้ึน
Integers จำนวนเตม็ Value ค่า, มูลค่า

Natural number

จำนวนธรรมชาติ

Associative Property Negative integers

คณุ สมบตั ริ ว่ มกัน, คณุ สมบตั ิเชอื่ มโยง จำนวนเตม็ ลบ

Commutative Property Opposite number

คณุ สมบัตกิ ารสับเปล่ียน, คณุ สมบตั ิการสลับท่ี จำนวนตัวเลขตรงกันขา้ ม

Dividend Positive integers

ตัวต้ังสำหรบั การหาร, ตวั ตัง้ หาร จำนวนเต็มบวก

Did you know?

Mathematics Book 1 1

1. Integers

Integers

Negative Zero Positive

Integers are numbers with no fractional part which include positive integers,
0 and negative integers. Integers are important numbers in mathematics as well as
in real life. These numbers let us know the position where one is standing and also
help in computing the efficiency in positive or negative numbers in almost every field.

1.1 Positive Integers

Positive integers are numbers that are on the right of 0 and are bigger than
0, also known as natural numbers or counting numbers. The smallest positive
number is 1.

0 1 2 34 5 6

Example 1

a. List the positive integers between 20 and 25.
b. List the positive integers that are more than 5 but less than 13 using a

number line.

Solution

a. The positive integers between 20 to 25 are 21, 22, 23, 24.

20 21 22 23 24 25
b. The positive integers that are more than 5 but less than 13 are 6, 7, 8,

9, 10, 11, 12.

5 6 7 8 9 10 11 12 13

We show positive numbers with a + sign

2 Mathematics Book 1

+5 means positive five

1.2 Negative Integers

Negative integers are numbers to the left of zero (0) and are less than 0. The
largest negative integer is -1.

-6 -5 -4 -3 -2 -1 0

Example 2

List the next three numbers in each sequence.

a. 0, -3, -6
b. From -7, increase by 3
c. From 4, decrease by 3

Solution

a. -15 -12 -9 -6 -3 0
Therefore, 0, -3, -6, -9, -12, -15

b. -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3
Therefore, -7, -4, -1, 2

c. -6 -5 -4 -3 -2 -1 0 1 2 3 4

Therefore, 4, 1, -2, -5

1.3 Zero

As a digit, zero (0) is used as a placeholder in place value systems. It is also
known as neutral as it is neither a negative nor a positive number.

Mathematics Book 1 3

1.4 Ordering Integers

-3 -2 -1 0 1 2 3

Numbers to the left Numbers to the right
of 0 are negative. of 0 are positive.

From the number line, we can observe that the integers on the right side of
the number line are greater than the ones on the left. With positive numbers, the
bigger the number, the more it represents. With negative numbers, the bigger the
digit, the smaller the value.

Example 3

1. −1 is less than 0, which can be expressed as − <

2. 2 is greater than −10, which can be expressed as > −

3. Arrange the following integers in ascending order.

a. −8, −12, −6, 5, 10, −1

b. −16, −1, 0, 2, −3, 4

Solution

a. −12, −8, −6, −1,5,10

b. −16, −3, −1,0,2,4

4. Fill in the boxes with the correct symbol ( > < ) then write it in

ordinary sentence.

a. −3 0

b. 5 −5

c. −4 6

d. −8 −7

4 Mathematics Book 1

Solution

a. −3 < 0 ; Negative three is less than 0.
b. 5 > − 5; Five is greater than negative five.
c. −4 < 6 ; Negative four is less than six.
d. −8 < −7 ; Negative eight is less than negative seven.

Exercise 1A

1. Identify the positive and negative integers.

Positive Negative

a. − , , − ,

b. . ̇ , , -10, 10


c. 1.234…, , 16, -1

d. − , . , ,


2. List the four numbers after c. −25, decreasing by 4.
a. 10, increasing by 7.

b. −5, increasing by 8. d. 2, decreasing by 5.

3. Write the next five numbers in each sequence.

a. 9, 1, -7… c. 12, 19, 26

b. 4, -2, -8 d. -8, -3, 2…

Mathematics Book 1 5

4. Arrange the following: 4.2) Descending
4.1) Ascending a. −2, −101, 12, −9, 15
b. −119, 51, −27, 32,0
a. 3, −8, 14, 1, 5

b. −38, −19, 47, 11, 7

5. Fill in the boxes with > , < , and to make the

sentence correct.

a. 13 −13

b. −22 −2

c. Fourteen is forty.

d. Negative ninety-nine is nineteen.

6. John borrowed ฿20,000 to pay for his trip. He promised to pay ฿4,000
every week.

0 2,000 4,000 6,000 8,000 10,000 12,000 14,000 16,000 18,000 20,000

a) . How much does he owe at the end of the first week?

b) How many weeks will it take him to pay back the full amount?

6 Mathematics Book 1

2. Properties of Integers

Properties Descriptions

(Let a, b and c be any integer)

Commutative Changing the order of the addends a+b=b+a
Property of does not change the sum. axb=bxa
(a + b) + c = a + (b + c)
Addition Changing the order of the factors
Commutative does not change the product.
Property of
Multiplication Changing the grouping of the
Associative addends does not change the sum.
Property of

Addition

Associative Changing the grouping of the (a x b) x c = a x ( b x c)
Property of factors does not change the a(b + c)=(a x b)+(a x c)
Multiplication product.

Distributive Multiplying a sum by a number is
Property the same as multiplying each
addend by that number and then
adding the two products.

Identity Property 1. Addition a+0=a
of Zero ▪ Adding 0 and any
number does not
change the value of
the number.

2. Multiplication

Identity Property ▪ The product of 0 and ax0=0
of 1 any number is 0. ax1=a

Multiplying 1 and any number does
not change the value of the
number.

Mathematics Book 1 7

Example 4

Look at the examples below:

1. Commutative Property of Addition
12 + 8 = 20
8 + 12 = 20

Thus, 12 + 8 = 8 + 12 since they are both equals to 20.

2. Commutative Property of Multiplication
14 × 10 = 140
10 × 14 = 140
Thus, 14 × 10 = 10 × 14 since they are both equals to 140.

3. Associative Property of Addition
(20 + 50) + 10 = 70 + 10 = 80
20 + (50 + 10) = 20 + 60 = 80

Thus, (20 + 50) + 10 = 20 + (50 + 10) since they are both equals
to 80.
4. Associative Property of Multiplication

(8 × 3) × 2 = 24 × 2 = 48
8 × (3 × 2) = 8 × 6 = 48
Thus, (8 × 3) × 2 = 8 × (3 × 2) since they are both equals to 48

5. Distributive Property
2(6 + 4) = 2 × 10 = 20
(2 × 6) + (2 × 4) = 12 + 8 = 20

Thus, 2(6 + 4) = (2 × 6) + (2 × 4) since multiplying a number by
the sum of two numbers is the same as the sum of the product of two numbers in
the parenthesis.

8 Mathematics Book 1

Example 5

Find the value of the variables and identify which property is used.

1. + = + Value of the Property
variable
z=3 Commutative Property of
Addition
2. + ( + ) = ( + ) + w = 2, t = 6 ,
3. × = × v = 13 Associative Property of
k=4 Addition

4. × ( × ) = ( × ) × p = 3, m = 7 Commutative Property of
Multiplication
5. (− + ) = (− × ) + f = −2
(− × ) b = 25 Associative Property of
6. × = Multiplication

Distributive Property

Identity Property of 1

7. + = c=0 Identity Property of 0

Exercise 1B

1. Evaluate the following:
a. 0 + (−5) =
b. (−9) × 1 =
c. (21 + 6) × −3 =
d. (15 ÷ 5) − 0 =
e. (1 − 1) ÷ 1 =

Mathematics Book 1 9

2. Find the value of the variable in each equation.
a. z + ( 5 + 6 ) = 10
b. w × 5 = 0
c. (21 × 3 ) + (−12 × 6) = y × 9
d. (18 × 8) + (v × −11) = (25 × 4)
e. (15 × −10) = ( 15 × p) + (6 × −5)

3. Fill in the boxes with the correct number.

a. 7 + 10 = 7 + −3

b. + ( 6 – 9) = 9 + 6

c. ( 5 × 100 ) + ( 5 × 30 + 5) = 5 × ( × 131 )
×) + (4 × 7)
d. 39 × 15 = ( + 39 ) × 15

e. ( 10 – 6 + 4 ) × 7 = ( 10 × 7) + (

4. Jonas has 12 marbles and his brother has 7. If we double both their
marbles;
a. Construct an equation.

b. How many marbles do they have now?
c. What property was used?

10 Mathematics Book 1

3. Addition of Integers

There are two ways to add integers: using a number line or using the
absolute value.

3.1 Using a Number Line

-3 -2 -1 0 1 2 3

To add a negative number, To add a positive number,
move to the left. move to the right.

Example 6

a. 2 + 3 = ?
b. (−2) – (−3) =?
c. 3 + (−2) = ?

d. (−3) + 2 =?

Solution

a.

-1 0 1 2 3 4 5

Thus, 2 + 3 = 5

b.

-5 -4 -3 -2 -1 0 1

Thus,(−2) – (−3) = −5

Mathematics Book 1 11

c.

-1 0 1 2 3 4 5

Thus, 3 + (−2) = 1

d. 1

-5 -4 -3 -2 -1 0

Thus, (−3) + 2 = −1

3.2 Using Absolute Value

33
-3 -2 -1 0 1 2 3

“3” is 3 units away from 0,
and “-3” is also 3 units away from 0.
So, the absolute value of 3 is 3 and the absolute value of -3 is also 3.

Example 6

a. The absolute value of 9 is 9.
b. The absolute value of -13 is 13.
c. The absolute value of -231 is 231.
d. |57| is 57.
e. |−91| is 91.

Note:
The absolute value of a number ( | | ) is the distance of that number from
0.

12 Mathematics Book 1

There are 2 conditions to remember when adding integers:
1. When adding integers having the same sign, add the numbers then
copy the sign.

Same sign Add the numbers. Copy the sign.

99 9

33 3

12 12

Example 7

a. 10 + 5 =?
The absolute value of 10 or |10| = 10
The absolute value of 5 or |5| = 5
Thus, 10 + 5 = 15

b. (−18) + (−7) =?
|−18| is 18
|−7| is 7

Thus, (−18) + (−7) = −25

2. When adding two integers having different signs, subtract the absolute
value of the numbers then copy the sign of the integer with the larger
number.

Different sign Subtract the Copy the sign of the
numbers. larger number.
8
5 8 8
5 5
3 3

Mathematics Book 1 13

Example 8

a. 18 + (−9) =?

The absolute value of 18 is 18
The absolute value of -9 is 9
Thus 18 + (−9) = 18 − 9 = 9
The result is positive since the sign of the larger absolute value is
positive.

b. (−23) + 15 =?

The absolute value of (-23) is 23
The absolute value of 15 is 15
We have (−23) + 15 = 23 − 15

=8
The result should be negative since the sign of the larger absolute value is
negative.
Thus (−23) + 15 = −8

Note: 2+5=7

Addends Sum

Exercise 1C e. (−9) + 9 =
f. (−41) + (−19) =
1. Find the value of the following. g. (−100) + 54 =
a. 15 + 28 = h. (−143) + (−309) =
b. 43 + (−15) =
c. (−20) + (−42) =
d. (−115) + 28 =

14 Mathematics Book 1

2. Find the value of the following equations.
a. [(−14) + 7] + (−2) =
b. (−2) + [4 + (−140)] =
c. (−450) + [(−350) + (−260)] =
d. [301 + (−107)] + (−125) =
e. (−117) + [(−1700) + 150] =

3. A submarine at 21 feet below sea level suddenly moves up about 6 feet. At
what depth is the submarine located now?

4. On a game show, Mark got to spin the wheel twice. He got 600 points the first
time. The second time, he got -600 points. Assuming he started with no
points, what was his total score?

5. Lucy had 140,000 baht. She loaned 50,000 baht to a friend, spent 31,000 baht
and received her 40,000 baht paycheck from work. How much money does
she have now?

6. Rey borrowed 18,500 baht to buy a computer and 28,000 baht to buy a
cellphone. How much does Rey owe altogether?

Mathematics Book 1 15

4. Subtraction of Integers

When subtracting two integers, change the sign of the subtrahend and
then apply addition of integers.

a. −

Change subtraction Change the second
into addition. number into its
opposite.
Copy

10 − 7 =

+ (− ) = =

b. –

Change subtraction Change the second
into addition. number into its
opposite.
Copy

− − (− ) =

− + = −

16 Mathematics Book 1

c. –

Change Change the
subtraction into second number
into its opposite.
addition.

Copy

− (− ) =

+ =

d. −

Change Change the
subtraction into second number
into its opposite.
addition.

Copy

− − =

− + (− ) = −

Note: 7+3=4 Difference
Minuend
Subtrahend

Mathematics Book 1 17

Exercise 1D

1. Find the value of the following.
a. 12 − (3 − 9) =
b. [(−4) − 80] − 100 =
c. (−55) + [(−12) − 20] =
d. (−15) + (16 − 15) =
e. (−55) + [(−12) − 20] =

2. Find the value of the variable.
a. 3 − e = −10
b. 80 − d = 49
c. 0 + (−0) = c
d. b − 25 = 10
e. (−19) − a = 50

3. An airplane takes off and then climbs 2,500 feet. After 20 minutes, the airplane
descends 150 feet. What is the airplane’s current height?

4. The highest temperature recorded in Changmai is 28℃ and the lowest is−2℃.
What is the difference between the highest and the lowest?

5. McDoods owes his sister 23,400 baht. If he paid 12,650 baht, how much does
he still owe his sister?

18 Mathematics Book 1

5. Multiplication of Integers

There are 2 conditions to remember when multiplying integers:
A. If the two integers have the same sign, then their product is positive.

Rules b. -3
-7
Example 9 21

a. 4
5
20

B. If the two integers have different signs, then their product is
negative.

Rules

Example 10 b. -11
8
a. 6
-5 -88
-30
5 × 2 = 10 Product
Note:
Multiplicand Multiplier

Mathematics Book 1 19

Exercise 1E

1. Find the value of the following:
a. (−7) × (13) =
b. (−6) × 3 × 5 =
c. (−1) × 40 × (−7) =
d. (−6) × (−5) × (−4) =
e. 11 × (−12) × (−2) =

2. Fill in the boxes with the correct number.

a. × (−3) = −39 f. 9 × × (−4) = −108

b. 7 × = 77 g. 11 × (−5) × = 165

c. × (−4) = 36 h. × (−3) × (−4) = −60

d. × (−9) = −117 i. (−1) × (−9) × =0

e. × 7 × 3 = −42 j. (−4) × × (−6) = 24

3. From sea level, a submarine descends 40 feet per minute. Where is the
submarine in relation to sea level 5 minutes after it starts descending?

4. A test has 10 questions. The teacher gives 3 points if the answer is correct
and minus 1 point if the answer is incorrect. A student answered 5
questions incorrectly. How many points did the student lose?

20 Mathematics Book 1

6. Division of Integers

Similar to multiplying integers, dividing integers is just dividing the numbers
normally but there are 2 conditions to remember:

A. If the two integers have the same sign, then their quotient is positive.

Rules

Example 11

a. 10 b. -9
5 -3

2 3

B. If the two integers have different sign, then their quotient is negative.

Rules b. 30
-5
Example 12 -6

a. -33
3

-11

Note: 6÷2=3

Dividend Divisor Quotient

Mathematics Book 1 21

Exercise 1F

1. Find the value of the following:
a. (−9) ÷ 9 =
b. 44 ÷ (−4) =
c. (−754) ÷ (50 + 8) =
d. (40 − 329) ÷ (−17) =
e. (64 − 100) ÷ (549 − 558) =

2. Fill in the boxes with the correct number.

a. ÷ (−3) = f. [(−45) ÷ ] ÷ 3 = −3

b. 20 ÷ = −5 g. [( ÷ 6)] + [(−16) ÷ (−4)] = 9

c. (−64) ÷ = −8 h. [(72 ÷ 9) − ( ÷ 11)] = 6

d. ÷ 1 = −13 i. [( ÷ 61) ÷ (48 ÷ 8)] = 0

e. [(−72) ÷ 8] ÷ = 3 j. [(−90) ÷ 6] ÷ (65 ÷ ) = −3

3. Mary owes 2,400,000 baht on her car loan. Each of her 4 children is willing
to pay an equal share of her loan. Find how much each of her children needs
to pay.

4. If 3,504 kg of wheat is packed in 48 bags, how much wheat will each bag
contain?

5. A plane can hold 1,008 passengers. If there are 12 rows of seats on the
plane, how many columns of seats are there?

22 Mathematics Book 1

Summary

• Negative numbers, zero and positive numbers are all integers.
• Positive numbers are numbers to the right of zero, also known as natural

numbers or counting numbers.
• Zero (0) is a neutral number since it is neither positive nor negative.
• Negative numbers are numbers to the left of zero and are less than 0.
• Commutative Property states that changing the order of the operands does

not change the result.
• Associative Property states that addition or multiplication can be done

regardless of the grouping and the result will still be the same.
• Identity Property of 1 states that any number multiplied by 1 stays the same.
• The absolute value of a number (| |) is the distance of that number from 0.
• When adding integers having the same sign, add the numbers then copy the

sign.
• When adding two integers having different signs, subtract the numbers and

copy the sign of the integer with the larger number.
• When subtracting two integers, change the sign of the subtrahend and then

apply addition of integers.
• The inverse of a number is its opposite.
• When multiplying two integers having the same sign, their product is

positive.
• When multiplying two integers having different signs, their product is

negative.
• When dividing two integers having the same sign, their quotient is positive.
• When dividing two integers having different signs, their quotient is

negative.

Mathematics Book 1 23

Revision Exercise

Part 1 (1-2)

1. Find the value of the following:
a. (−14) + (−9) − (−33) =
b. (−7) + 4 − 9 × 2 =
c. 4 + (−4) − 4 × (−4) ÷ 4 =
d. [40 ÷ (−5)] ÷ [(−12) ÷ (−6)] =
e. [(−30) ÷ 6] × (−16) ÷ [(−5) − (−4)] =

2. Given that p = −4, q = −6, r = 8 and s = −2
a. Find p + q − r − s

b. Find [(r ÷ p) × q]

c. Find [r × (p + q)] ÷ s

d. Find (r × s − p × q) ÷ (p − q)

24 Mathematics Book 1

Part 2 (3-18) 8. Which of the following is true?
a. Negative integers are
Choose the correct answer. whole numbers.
3. Which of the following is correct? b. Zero is a counting number.
a. −2 > 0 c. All integers are natural
b. −9 > −8 numbers
c. −5 < −6 d. Positive integers are
d. −7 < −3 integers.

4. Which of the following expressions 9. What property is applied in 5 × 4 =
is equal to fourteen? 4 × 5?
a. −10 + 4 a. Identity
b. 10 − (−4) b. Commutative
c. −10 − 4 c. Associative
d. 10 + (−4) d. Distributive

5. What is the value of 10. What property is used in 2 ×
13 + 8 × 13 = (2 + 8) × 13?
[(−10) ÷ 2] × (−4)? a. Identity
b. Commutative
a. 20 c. Associative
b. 2 d. Distributive
c. −9
d. −12 11. What is the sign of the quotient
of two negative numbers?
6. What is the value of a. Always positive
b. Always negative
[(−4) × (−9) × (−25)] ÷ [(−2) × c. Either negative or positive
d. 0
(−3) × (−5)]?

a. 10
b. 20
c. 30
d. 40

7. Which of the following is in
ascending order?
a. −7, −2,1,6,9
b. −6, −8, −10, −12, −14
c. 3,1,0, −2, −5
d. 0, −1, −2, −3, −4

Mathematics Book 1 25

12. What is the sign of the product of 16. A submarine dove 836 ft. It rose at
a positive and a negative numbers? a rate of 22 ft. per minute. What was
a. Always positive the depth of the submarine after 12
minute?
b. Always negative a. 452 ft.
b. 572 ft.
c. Either negative or positive c. -472 ft.
d. 472 ft.
d. 0
17. A vendor bought 7 dozen eggs.
13. A man is three times as old as his He packed them in packages of 5.
son. What is the man’s age if his son How many packets did he pack and
is 13 years old? how many leftover eggs?
a. 30 years old a. 5 packets, 2 leftover eggs
b. 12 packets, 2 leftover eggs
b. 39 years old c. 16 packets, 4 leftover eggs
d. 17 packets, 4 leftover egg
c. 41 years old
18. Joy owns a coffee shop. On
d. 52 years old Wednesday, she made a loss of
1,100 baht and on Thursday a loss of
14. The temperature at midday was 1,500 baht. Then on Friday she
7⁰C. By midnight, it dropped by made a profit of 1,300 baht and on
15⁰C. What was the temperature by Saturday a profit of 1,400 baht. How
midnight? much was her gain?
a. 8⁰C a. 1,100 baht
b. 22⁰C b. 1,000 baht
c. −8⁰C c. 100 baht
d. −22⁰C d. 110 baht

15. A monkey sits on a limb that is 25
ft. above the ground. He swings up
10 ft., climbs up 6 ft. more and then
jumps down 13 ft. How far off the
ground is the monkey now?
a. 31 ft.
b. 25 ft.
c. 28 ft.
d. 18 ft.

26 Mathematics Book 1

Fractions and Decimals

Mathematical Terms

Decimal ทศนิยม Place Value คา่ ประจำหลัก
Proper Fraction เศษสว่ นแท้
Digit เลขโดด

Equivalent เทา่ กับ, เสมือน Round Off ปัดเศษ

Estimate ประมาณ Least Common Multiple

เศษสว่ น ตัวคูณรว่ มนอ้ ย (ค.ร.น.)

Fraction

Improper Fraction เศษสว่ นเกนิ Mixed Fraction

เศษสว่ นจำนวนคละ

Denominator Numerator

ตวั เลขท่ีอยสู่ ่วนล่างของเศษสว่ น ตวั เศษ, เลขเศษ

Greatest Common Divisor Recurring Decimal

ตัวหารร่วมมาก (ห.ร.ม.) ทศนยิ มไมร่ ู้จบ

Terminating Decimal

ทศนิยมรจู้ บ

Did you know?

From as early as 1800 BC, the
Egyptians were writing fractions.
The ancient Egyptian writing system
was all in pictures which were called
hieroglyphs and in the same way,
they had pictures for numbers.

Mathematics Book 1 27

1. Fractions

1.1 Definition

A fraction, (from Latin fractus, "broken"), represents a part of a whole. The
top number is called the numerator which says how many parts we have. The
bottom number is called the denominator which says how many equal parts the
whole is divided into.

2 Numerator
3 Denominator

There are 3 types of fraction:
o Proper Fractions are fractions where the numerator is less than
the denominator.
o Improper Fractions are fractions where the numerator is greater
than the denominator.
o Mixed Fractions are fraction where it is a combination of a whole
number and a proper fraction.

1.2 Equivalent Fractions

Two fractions are equivalent if they have the same value. Sometimes,
fractions may look different and have different numbers, but they have the same
value. One of the simplest examples of equivalent fraction is the number 1. If the
numerator and the denominator are the same, then the fraction has the same
equivalent value as 1.

2

2 is equivalent to 1 since 2 ÷ 2 = 1

7

7 is equivalent to 1 since 7 ÷ 7 = 1

To write equivalent fractions, we multiply or divide both numerator and
denominator by the same number.

28 Mathematics Book 1

Study the following examples below.

Example 1

List the equivalent fraction of

a. 8 b. 20

12 50

Solution

a. = 8×2 =

12×2 Multiply both the numerator and
denominator by the same number.
16 = 16×3 =

24 24×3

Thus , , are equivalent fractions.


b. = 20÷2 = Divide both the numerator and
denominator by the same number.
50÷2

10 = 10÷5 =
25 50÷5

Thus , , are equivalent fractions.


1.3 Comparing Fractions

1.3.1 Same Denominator

When the denominators of two fractions are the same, we can compare by

using the numerator.

Consider the fractions 2 and 3
5 5

Since their denominators are both 5 and 2 < 3

Therefore, 2 < 3
5 5

Mathematics Book 1 29

1.3.2 Different Denominator

When the denominators of two fractions are not the same, we have to

change the fractions so that they have the same denominator by finding the Least

Common Multiple (LCM) of the denominators and then compare the numerators.

Consider the fractions 5 and 11
7 14

The LCM of 7 and 14 is 14 so, 5 = 5×2 = 10
7 7×2 14

Therefore, 10 < 11
14 14

Example 2

Determine which fraction is greater.

a. 5 or 3 b. −5 or −7
6 5 8 9

So1l.ution

a. The LCM of 6 and 5 is 30. b. The LCM of 8 and 9 is 72.

5×5 = and 3×6 = −5×9 = − and −7×8 = −

6×5 5×6 8×9 9×8

25 > 18 Therefore, 5 > 3 −45 > −56 Therefore, −5 > −7
6 5 8 9

Example 3

Arrange the following fractions in ascending order.

a. 3 ,1,5
4
38

Solutiobn.

a. The LCM of 3, 4 and 8 is 24.

3×6 = ; 1×8 = ; 5×3 =

4×6 3×8 8×3

8 < 15 < 18 Therefore, 1 , 5 , 3
3 8 4

30 Mathematics Book 1

Exercise 2A

1. Compare the fractions by writing < , > or =.

a. 3 and 4 f. 1 1 and 1 3
4 7 3
4

b. −6 and −15 g. −2 11 and −38
7 21 13 13

c. 11 and 15 h. 12 and 1 1
27
18 4 2

d. −5 and −3 i. 1 8 and 1 11
3 2 15
20

e. −7 and −21 j. 1 and −5
6 18 6 9

2. Arrange the following fractions in ascending order.

a. 2,3,7

348

b. 1, 3 , 5

6 16 24

c. 11 , 13 , 19

12 18 30

d. −1 , −3 , 5 , 7

2 5 8 16

3. Arrange the following in descending order.

a. 3,4, 9

4 5 10

b. 3,5, 7

4 6 10

c. 2 , 3 , 4 , 13

3 5 7 35

d. −1 , −3 , 1 , 7

6 16 32 48

Mathematics Book 1 31

2. Addition and Subtraction of Fraction

2.1 Addition of Fractions

2.1.1 Same Denominator

To add two fractions with the same denominator, we simply add their
numerators and keep the denominator.

e.g. 1 + 2 = 1+2

55 5

=3

5

2.1.2 Different Denominator

To add two fractions with different denominators, we must make the
denominator the same by multiplying both the numerator and denominator by
their LCM. Then add the numerators.

e.g. 1 + 1 = 1×4 + 1×3 = 4 + 3

3 4 3×4 4×3 12 12

= 4+3 = 7

12 12

Example 4

Find the value of the following fractions.

a. ቀ−3ቁ + (−1) d. (−5) + 1
2
55

b. −2 1 + (−5) e. 2 1 + 1 1 + (−1)
7 2
46 3

c. 3+3

4

32 Mathematics Book 1

Solution ቀ−3ቁ + ቀ−1ቁ = (−3)+(−1)

a. 55 5

= −4

5

b. −2 1 + ቀ−5ቁ = ቀ−9ቁ + (−5)
46 46

= −9×3 + −5×2

4×3 6×2

= (−27)+(−10)

12

= −37 = −3 1

12 2

c. 3 + 3 = 3×4 + 3

4 1×4 4

= 12+3 = 15 = 3 3

444

d. (−5) + 1 = −5×2 + 1

2 1×2 2

= −10+1

2

= −9 = −4 1

22

e. 2 1 + 1 1 + ቀ−1ቁ = 15 + 3 + (−1)
723 72 3

= (15)(6)+(3)(21)+(−1)(14)

42

= 90+63+(−14)

42

= 139 = 3 13

42 42

Mathematics Book 1 33

2.2 Subtraction of Fractions

2.2.1 Same Denominator

To subtract two fractions with the same denominator, we simply subtract
their numerators and keep the denominator.

e.g. 4 − 2 = 4−2

55 5

=2

5

2.2.2 Different Denominator

To subtract two fractions with different denominators, we must make the
denominator the same by multiplying both the numerator and denominator by
their LCM. Then subtract the numerators.

e.g. 9 − 1 = 9×2 − 1×5

10 4 10×2 4×5

= 18−5 = 13

20 20

Example 5

Find the value of the following fractions.

a. 4−3 d. ቀ−3ቁ − ቀ−4ቁ − 7
10
77 4 5

b. 5 − (−1) e. ቀ−1 1ቁ − 1 − 2 2
3
82 3

c. −2 − 3

4

34 Mathematics Book 1

Solution

a. 4 − 3 = 4−3 =

7 7 7

b. 5 − ቀ−1ቁ = 5+1 = 5 + 1×4

82 82 8 2×4

= 5 + 4 = 5+4

88 8

= 9 =

8

c. −2 − 3 = −2 − 3

4 14

= (−2)×4 − 3 = −8 − 3

1×4 4 4 4

= −11 = −

4

d. ቀ−3ቁ − ቀ−4ቁ − 7

4 5 10

= (−3)(5)−(−4)(4)−(7)(2)

20

= −15+16−14 = −

20

e. ቀ−1 1ቁ − 1 − 2 2 = −4 − 1 − 8
3 33 3

= −4−1(3)−8

3

= −4−3−8

3

= −15 = −

3

Mathematics Book 1 35

Exercise 2B

1. Solve the following:

a. ቀ−1 1ቁ + ቀ−3ቁ =

9 18

b. 3+ 1 1 + (−1) =

4 4

c. 5 − 1 + ቀ− 65ቁ + 2 2 =
6 3 3

d. ቀ5 + 11ቁ − ቀ− 1ቁ =
74 7

e. ቀ2 1 − 1 1ቁ − ቀ1 1 − 1 1ቁ =
42 34

f. [ቀ−6 2ቁ + 9] − [ቀ−1 1ቁ + 2] =

3 23

2. John’s height was153 3 cm last year. If his height has increased by 2 1 cm
4 2

since then, what is his height now?

3. Jane spent 1 of her money on books and 2 on stationary. What fraction did
3 3

she spend? What fraction of her money left?

4. A group of students went to the school canteen, 2 of them bought fried rice,
5

1 of them bought bread. The rest bought juice. What fraction of the group
3

bought food? What fraction bought drink?

36 Mathematics Book 1

3. Multiplication and Division of Fraction

3.1 Multiplication of Fractions

To multiply fractions, all we have to do is multiply the numerators and

denominators and simplify the result.
×
× = ×

There are some steps to follow in multiplying fractions:
o Convert mixed fraction to improper fraction
o If the fractions have a common factor, divide both numerator and
denominator by the common factor before multiplying.
o Multiply the numerators.
o Multiply the denominators.
o The product must be in its simplest form.

Example 6

Find the product of:

a. ቀ−1 1ቁ × ቀ−2 1ቁ =?

34

b. ቀ−3 1ቁ × ቀ−4 1ቁ =?

34

Solution

a. ቀ−1 1ቁ × ቀ−2 1ቁ = (− 4) × (− 9)

34 34

= (−4)×(−9)

3×4

= 36 = 3

12

b. ቀ−3 31ቁ × ቀ−4 41ቁ = ቀ− 130ቁ × ቀ− 147ቁ

= (−10)×(−17)

3×4

= 170 = 85 or 14 1
12 6 6

Mathematics Book 1 37

Exercise 2C

1. Solve the following:
a. ቀ−2 2ቁ × 5 =

7 32

b. ቀ− 71ቁ × ቀ− 78ቁ × 2 2 =
3

c. ቀ− 1ቁ × 2 × ቀ5ቁ × (−6) =

658

d. [ቀ− 3 ቁ × 5] + [ቀ− 3 ቁ × 15] =
10 9 10 18

e. [3 × ቀ− 4ቁ] + ቀ1 × 8ቁ − ቀ3 × 12ቁ =
4 9 49 4 15

2. A truck is carrying 150 boxes. If each box weighs 15 3 , what is the weight
5

of the boxes the truck is carrying?

3. A son is 1 times as old as his father now. What is the son’s age if his father
6

was 41 years old last year?

4. John had 56 candies. He gave 3 of the candies to Joe. Joe then gave 2 of what
4 7

he received to Jane. How many candies did Jane get?

38 Mathematics Book 1