Contents
Chapter 1
Whole Numbers ....................................................... 1
Chapter 2
Operations on Whole Numbers ..................................... 9
1
1
2
3
Chapter 3
5
6
7
8
9
Equivalent fractions ......................................................................
Comparing fractions.....................................................................
Simplest forms of fractions...........................................................
Fractions equivalent to whole numbers ......................................
Proper fractions and improper fractions .....................................
Mixed numbers ............................................................................
28
30
32
36
39
40
Addition of fractions .....................................................................
Properties of addition of fractions ................................................
Subtraction of fractions .................................................................
Solving word problems involving addition and subtraction
of fractions ....................................................................................
Multiplication of fractions .............................................................
Reciprocal of a fraction ................................................................
Division of fractions ......................................................................
Performing combined operations of fractions.............................
Fraction patterns............................................................................
47
49
51
54
55
63
65
68
71
Decimals .............................................................. 75
1
2
3
4
5
6
Chapter 7
16
18
20
23
Operations on Fractions ............................................ 46
1
2
3
4
Chapter 6
Constructing bar charts .................................................................
Bar chart with a jagged line ..........................................................
Multiple bar charts........................................................................
Probability ....................................................................................
Fractions .............................................................. 27
1
2
3
4
5
6
Chapter 5
Performing combined operations ................................................. 10
Using combined operations to solve word problems ................... 11
Creating and solving word problems based on number ................
sentences ...................................................................................... 13
Statistics and Probability............................................. 15
1
2
3
4
Chapter 4
Rounding off whole numbers ......................................................... 2
Reading and writing 2-decimal place numbers .........................
Place values and digit values of digits in decimals .....................
Writing decimals in expanded form .............................................
Comparing and ordering decimals ..............................................
Decimals and fractions .................................................................
Solving word problems involving decimals ..................................
76
77
78
79
84
88
Addition, Subtraction and Multiplication of Decimals .......... 92
1
2
3
Addition of decimals .................................................................... 93
Properties of addition of decimals ............................................... 95
Subtraction of decimals................................................................. 97
iii
4
5
6
7
8
Chapter 8
Percentage ............................................................111
1
2
3
4
Chapter 9
Types of triangles ........................................................................ 169
Axes of symmetry of triangles .................................................... 171
Base, base angles, vertex and height of a triangle ................... 173
Drawing triangles ........................................................................ 174
Interior angles of a triangle ........................................................ 178
Perimeter of a triangle ................................................................ 180
Area of a triangle ........................................................................ 182
Circles ................................................................ 187
1
2
Chapter 15
Types of quadrilaterals ............................................................... 156
Axes of symmetry of quadrilaterals ........................................... 159
Drawing rectangles ...................................................................... 160
Perimeter of a quadrilateral ........................................................ 162
Area of a rectangle ..................................................................... 164
Triangles ............................................................. 168
1
2
3
4
5
6
7
Chapter 14
Drawing parallel lines using a set square .................................. 150
Quadrilaterals ....................................................... 155
1
2
3
4
5
Chapter 13
Types of angles ........................................................................... 141
Measuring angles ....................................................................... 143
Drawing angles using a protractor............................................. 147
Parallel lines ......................................................... 147
1
Chapter 12
Length .......................................................................................... 135
Mass ............................................................................................ 136
Volume......................................................................................... 138
Angles ............................................................... 140
1
2
3
Chapter 11
Using fractions to solve multiplication and division problems... 112
Percentage ................................................................................... 117
Discount ........................................................................................ 123
Profit and loss .............................................................................. 125
Measurements ...................................................... 134
1
2
3
Chapter 10
Solving word problems involving addition and subtraction
of decimals .................................................................................... 99
Multiplication of decimals ............................................................ 101
Solving word problems involving multiplication of decimals ...... 106
Performing combined operations on decimals........................... 107
Decimal patterns .......................................................................... 108
Drawing circles ............................................................................ 188
Using circles to create designs ................................................... 189
Three-Dimensional Geometric Shapes and Volume of Cuboid 191
1
2
3
4
Three-dimensional shapes (3-D shapes) ...................................
Volume.........................................................................................
Relationships between units of volume ......................................
Solving word problems involving volume / capacity ................
iv
192
196
201
202
Ch a p
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te
1
Whole Numbers
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population of Thailand is 69,518,585. Can
you round it up to the nearest thousand?
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Whole Numbers
CHAPTER
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Mathematics Pratomsuksa 5
1
1
Rounding off whole numbers
Sometimes we need to round off a number to the nearest
ten, hundred, thousand, and so on.
A
Rounding off to the nearest ten
How do you round off a number to the nearest ten?
Let’s look at some examples.
1
20
Round off 23 to the nearest ten.
21
22
23
24
25
26
27
28
29
30
23 lies between 20 and 30.
23 is closer to 20 than to 30.
Therefore, when 23 is rounded off to the nearest ten, it becomes 20.
2
80
Round off 89 to the nearest ten.
81
82
83
84
85
86
87
88
89
90
89 lies between 80 and 90.
89 is closer to 90 than to 80.
Therefore, when 89 is rounded off to the nearest ten, it becomes 90.
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Mathematics Pratomsuksa 5
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Whole Numbers
3
Round off 65 to the nearest ten.
60
61
62
63
64
65
66
67
68
69
70
65 lies halfway between 60 and 70.
In such a situation, 65 is rounded up to 70 as the nearest ten.
Before rounding off a number to the nearest ten, look at the digit
in the ones place.
• If the digit in the ones place is less than 5, then retain the digit
in the tens place and replace the digit in the ones place with zero.
• If the digit in the ones place is 5 or more than 5, then add 1
to the digit in the tens place and replace the digit in the ones
place with zero.
1.
(a)
(b)
(c)
2.
to the nearest ten.
Round off the number in the
30
31
32
33
34
35
36
37
38
39
40 290
291
292
293
294
295
296
297
298
299
300
830
831
832
833
834
835
836
837
838
839
840
Round off each number to the nearest ten.
(a) 38
(b) 75
(c) 442
(d) 916
(e) 5,187
(f) 23,654
(g) 32,349
(h) 331,99
Whole Numbers
CHAPTER
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Mathematics Pratomsuksa 5
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B
Rounding off to the nearest hundred
4
300
Round off 361 to the nearest hundred.
310
320
330
340
350
360
370
380
390
400
361
361 lies between 300 and 400.
361 is closer to 400 than to 300.
Therefore, when 361 is rounded off to the nearest hundred, it becomes
400.
5
700
Round off 736 to the nearest hundred.
710
720
730
740
750
760
770
780
790
800
736
736 lies between 700 and 800.
736 is closer to 700 than to 800.
Therefore, when 736 is rounded off to the nearest hundred it becomes
700.
6
400
Round off 450 to the nearest hundred.
410
420
430
440
450
460
470
480
490
500
450 lies halfway between 400 and 500.
In such a situation, 450 is rounded up to 500 as the nearest hundred.
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Mathematics Pratomsuksa 5
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Whole Numbers
Before rounding off a number to the nearest hundred, look at the
digit in the tens place. If it is less than 5, then retain the digit in
the hundreds place and replace the digits to its right with zeros.
If the digit in the tens place is 5 or more, then add 1 to the digit
in the hundreds place and replace the digits to its right with zeros.
1.
to the nearest hundred.
Round off the number in
7
500
Answer:
(a)
(b)
510
520
530
540
550
560
570
580
590
600
570 is rounded off to 600 as the nearest
hundred.
400
410
420
430
440
450
460
470
480
490
500
300
310
320
330
340
350
360
370
380
390
400
376
(c)
6,800 6,810 6,820 6,830 6,840 6,850 6,860 6,870 6,880 6,890 6,900
6,818
(d)
2.
2,600 2,610 2,620 2,630 2,640 2,650 2,660 2,670 2,680 2,690 2,700
Round off each number to the nearest hundred.
(a) 623
(b) 4,599
(c) 71,728
(d) 446,085
Whole Numbers
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Mathematics Pratomsuksa 5
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C
Rounding off to the nearest thousand
8
6,000
Round off 6,750 to the nearest thousand.
6,100
6,200
6,300
6,400
6,500
6,600
6,700
6,800
6,900
7,000
6,750
6,750 lies between 6,000 and 7,000.
6,750 is closer to 7,000 than to 6,000.
Therefore, when 6,750 is rounded off to the nearest thousand it becomes
7,000.
9
7,000
7,100
Round off 7,500 to the nearest thousand.
7,200
7,300
7,400
7,500
7,600
7,700
7,800
7,900
8,000
7,500 lies halfway between 7,000 and 8,000.
In such a case, 7,500 is rounded up to 8,000 as the nearest thousand.
10
9,000
Round off 9,492 to the nearest thousand.
9,100
9,200
9,300
9,400
9,500
9,600
9,700
9,800
9,900 10,000
9,492
9,492 lies between 9,000 and 10,000.
9,492 is closer to 9,000 than to 10,000.
Therefore, when 9,492 is rounded off to the nearest thousand it becomes
9,000.
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Mathematics Pratomsuksa 5
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Whole Numbers
Before rounding off a number to the nearest thousand, look at the
digit in the hundreds place.
• If it is less than 5, then retain the digit in the thousands place
and replace the digits to its right with zeros.
• If the digit in the hundreds place is 5 or more, then add 1 to
the digit in the thousands place and replace the digits to its right
with zeros.
Round off each number to the nearest thousand.
1.
3,211
2.
4,684
3.
51,300
4.
206,520
5.
1,307,680
6.
40,180,325
Whole numbers
Rounding off
Nearest ten
Nearest hundred
Whole Numbers
CHAPTER
Nearest thousand
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Mathematics Pratomsuksa 5
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1.
2.
Round off to the nearest ten.
(a) 44
(b) 85
(c) 313
(d) 702
(e) 2,577
(f) 6,115
Round off to the nearest hundred.
(a) 555
(b) 983
(c) 1,074
(d) 4,269
(e) 7,991
(f) 14,036
3. Round off to the nearest thousand.
8
(a) 2,499
(b) 5,501
(c) 8,089
(d) 39,782
(e) 42,164
(f) 507,806
Mathematics Pratomsuksa 5
CHAPTER
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Whole Numbers