ARCTIC HARE MATHEMATICS
1
LES 1
LEARNING AND
EVALUATION
SITUATION
Name:
Shopping
_
at the Co op
STUDENT WORKBOOK
The Kativik School Board and
Publisher would like to thank
all those who contributed,
from near and far, to the
development and production
of this project.
Services
d’édition
Kativik
School
Danielle Guy
Board
Publisher
Services d’édition
Danielle Guy
Images References
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Rocket400 Studio/Shutterstock.com • ivelly/Shutterstock.com • objectsforall/Shutterstock.com • Anteromite/Shutterstock.com • II Jonathan Feinstein/Shutterstock.
com • 1, 61, 73, 79, © risteski goce/Shutterstock.com • Edyta Pawlowska/Shutterstock.com • Kesu/Shutterstock.com • Skyline/Shutterstock.com •
2 © Sylverarts/Shutterstock.com • 6 © Sylverarts/Shutterstock.com • 11 © Orla/Shutterstock.com • 14 © R. Gino Santa Maria/Shutterstock.com • 17 © sevenke/
Shutterstock.com • Fedorov Oleksiy/Shutterstock.com • Volodymyr Krasyuk/Shutterstock.com • 18 © Africa Studio/Shutterstock.com • 22 © ra3rn/Shutterstock.
com • idea for life/Shutterstock.com • 23 © Anan Kaewkhammul/Shutterstock.com • Anan Kaewkhammul/Shutterstock.com • 17 © Yasonya/Shutterstock.com •
23 © Valery Kraynov/Shutterstock.com • 24 © iStockphoto.com/peterspiro • iStockphoto.com/kenneth-cheung • Georgy Markov/Shutterstock.com • Robert
Spriggs/Shutterstock.com • 25 © Jonas Jensen/Shutterstock.com • 27 © Voronin76/Shutterstock.com • 29 © Seregam/Shutterstock.com • 30 © vectorlib-com/
Shutterstock.com • Africa Studio/Shutterstock.com • 31 © iStockphoto.com/peterspiro • iStockphoto.com/kenneth-cheung • iStockphoto.com/LongHa2006 •
Georgy Markov/Shutterstock.com • Robert Spriggs/Shutterstock.com • 32 © Yellowj/Shutterstock.com • 36 © maisicon/Shutterstock.com • kuppa/Shutterstock.
com • LockStockBob/Shutterstock.com • 37 © Dionisvera/Shutterstock.com • 41 © Robert Spriggs/Shutterstock.com • 42 © urfin/Shutterstock.com •
44 © Harvepino/Shutterstock.com • DVARG/Shutterstock.com • 45 © Africa Studio/Shutterstock.com • Tovkach Oleg /Shutterstock.com • Regissercom/
Shutterstock.com • Picsfive/Shutterstock.com • 46 © Artmim/Shutterstock.com • 48 © graja/Shutterstock.com • 50 © Igor Kovalchuk/Shutterstock.com •
51 © mareandmare/Shutterstock.com • 53 © Jiri Hera/Shutterstock.com • Lizard/Shutterstock.com • Robert Spriggs/Shutterstock.com • 55 © George Dolgikh/
Shutterstock.com • Z.H.CHEN/Shutterstock.com • 56 © TRINACRIA PHOTO/Shutterstock.com • Ivaschenko Roman/Shutterstock.com • 58 © 2012 Photos.com,
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Shutterstock.com • Africa Studio/Shutterstock.com • Denis and Yulia Pogostins/Shutterstock.com • 76 © risteski goce/Shutterstock.com • Tyler Olson/Shutterstock.
com • 80 © Danny Smythe/Shutterstock.com • danilo ducak/Shutterstock.com • 81 © SimonCPhoto /Shutterstock.com • miroshnik /Shutterstock.com •
84 © Sylverarts/Shutterstock.com • 89 © sommthink /Shutterstock.com • 93 © sevenke/Shutterstock.com • Fedorov Oleksiy /Shutterstock.com • Volodymyr
Krasyuk/Shutterstock.com • 95 © Big Pants Production /Shutterstock.com • maxim ibragimov/Shutterstock.com • maisicon/Shutterstock.com • 98 © sommthink/
Shutterstock.com • Robert Spriggs/Shutterstock.com • 103 © sommthink/Shutterstock.com • Robert Spriggs/Shutterstock.com • 106 © olavs/Shutterstock.com •
Paul Turner/Shutterstock.com • Volosina/Shutterstock.com • James Steidl/Shutterstock.com • 108 © 2012 Photos.com, a division of Getty Images 90310832 •
Tischenko Irina/Shutterstock.com • johnfoto18/Shutterstock.com • Galayko Sergey/Shutterstock.com
MATHEMATICS 1.0
Learning and Evaluation Situation 1
© 2012, Kativik School Board
Administrative Centre
9800 boul. Cavendish, suite 400, Saint-Laurent (Québec) H4M 2V9
Telephone: (514) 482-8220 • Fax: (514) 482-8278
Kuujjuaq Office
P.O. Box 150, Kuujjuaq (Québec) J0M 1C0
Telephone: (819) 964-1136 • Fax: (819) 964-1141
All rights reserved.
It is illegal to reproduce this publication, in full or in part, in any form
or by any means, without first obtaining written permission from the
Kativik School Board.
Printed in Canada
2nd Edition 08-2012
Table of Contents
APPLICATION SITUATIONS
CONCEPTS AND PROCESSES
APPLICATION QUESTIONS
1
1.1 Whole Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Adding and Subtracting
Whole Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.3 Multiplying and Dividing
Whole Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
A. The Best Buy . . . . . . . . . . . . . . . . . 56
B. A Friendly Snack . . . . . . . . . . . . . 58
2
2.1 Prime and Composite Numbers . . . . . . . . . . . . . 62
2.2 Factoring Composite Numbers . . . . . . . . . . . . . . 63
2.3 Powers of Whole Numbers . . . . . . . . . . . . . . . . . . 67
Counting Cases . . . . . . . . . . . . . . . . . 70
3
3.1 Order of Operations . . . . . . . . . . . . . . . . . . . . . . . . . . 74
A Raffle . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4
4.1 Decimal Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.2 Adding and Subtracting
Decimal Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
4.3 Multiplying and Dividing
Decimal Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
A. Paying the Bill . . . . . . . . . . . . . . . . 106
B. Too Expensive . . . . . . . . . . . . . . . . 108
Application Situation 1
1.1 Whole Numbers
1.2 Adding and Subtracting
Whole Numbers
1.3 Multiplying and Dividing
Whole Numbers
A. The Best Buy
B. A Friendly Snack
Application Situation 1 | LES 1
APPLICATION QUESTIONS
1
1.1
Whole Numbers
1.1 Whole Numbers
KNOWLEDGE KEY WHAT
IS A WHOLE
NUMBER?
KNOWLEDGE
KEY WHAT
IS A WHOLE NUMBER?
A whole number is Agreater
or equal
to 0. than or equal to 0.
whole than
number
is greater
EXAMPLES
EXAMPLES
0, 12, 785, 1 690, 25
408785,
are whole
0, 12,
1 690,numbers.
25 408 are whole numbers.
Do not confuse digits
numbers!
Do with
not confuse
digits with numbers!
The digits are the ten
that
from
0 to 9.that go from 0 to 9.
Thesymbols
digits are
thegoten
symbols
Digits are used to write
Digitsnumbers.
are used to write numbers.
EXAMPLES
EXAMPLES
• 421 is a number•made
of athe
digits: made
4, 2 and
1. digits: 4, 2 and 1.
421 is
number
of the
• 3 535 is a number
made
of athe
digits: made
3, 5 ,of 3theand
5 .3, 5 , 3 and 5 .
• 3
535 is
number
digits:
• 7 is a number made
of athe
digit 7made
.
• 7 is
number
of the digit 7 .
Digits
≥0
Whole number
1.1 Whole Numbers
2
1.1 Whole Numbers
LES 1 | Application Situation 1
Digi
≥0
Whole number
Application Situation 1  LES 1
2
Application Situation 1  LES 1
1.1 Whole Numbers
KNOWLEDGE KEY EVEN AND ODD WHOLE NUMBERS
All whole numbers except 0 are either even or odd.
• An even number can be evenly divided by 2.
Examples: 6, 14, 20, 42, 244, 698
• An odd number cannot be evenly divided by 2.
Examples: 3, 5, 11, 53, 79
CHECK POINT
Determine if the numbers below are even or odd.
Put a checkmark in the correct column.
its
2
WHOLE NUMBER
EVEN NUMBER
a)
4

b)
1 946

c)
222

d)
93
e)
570
f)
6 421

g)
666 888 333

h)
76 286
1.1 Whole Numbers
1.1 Whole Numbers
ODD NUMBER



Application Situation 1  LES 1
Application Situation 1 | LES 1
3
3
KNOWLEDGE KEY PLACE VALUE OF WHOLE NUMBERS
Every digit in a number has a place. Each place has a different value.
We can use a place value table to help us find the value
of the digits in a number.
• As we move to the left each place gets 10 times larger.
• As we move to the right each place gets 10 times smaller.
A place value table has periods made up of ones, thousands, millions,
and billions.
EXAMPLE
Show 14 352 726 954 in a place value table.
10 000
Tens
Ones
Hundreds
Tens
Hundred
Billions
Ten
Billions
Billions
Hundred
Millions
Ten
Millions
(HB)
(TB)
(B)
(HM)
(TM)
(M)
(HTH)
(TTH)
(TH)
1
4
3
5
2
7
2
6
1
100 000
Hundreds
10
1 000 000
Ones
100
10 000 000
Tens
1 000
100 000 000
Hundreds
Ones
Hundreds
Tens
Ones
Hundred
Ten
Millions Thousands Thousands Thousands Hundreds
Tens
Ones
(H)
(T)
(O)
9
5
4
• 14 is in the
billions
period.
• 352 is in the
millions
period.
• 726 is in the
thousands
period.
• 954 is in the
ones
period.
14 352 726 954
Billions
Millions
Thousands
Hundreds
Tens
Ones
Ones
Application Situation 1  LES 1
1.1 Whole Numbers
4
ONES
(1)
1 000 000 000
THOUSANDS
(1 000)
10 000 000 000
MILLIONS
(1 000 000)
100 000 000 000
BILLIONS
(1 000 000 000)
LES 1 | Application Situation 1
4
1.1 Whole Numbers
CHECK POINT
1. Put the number 93 874 in a place value table.
100 000
10 000
Hundreds
Tens
Ones
Hundreds
Tens
Hundred
Billions
Ten
Billions
Billions
Hundred
Millions
Ten
Millions
(HB)
(TB)
(B)
(HM)
(TM)
1
1 000 000
Ones
10
10 000 000
Tens
100
100 000 000
Hundreds
ONES
(1)
1 000
1 000 000 000
THOUSANDS
(1 000)
10 000 000 000
MILLIONS
(1 000 000)
100 000 000 000
BILLIONS
(1 000 000 000)
Ones
Hundreds
Tens
Ones
Hundred
Ten
Millions Thousands Thousands Thousands Hundreds
Tens
Ones
(M)
(HTH)
(TTH)
(TH)
(H)
(T)
(O)
9
3
8
7
4
b) 4 is in the
tens
column.
c) 8 is in the
hundreds
column.
d) 7 is in the
thousands
column.
e) 9 is in the
ten thousands
column.
f) 3 is in the
hundred thousands
column.
g) 1 is in the
millions
column.
h) 5 is in the
ten millions
column.
i) 6 is in the
hundred millions
column.
j) 3 is in the
billions
column.
k) 7 is in the
ten billions
column.
l) 9 is in the
hundred billions
column.
1.1 Whole Numbers
1.1 Whole Numbers
Ones
Thousands
Millions
Billions
Application Situation 1  LES 1
Application Situation 1 | LES 1
PERIOD
column.
PERIOD
ones
PERIOD
a) 2 is in the
PERIOD
2. Write the location of each digit in the number 973 651 397 842.
5
5
To calculate the value of a digit in a number, multiply the digit by its place value.
EXAMPLE
Calculate the value of the digits 4, 6 and 3 in the number 15 302 726 954.
10 000
Tens
Ones
Hundreds
Tens
Hundred
Billions
Ten
Billions
Billions
Hundred
Millions
Ten
Millions
(HB)
(TB)
(B)
(HM)
(TM)
(M)
(HTH)
(TTH)
(TH)
1
5
3
0
2
7
2
6
ones
=
1
Ones
Hundreds
Tens
Ones
Hundred
Ten
Millions Thousands Thousands Thousands Hundreds
Tens
Ones
(H)
(T)
(O)
9
5
4
column.
The ones column has a value of
4×
1
100 000
Hundreds
10
1 000 000
Ones
100
10 000 000
Tens
1 000
100 000 000
Hundreds
• 4 is in the
1
thousands
column.
The thousands column has a value of
6×
1 000
• 3 is in the
.
4__
• 6 is in the
=
1 000
3×
.
6 000__
column.
hundred millions
The hundred millions column has a value of
6
ONES
(1)
1 000 000 000
THOUSANDS
(1 000)
10 000 000 000
MILLIONS
(1 000 000)
100 000 000 000
BILLIONS
(1 000 000 000)
100 000 000
=
100 000 000
.
300 000 000 __
Application Situation 1  LES 1
1.1 Whole Numbers
LES 1 | Application Situation 1
6
1.1 Whole Numbers
CHECK POINT
Put the number 88 632 954 176 in a place value table.
Calculate the value of each digit.
10 000
Hundreds
Tens
Ones
Hundreds
Tens
Hundred
Billions
Ten
Billions
Billions
Hundred
Millions
Ten
Millions
(HB)
(TB)
(B)
(HM)
(TM)
(M)
(HTH)
(TTH)
(TH)
8
8
6
3
2
9
5
4
a) 6
1
100 000
Ones
10
1 000 000
Tens
100
10 000 000
Hundreds
1 000
100 000 000
ONES
(1)
1 000 000 000
THOUSANDS
(1 000)
10 000 000 000
MILLIONS
(1 000 000)
100 000 000 000
BILLIONS
(1 000 000 000)
Ones
Hundreds
Tens
Ones
Hundred
Ten
Millions Thousands Thousands Thousands Hundreds
Tens
Ones
(H)
(T)
(O)
1
7
6
=
6
b) 7 × 10
=
70
c) 1
=
100
d) 4 × 1 000
=
4 000
e) 5
=
50 000
f) 9 × 100 000
=
900 000
g) 2 × 1 000 000
=
2 000 000
h) 3 × 10 000 000
=
30 000 000
i) 6
× 100 000 000
=
600 000 000
j) 8
× 1 000 000 000
=
8 000 000 000
k) 8
× 10 000 000 000
=
80 000 000 000
× 1
× 100
× 10 000
1.1 Whole Numbers
1.1 Whole Numbers
Application Situation 1  LES 1
Application Situation 1 | LES 1
7
7
KNOWLEDGE KEY INSIGNIFICANT ZERO — WHOLE NUMBERS
A zero at the beginning of a whole number doesn't count.
EXAMPLE 1
021
and
21
10
1
100
10
1
ONES (1)
100
ONES (1)
Hundreds
Tens
Ones
Hundreds
Tens
Ones
Hundreds
Tens
Ones
Hundreds
Tens
Ones
(H)
(T)
(O)
(H)
(T)
(O)
0
2
1
2
1
There are:
• 0 hundreds
• 2 tens
• 1 one
There are:
• 2 tens
EXAMPLE 2
00500
one
500
10
1
10 000
1 000
100
10
1
ONES
(1)
100
THOUSANDS
(1 000)
1 000
ONES
(1)
Tens
Ones
Hundreds
Tens
Ones
Tens
Ones
Hundreds
Tens
Ones
Ten
Thousands Thousands Hundreds
(TTH)
(TH)
(H)
0
0
5
Tens
(T)
Ones
(O)
0
0
There are:
• 0 ten thousands
• 0 thousands
• 5 hundreds
• 0 tens
• 0 ones
Ten
Thousands Thousands Hundreds
(TTH)
(TH)
(H)
Tens
(T)
Ones
(O)
0
0
5
There are:
5 hundreds
•
•
0 tens
•
0 ones
00500 = 500
Application Situation 1  LES 1
1.1 Whole Numbers
8
and
1
10 000
THOUSANDS
(1 000)
•
021 = 21
LES 1 | Application Situation 1
8
1.1 Whole Numbers
A zero at the end of a whole number changes the number.
EXAMPLE
10
1
10 000
1 000
100
10
1
ONES
(1)
100
THOUSANDS
(1 000)
1 000
ONES
(1)
42 700
and
10 000
THOUSANDS
(1 000)
427
Tens
Ones
Hundreds
Tens
Ones
Tens
Ones
Hundreds
Tens
Ones
Ten
Thousands Thousands Hundreds
(TTH)
(TH)
(H)
4
Tens
(T)
Ones
(O)
2
7
Ten
Thousands Thousands Hundreds
(TTH)
(TH)
(H)
Tens
(T)
Ones
(O)
0
0
4
There are:
• 4 hundreds
• 2 tens
• 7 ones
2
7
There are:
4 ten thousands
•
Does not equal
•
2
thousands
•
7
hundreds
•
0
teens
•
0
ones
427 ≠ 42 700
CHECK POINT
Circle the numbers that have insignificant zeros.
a) 50
e) 00394
i) 00400
m) 9
b) 0600
f) 64900
j) 3200
n) 04
c) 5240
g) 00642
k) 090
o) 10
d) 15
h) 015
l) 320
p) 150
1.1 Whole Numbers
1.1 Whole Numbers
Application Situation 1 | LES 1
Application Situation 1  LES 1
9
9
READING AND WRITING WHOLE NUMBERS
KNOWLEDGE KEY
Simple Words
Some numbers are written using one word.
The numbers up to 19
0
zero
5
five
10
ten
15
fifteen
1
one
6
six
11
eleven
16
sixteen
2
two
7
seven
12
twelve
17
seventeen
3
three
8
eight
13
thirteen
18
eighteen
4
four
9
nine
14
fourteen
19
nineteen
The tens up to 90
20
twenty
40
forty
60
sixty
80
eighty
30
thirty
50
fifty
70
seventy
90
ninety
Compound Words
All the other numbers are written by combining simple words.
For numbers less than 99 put a hyphen between the two words.
21
twenty-one
132
one hundred thirty-two
48
forty-eight
301
three hundred one
53
fifty-three
450
four hundred fifty
89
eighty-nine
721
seven hundred twenty-one
Application Situation 1  LES 1
1.1 Whole Numbers
10
LES 1 | Application Situation 1
10
1.1 Whole Numbers
CHECK POINT
1. Write the following numbers in words.
a) 26
twenty-six
b) 943
nine hundred forty-three
c) 5
five
d) 807
eight hundred seven
e) 1 707
one thousand seven hundred seven
f) 467 293
four hundred sixty-seven thousand two hundred ninety-three
g) 19
nineteen
h) 2 817
two thousand eight hundred seventeen
i) 78 345
seventy-eight thousand three hundred forty-five
2. Write the following numbers in digits.
a) Four hundred six 406
b) Thirty-nine 39
c) Eight thousand six hundred fifty-two 8 652
d) Eleven 11
e) Six hundred twenty-four thousand eight hundred ninety-two 624 892
f) Four million five hundred twenty thousand 4 520 000
g) Nine hundred thirty-two 932
h) Sixty-eight 68
i) Thirteen thousand seven hundred twenty-four 13 724
1.1 Whole Numbers
1.1 Whole Numbers
Application Situation 1  LES 1
Application Situation 1 | LES 1
11
11
KNOWLEDGE KEY
STANDARD AND EXPANDED FORMS OF WHOLE NUMBERS
There are two ways of showing numbers.
The regular way to write numbers is called standard form.
Example: 654, 18, 3, 91, 763
In expanded form we show the value of each digit in the number.
Example: 3 248 = (3 ×1 000) + (2 × 100) + (4 × 10) + (8 × 1)
EXAMPLE 1 Write 41 869 in expanded form.
41 869
Four ten
thousands
+
One
thousand
+
Eight
hundreds
+
Six
tens
+
Nine
ones
40 000
+
1 000
+
800
+
60
+
9
(4 × 10 000)
+
(1 × 1 000)
+
( 8 × 100)
+
( 6 × 10)
+
( 9 × 1)
EXAMPLE 2 Write this number in standard form.
(8 × 10 000) +
(2 × 1 000)
+
(7 × 100)
+
(2 × 10)
+
(4 × 1)
80 000
+
2 000
+
700
+
20
+
4
Eight ten
thousands
+
Two
thousands
+
Seven
hundreds
+
Two
tens
+
Four
ones
8
2
2
4
Application Situation 1  LES 1
1.1 Whole Numbers
12
7
LES 1 | Application Situation 1
12
1.1 Whole Numbers
CHECK POINT
1. Write the following numbers in expanded form. Show your work.
a) 41 869
Four ten
One
Eight
Six
Nine
thousands
+
thousand
+
hundreds
+
tens
+
ones
40 000
+
1 000
+
800
+
60
+
9
(4 × 10 000)
+
(1 × 1 000)
+
(8 × 100)
+
(6 × 10)
+
(9 × 1)
b) 5 431
Five
thousands
+
Four
hundreds
+
Three
tens
+
One
one
5 000
+
400
+
30
+
1
(5 × 1 000)
+
(4 × 100)
+
(3 × 10)
+
(1 × 1)
2. Write the following numbers in standard form. Show your work.
a) (6 × 1 000) +
6 000
Six
thousands
+
+
(5 × 100)
+
500
+
Five
hundreds
+
(9 × 10)
90
Nine
tens
+
+
+
(6 × 1)
6
Six
ones
= 6 596
b) (8 × 10 000) + (3 × 1 000) +
(4 × 100)
+
(8 × 10)
+
+
400
+
80
+
80 000
Eight ten
thousands
+
3 000
Three
thousands
+
+
Four
hundreds
+
Eight
tens
+
(2 × 1)
2
Two
ones
= 83 482
1.1 Whole Numbers
1.1 Whole Numbers
Application Situation 1  LES 1
Application Situation 1 | LES 1
13
13
COMPARING WHOLE NUMBERS
KNOWLEDGE KEY
To compare whole numbers we use the greater than (>), less than (<)
or equal (=) sings.
These signs show us the value of a number relative to another number.
<
=
>
Greater than
Equal
Less than
EXAMPLES
• Compare the numbers 7 and 3.

>
3
• Compare the numbers 16 and 19.
 16 <
19
• Compare the numbers 5 and 3 + 2. 
7
5
3+2
=
Sometimes we have to interpret data before we can compare numbers.
1) Number of balls >
number of dots.
2) Number of balls =
3) Number of balls <
number of dots.

number of dots.


1) There are 4 balls and 3 dots.  4
>
3
2) There are 4 balls and 4 dots.  4
=
4
3) There are 3 balls and 5 dots.  3
<
5
3
<
4
or
5
>
3
Application Situation 1  LES 1
1.1 Whole Numbers
14
or
LES 1 | Application Situation 1
14
1.1 Whole Numbers
To compare whole numbers:
1) Put the numbers in a place value table.
2) Compare the digits starting from the left.
As soon as one digit is larger than the other, that number is also larger
than the other.
EXAMPLE
Compare 12 987 and 12 984.
10 000
1 000
100
10
1
ONES
(1)
100 000
THOUSANDS
(1 000)
Hundreds
Tens
Ones
Hundreds
Tens
Ones
Hundred
Ten
Thousands Thousands Thousands
(HTH)
Hundreds
Tens
Ones
(TTH)
(TH)
(H)
(T)
(O)
1
2
9
8
7
1
2
9
8
4
12 987 has:
• 1 ten thousands
12 984 has:
• 1 ten thousands
•
2
thousands
• 2
thousands
•
9
hundreds
• 9
hundreds
•
8
tens
• 8
tens
•
7
ones
•
4
ones
equal
equal
equal
equal
12 987
12 984
7 is larger than 4
12 987
1.1 Whole Numbers
> 12 984
Application Situation 1 | LES 1
15
If all the digits in two numbers are the same, then the numbers are equal.
EXAMPLE
Compare 854 and 854.
100
10
1
ONES
(1)
Hundreds
Tens
Ones
Hundreds
Tens
Ones
(H)
(T)
(O)
8
5
4
8
5
4
854 has:
854 has:
•
8
hundreds
•
8
hundreds
•
5
tens
•
5
tens
•
4
ones
•
4
ones
equal
equal
equal
854
854
854
854
=
CHECK POINT
Compare the following numbers.
a) 16 > 9
c) 397 <
b) 763 < 8 402
d) 27 < 136
16
1.1 Whole Numbers
LES 1 | Application Situation 1
463
e) 24 = 24
f) 8 > 4
1.1 Whole Numbers
Application Situation 1  LES 1
16
KNOWLEDGE KEY ORDERING WHOLE NUMBERS
To put numbers in increasing order,
Increasing
order
start with the smallest number and finish with
the largest number.
Example: 2, 17, 395, 487
To put numbers in decreasing order,
Decreasing
order
start with the largest number and finish with
the smallest number.
Example: 487, 395, 17, 2
ACTIVITY 1
Put the numbers 142, 19, 68 and 5 in increasing order.
Step 1
142
• Make a list of the numbers.
19
• Line them up using the ones column.
68
5
Step 2
Old list
New list
142
142
• Smallest number: 5
19
19
• Cross it off the list.
68
68
• Find the smallest number and write it down.
5
1.1 Whole Numbers
1.1 Whole Numbers
Application Situation 1  LES 1
Application Situation 1 | LES 1
17
17
Step 3
Old list
New list
142
142
• Smallest number: 19
19
68
• Cross it off the list.
68
• Find the smallest number and write it down.
Step 4
Old list
• Find the smallest number and write it down.
142
New list
142
68
• Smallest number: 68
• Cross it off the list.
Step 5
Old list
• Find the smallest number and write it down.
142
New list
None
• Smallest number: 142
• Cross it off the list.
Step 6
• Write down the numbers in increasing order.
• 5
18
, 19
1.1 Whole Numbers
, 68
, 142
or
LES 1 | Application Situation 1
5 < 19 < 68 < 142
1.1 Whole Numbers
Application Situation 1  LES 1
18
ACTIVITY 2
Put the numbers 7, 26, 11, 842 and 327 in decreasing order.
Step 1
7
• Make a list of the numbers.
26
• Line them up using the ones column.
11
842
327
Step 2
Old list
New list
7
7
• Largest number: 842
26
26
• Cross it off the list.
11
11
• Find the largest number and write it down.
842
327
327
Step 3
Old list
New list
7
7
• Largest number: 327
26
26
• Cross it off the list.
11
• Find the largest number and write it down.
11
327
Step 4
Old list
New list
7
7
• Largest number: 26
26
11
• Cross it off the list.
11
• Find the largest number and write it down.
1.1 Whole Numbers
1.1 Whole Numbers
Application Situation 1 | LES 1
Application Situation 1  LES 1
19
19
Step 5
Old list
7
• Find the largest number and write it down.
New list
7
11
• Largest number: 11
• Cross it off the list.
Step 6
Old list
New list
7
None
• Find the largest number and write it down.
• Largest number: 7
• Cross it off the list.
Step 7
• Write down the numbers in decreasing order.
• 842 , 327 , 26
, 11
,7
or
842 > 327 > 26 > 11 > 7
CHECK POINT
1. Put the following numbers in increasing order.
a) 34, 7, 18, 911
7
, 18
, 34
, 911
b) 16, 842, 3 876, 10
10
, 16
, 842
, 3 876
c) 384, 7 967, 27, 5
5
, 27
, 384
, 7 967
2. Put the following numbers in decreasing order.
a) 16, 9, 84, 627
627
, 84
, 16
, 9
b) 392, 14, 75, 1
392
, 75
, 14
, 1
c) 31, 56, 8 472, 439
8 472 , 439
, 56
, 31
201.1 Whole Numbers
LES 1 | Application Situation 1
20
1.11 Whole Numbers
Application Situation 1  LES
KNOWLEDGE KEY ROUNDING WHOLE NUMBERS
We can round a number to get a rough idea of its value.
To round a number we look at the place value of its digits.
• If this digit is greater than or equal to ( ≥) 5 we round up.
• If this digit is less than (<) 5 we round down.
EXAMPLE
Round 176 to the nearest hundred.
Step 1 Find the nearest hundred larger than 176.
200
Step 2 Find the nearest hundred smaller than 176.
100
Step 3 Look at the digit one place to the right. 176
• The number to the right of the hundred is 7 .
• 7 is > 5, so we round up .
Step 4 Round 176 to the nearest hundred.
200
CHECK POINT
1. Round the following numbers to the nearest ten.
a) 14 → 10
c) 15
b) 97 → 100
d) 146 → 150
e) 3 984
→ 20
→ 3 980
f) 10 569 → 10 570
2. Round the following numbers to the nearest thousand.
a) 984
→ 1 000
b) 6 149 → 6 000
1.1 Whole Numbers
1.1 Whole Numbers
c) 22 846 → 23 000
e) 2 352 → 2 000
d) 5 831
f) 526
→ 6 000
→ 1 000
Application Situation 1  LES 1
Application Situation 1 | LES 1
21
21
KNOWLEDGE KEY
ESTIMATING WITH WHOLE NUMBERS
ACTIVITY
Today, my friends and I went shopping.
• Adami bought 10 oranges.
• Sarah bought 14.
• I bought 27.
We want to know how many oranges we bought in total.
To do quick calculations we can round numbers
to make them easier to work with.
This will give us an estimate or approximate value of the total.
The estimate or approximate value will be close to the actual total.
Person
Exact Number
Rounded Number
Adami
10
10
Sarah
14
10
Me
27
30
• Approximate total:
10
+ 10
+ 30
= 50
We bought approximately 50 oranges.
• Exact total:
10
+ 14
+ 27
= 51
We bought exactly 51 oranges.
Application Situation 1  LES 1
1.1 Whole Numbers
22
LES 1 | Application Situation 1
22
1.1 Whole Numbers
1.2 Adding and Subtracting
1.2 Adding
and Subtracting Whole
Whole Numbers
Numbers
KNOWLEDGE KEY WHAT IS ADDITION?
To add means to combine.
EXAMPLE
=
+
18
6
24
• The sign for addition is +.
13
It is read as “plus.”
• The numbers we add together are
called addends.
• The result of an addition is called
the sum.
1.2 Adding and Subtracting Whole Numbers
1.2 Adding and Subtracting Whole Numbers
4
Sign
+
2
19
Addend
Addend
Addend
Sum
Application Situation 1 | LES 1
Application Situation 1  LES 1
23
23
EXAMPLES
1)
+
0 cm
1
2
3
4
EXAMPLES
0 cm
5
4
1)
0 cm
2)
=
1
1
2
3
4
5
4
0 cm
4
1
1
2
3
4
5
=
2
3
4
5
0 cm
1
1
2
3
4
5
5
=
+
3
=
20
3
3)
0 cm
5
+
2)
5
1
+
2
3
23
20
23
3)
+
=
+
10
24
10
1.2 Adding and Subtracting Whole Numbers
LES 1 | Application Situation 1
1.2 Adding and Subtracting Whole Numbers
=
33
13 13
Application Situation 1  LES 1
24
1.2 Adding and Subtracting Whole Numbers
Application Situation 1  LES 1
24
KNOWLEDGE KEY PROPERTIES OF ADDITION
Addition Table
+
1
2
3
4
5
6
7
8
9
10 11 12
1
2
3
4
5
6
7
8
9
10
11
12
13
2
3
4
5
6
7
8
9
10
11
12
13
14
3
4
5
6
7
8
9
10
11
12
13
14
15
4
5
6
7
8
9
10
11
12
13
14
15
16
Commutative means the
5
6
7
8
9
10
11
12
13
14
15
16
17
order of terms is not
6
7
8
9
10
11
12
13
14
15
16
17
18
important.
7
8
9
10
11
12
13
14
15
16
17
18
19
8
9
10
11
12
13
14
15
16
17
18
19
20
9
10
11
12
13
14
15
16
17
18
19
20
21
10
11
12
13
14
15
16
17
18
19
20
21
22
11
12
13
14
15
16
17
18
19
20
21
22
23
12
13
14
15
16
17
18
19
20
21
22
23
24
• The addition table is
symmetrical.
• Addition is
commutative.
Example: 7 + 4 = 4 + 7
EXAMPLE
+
7
=
4
+
4
11
=
7
11
CHECK POINT
Add.
a) 6 + 10 = 16
c) 9 + 3 = 12
e) 11 + 8 = 19
b) 4 + 7 = 11
d) 7 + 5 = 12
f) 16 + 3 = 19
1.2 Adding and Subtracting Whole Numbers
1.2 Adding and Subtracting Whole Numbers
Application Situation 1  LES 1
Application Situation 1 | LES 1
25
25
KNOWLEDGE KEY ADDING WHOLE NUMBERS
Sometimes when we add the digits in a column the sum is a 2-digit number.
Since there can only be one digit in each place we have to regroup.
Regrouping is another way of showing a number so that there is only 1 digit in
each place.
EXAMPLE
Add 2 974 + 590 + 4 281 + 63
Thousands
Hundreds
Tens
Ones
2 974
590
Step 1
Line up the numbers in columns based on
the place value of their digits.
4 281
+
63
2 974
590
4 281
+
Step 2
Add the digits in the ones column.
• 4+0+1+3= 8
• Write the 8 under the line in the
ones
column.
63
8
1.2 Adding and Subtracting Whole Numbers
26
LES 1 | Application Situation 1
Application Situation 1  LES 1
26
1.2 Adding and Subtracting Whole Numbers
3
2 974
590
4 281
+
63
08
1
Add the digits in the tens column.
• 7 + 9 + 8 + 6 = 30
• 30 tens = 3
hundreds + 0
tens
• Write the 0 under the line in the
tens
column.
• Carry the 3 to the top of
the
hundreds
column.
3
2 974
590
4 281
+
Step 3
63
908
Step 4
Add the digits in the hundreds column.
• 3 + 9 + 5 + 2 = 19
• 19 hundreds = 1
thousand + 9
• Write the 9 under the line in the
hundreds
hundreds
column.
• Carry the 1 to the top of
the
thousands
column.
1
2 974
590
4 281
+
Step 5
Add the digits in the thousands column.
• 1+2+4= 7
• Write the 7 under the line in
the
thousands
column.
63
7 908
1.2 Adding and Subtracting Whole Numbers
1.2 Adding and Subtracting Whole Numbers
Application Situation 1  LES 1
Application Situation 1 | LES 1
27
27
CHECK POINT
Add.
a)
63
5
68
+
b)
c)
d)
e)
11
+ 987
998
1 1
3 682
+ 543
4 225
27
+
81
108
2 1
57
187
+9 465
9 709
f)
3
9
12
+
g)
5
17
+ 364
386
h)
i)
j)
1
m)
1
n)
2 983
+ 826
3 809
1
72
11
+
99
182
1
+
1 1
147
+
73
220
942
+
13
955
l)
1
1.2 Adding and Subtracting Whole Numbers
LES 1 | Application Situation 1
28
k)
1
19
+ 642
661
+
o)
16
16
32
45
12
57
1
12
7
+ 142
161
28
Application Situation 1  LES 1
1.2 Adding and Subtracting Whole Numbers
KNOWLEDGE KEY WORD PROBLEMS – ANOTHER WAY OF SHOWING
ADDITION
1. 5 students are in the schoolyard.
48 students and 6 teachers join them.
5
+ 48 + 6 = 59
How many people are in the
schoolyard?
in the
There are 59 people
school yard.
2. Louisa is 171 cm tall.
Aqikki is 7 cm taller than Louisa.
171 cm
+ 7 cm
=
178 cm
How tall is Aqikki?
Aqikki is 178 cm
tall.
3. Julia wants a jacket that costs $40
and a hat that costs $25.
+ $25
$40
= $65
How much money will she spend
in total?
Julia will spend $65
.
4. A snowmobile weighs 653 kg.
Adami weighs 76 kg.
653 kg
+ 76 kg
= 729 kg
How much does the snowmobile
weigh with Adami sitting on it?
The snowmobile weighs
729 kg
1.2 Adding and Subtracting Whole Numbers
1.2 Adding and Subtracting Whole Numbers
with Adami sitting on it.
Application Situation 1  LES 1
Application Situation 1 | LES 1
29
29
KNOWLEDGE KEY WHAT IS SUBTRACTION?
To subtract means to take away.
Subtraction is the opposite of addition.
EXAMPLE
–
=
6
3
3
or
+
3
=
3
6
• The sign for subtraction is –.
178
It is read as “minus.”
• The number we start with
is called the minuend.
• The numbers we subtract
are called subtrahends.
• The result of a subtraction
is called the difference.
1.2 Adding and Subtracting Whole Numbers
30
LES 1 | Application Situation 1
35
Sign
–
12
131
Minuend
Subtrahend
Subtrahend
Difference
Application Situation 1  LES 1
30
1.2 Adding and Subtracting Whole Numbers
EXAMPLES
1)
–
0 cm
1
2
3
4
=
0 cm
5
4
1
2
3
4
5
0 cm
1
1
2
3
4
5
3
2)
–
20
=
3
17
3)
–
10
1.2 Adding and Subtracting Whole Numbers
1.2 Adding and Subtracting Whole Numbers
=
3
7
Application Situation 1 | LES 1
Application Situation 1  LES 1
31
31
KNOWLEDGE KEY PROPERTIES OF SUBTRACTION
Subtraction Table
• The subtraction table is
not symmetrical.
• Subtraction is
not commutative.
Not commutative means
the order of terms is
important.
Example: 7 − 4 ≠ 4 − 7
EXAMPLE
−
1
1
0
2
1
0
3
2
1
0
4
3
2
1
0
5
4
3
2
1
0
6
5
4
3
2
1
0
7
6
5
4
3
2
1
0
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
10
9
8
7
6
5
4
3
2
1
0
11
10
9
8
7
6
5
4
3
2
1
0
12
11
10
9
8
7
6
5
4
3
2
1
2
–
7
3
4
6
7
8
9
10 11 12
X
0
=
4
–
4
5
3
=
?
7
CHECK POINT
Subtract.
a) 10 – 7 = 3
c) 12 – 6 = 6
e) 17 – 13 = 4
b) 19 – 5 = 14
d) 13 – 3 = 10
f) 24 – 8 = 16
1.2 Adding and Subtracting Whole Numbers
32
LES 1 | Application Situation 1
Application Situation 1  LES 1
32
1.2 Adding and Subtracting Whole Numbers
KNOWLEDGE KEY SUBTRACTING WHOLE NUMBERS
Sometimes the digit to subtract in a column is too big. For example 7 – 9 = ?
When this happens we have to regroup. We have to borrow from another column.
EXAMPLE
Subtract 2 974 – 590
Thousands
Hundreds
Tens
Ones
2 974
–
590
Step 1
Line up the numbers in columns based on
the place value of their digits.
• The largest number must be on the top.
• The smallest number must be on the bottom.
2 974
–
590
4
81
2 9 74
–
590
84
Step 2
Subtract the digits in the ones column.
• 4–0= 4
• Write the 4 under the line in the
Step 3
ones
column.
Subtract the digits in the tens column.
• 7 – 9 = ? We don’t have enough to take away 9.
• We need to borrow from the next column on the left.
• 1 hundred = 10
tens.
• Add the tens: 10 tens + 7 tens = 17 tens.
• Now we can subtract! 17 – 9 = 8
• Write the 8 under the line in the
1.2 Adding and Subtracting Whole Numbers
1.2 Adding and Subtracting Whole Numbers
.
tens
column.
Application Situation 1  LES 1
Application Situation 1 | LES 1
33
33
8
2 974
–
590
384
2 974
–
590
2 384
Step 4
Subtract the digits in the hundreds column.
• 8–5 = 3
• Write the 3 under the line in the
Step 5
hundreds
column.
Subtract the digits in the thousands column.
• 2–0= 2
• Write the 2 under the line in the
column.
thousands
CHECK POINT
Subtract.
a)
31
146
–
28
118
b)
–
c)
34
17
5
12
8 131
942
76
–
3
863
d)
24
12
12
–
e)
f)
642
– 311
331
0 1
1 684
– 942
742
LES 1 | Application Situation 1
1.2 Adding and Subtracting Whole Numbers
g)
21
–
h)
i)
32
26
6
3 z1
86 412
1 218
–
63
85 131
0 151
164
–
87
77
1.2 Adding and Subtracting Whole Numbers
Application Situation 1  LES 1
34
KNOWLEDGE KEY WORD PROBLEMS – ANOTHER WAY OF SHOWING
SUBTRACTION
1. Elaisa has a ribbon that is 75 cm long. She
cuts off 25 cm. How much ribbon is left?
75 cm
75 cm
– 25 cm
= 50 cm
There is 50 cm
of ribbon left.
25 cm
remainder
2. You are knitting a scarf that you want to be
120 cm long. You have 80 cm finished. How
much more do you need to reach 120 cm?
120 cm
80 cm
and 30 cm?
75 cm
Difference
4. You had a bag of 100 balloons.
You used 63 at your sister’s
birthday party.
How many balloons are left?
1.2 Adding and Subtracting Whole Numbers
1.2 Adding and Subtracting Whole Numbers
= 40 cm
– 80 cm
more.
I need to knit 40 cm
?
3. What is the difference between 75 cm
30 cm
120 cm
75 cm
– 30 cm
= 45 cm
The difference is 45 cm
100
– 63
There are 37
= 37
balloons left.
Application Situation 1  LES 1
Application Situation 1 | LES 1
.
35
35
ultiplying and Dividing
M
1.3 MultiplyingWhole
and Dividing
Whole Numbers
Numbers
1.3
KNOWLEDGE KEY WHAT IS MULTIPLICATION?
Multiplication is a short cut we can use to add.
EXAMPLE
+
3
=
3
or
There are
2 groups of 3
bananas.
2 × 3 = 6
6
• The sign for multiplication is ×.
Sign
It is read as “times” or “multiplied by.”
• The numbers we multiply together
12
×
are called factors.
• The result of a multiplication is called
4
48
the product.
Factor
Factor
Product
EXAMPLE
There are 5 groups of berries.
Each group has 10 berries.
There are:
rows
•
5
•
10 berries per row
To find out how many berries there are we can:
Add the number of berries in each row.
10 + 10 + 10 + 10 + 10 = 50
36
LES 1 | Application Situation 1
or
Multiply the number of rows by the
number of berries in each row.
5 × 10 = 50
1.3 Multiplying and Dividing Whole Numbers
KNOWLEDGE KEY PROPERTIES OF MULTIPLICATION
Multiplication Table
×
1
2
3
4
5
6
7
8
9
10 11 12
1
1
2
3
4
5
6
7
8
9
10
11
12
2
2
4
6
8
10
12
14
16
18
20
22
24
3
3
6
9
12
15
18
21
24
27
30
33
36
4
4
8
12
16
20
24
28
32
36
40
44
48
Commutative means the
5
5
10
15
20
25
30
35
40
45
50
55
60
order of terms is not
6
6
12
18
24
30
36
42
48
54
60
66
72
important.
7
7
14
21
28
35
42
49
56
63
70
77
84
Example: 2 × 6 = 6 × 2
8
8
16
24
32
40
48
56
64
72
80
88
96
9
9
18
27
36
45
54
63
72
81
90
99
108
10
10
20
30
40
50
60
70
80
90
100 110 120
11
11
22
33
44
55
66
77
88
99
110 121 132
12
12
24
36
48
60
72
84
96
108 120 132 144
• The multiplication table
is symmetrical.
• Multiplication
is commutative.
EXAMPLE
6 cm
6 cm
2
2 cm
2 cm
×
2 cm
6
×
1.3 Multiplying and Dividing Whole Numbers
6
cm
2 cm
2
cm
2 cm
=
12
cm
=
12
cm
2 cm
Application Situation 1 | LES 1
37
KNOWLEDGE KEY SPECIAL RULES
Multiplication by
Multiplication by
Multiplication by
0
1
10
Multiplying any number Multiplying any number
Multiplying any number
by 0 always
by 1 doesn’t change
by 10 adds a zero to the
gives 0.
the number.
end of the number.
EXAMPLE
EXAMPLE
EXAMPLE
0×5=0
1×5=5
10 × 5 = 50
0 × 73 =
1 × 73 =
0
0 × 5 102 =
73
10 × 73 = 730
1 × 5 102 = 5 102
10 × 5 102 = 51 020
a) 6 × 7 = 42
g) 12 × 0 = 0
m) 7 × 5 = 35
b) 9 × 9 = 81
h) 8 × 8 = 64
n) 4 × 3 = 12
c) 8 × 0 = 0
i) 7 × 6 = 42
o) 2 × 5 = 10
d) 9 × 10 = 90
j) 9 × 2 = 18
p) 4 × 4 = 16
e) 12 × 6 = 72
k) 3 × 4 = 12
q) 9 × 7 = 63
f) 9 × 9 = 81
l) 0 × 11 = 0
r) 5 × 1 = 5
0
CHECK POINT
Multiply.
LES 1Numbers
| Application Situation 1
38 1.3 Multiplying and Dividing Whole
38
1.3 Multiplying
and Dividing
Whole
Application Situation
1  LES
1 Numbers
KNOWLEDGE KEY MULTIPLYING WHOLE NUMBERS − 2 DIGITS BY 1 DIGIT
To multiply whole numbers, line up the numbers so that all the ones are
in the same column.
EXAMPLE
Multiply 29 × 6
METHOD 1 − List all the partial products and add them together.
29
×
+
6
54
Step 1
Multiply 6 × 9 = 54
120
Step 2
Multiply 6 × 20 = 120
170
Step 3
Add the partial products.
METHOD 2 − Use what you know about regrouping.
5
29
×
Step 1
Multiply the ones digit of the bottom number by the
6
ones digit of the top number.
4
• Multiply 6 × 9 = 54
• Write the 4 under the line in the
• Carry the 5 to the
5
29
×
6
174
Step 2
tens
ones
column.
column.
Multiply the ones digit of the bottom number by the
tens digit of the top number.
• Multiply 6 × 2 = 12
• Add 5: 12 + 5 = 17
• Write the 7 under the line in the
• Carry the 1 under the line in the
Multiplyingand
andDividing
DividingWhole
WholeNumbers
Numbers
1.3 1.3
Multiplying
tens
column.
hundreds
column.
Application Situation 1 Application
| LES 1 Situation 1  LES 1
3939
KNOWLEDGE KEY MULTIPLYING WHOLE NUMBERS − 2 DIGITS BY 2 DIGITS
EXAMPLE
Multiply 37 × 24
METHOD 1 − List all the partial products and add them together.
37
×
+
24
28
Step 1
Multiply 4 × 7 = 28
120
Step 2
Multiply 4 × 30 = 120
140
Step 3
Multiply 20 × 7 = 140
600
Step 4
Multiply 20 × 30 = 600
888
Step 5
Add the partial products.
METHOD 2 − Use what you know about regrouping.
2
×
37
Step 1
24
ones digit of the top number.
8
Multiply the ones digit of the bottom number by the
• Multiply 4 × 7 = 28
• Write the 8 under the line in the
• Carry the 2 to the
2
×
tens
37
Step 2
24
tens digit of the top number.
148
ones
column.
column.
Multiply the ones digit of the bottom number by the
• Multiply 4 × 3 = 12
• Add 2: 12 + 2 = 14
column.
• Write the 4 under the line in the
tens
• Write the 1 under the line in the
hundreds
LES 1Numbers
| Application Situation 1
40 1.3 Multiplying and Dividing Whole
column.
40
Application Situation
1  LES
1 Numbers
1.3 Multiplying
and Dividing
Whole
×
37
Step 3
24
• We do this because we are moving into the
148
0
1
×
Write a zero under the line in the ones column.
tens column of the bottom number.
• The 0 represents a factor of 10.
37
Step 4
24
ones digit of the top number.
148
40
Multiply the tens digit of the bottom number by the
• Multiply 2 × 7 = 14
• Write the 4 under the line in the
• Carry the 1 to the
1
×
tens
37
Step 5
24
tens digit of the top number.
148
740
tens
column.
column.
Multiply the tens digit of the bottom number by the
• Multiply 2 × 3 = 6
• Add 1: 6 + 1 = 7
• Write the 7 under the line in the
37
Step 6
×
24
• Add 148 + 740 = 888
+
148
740
888
1.3 Multiplying and Dividing Whole Numbers
1.3 Multiplying and Dividing Whole Numbers
hundreds
column.
Application Situation 1  LES 1
Application Situation 1 | LES 1
41
41
KNOWLEDGE KEY MULTIPLYING WHOLE NUMBERS
3 DIGITS BY 1 DIGIT
EXAMPLE
867 × 5
METHOD 1
METHOD 2
3
867
×
867
5
×
35
5
4 335
300
+4 0 0 0
4 335
3 DIGITS BY 2 DIGITS
EXAMPLE
523 × 74
METHOD 1
METHOD 2
523
×
74
12
1
80
1
523
×
74
2 092
2 000
+3 6 6 1 0
210
38 7 0 2
1 400
+3 5 0 0 0
38 702
42
1.3 Multiplying and Dividing Whole
LES 1Numbers
| Application Situation 1
42
Application Situation
1  LES
1 Numbers
1.3 Multiplying
and Dividing
Whole
CHECK POINT
Multiply.
a)
2
63
9
×
f)
8
7
×
567
1
2
k)
×
1
584
56
+
b)
1
24
24
×
g)
1
12
6
×
c)
319
463
×
1
4
3
h)
×
1
×
27
98
216
+
2 430
2 646
1.3 1.3
Multiplying
Multiplyingand
andDividing
DividingWhole
WholeNumbers
Numbers
28 770
30 003
12
12
×
24
120
144
+
1
i)
+253 800
335 862
3
×
7 578
e)
1
m)
76 140
+ 127 600
147 698
6
5
846
397
1
19 140
842
9
1
5
4
1
5 922
1 1
3 1
1
411
73
1 233
+
957
×
×
480
576
3
1 5
2
d)
l)
1
+
4 380
4 964
72
96
18
4
n)
3 1
742
9
×
6 678
72
j)
×
5
6
73
68
3
2
o)
×
1
30
541
95
2 705
+
1
48 690
51 395
Application Situation 1 Application
| LES 1 Situation 1  LES 1
4343
KNOWLEDGE KEY WORD PROBLEMS – ANOTHER WAY OF SHOWING
MULTIPLICATION
1. A loaf of bannock costs $2.
How much money does it cost to buy 3
$2 ×
$3 =
$6
loaves?
It costs $6 to buy 3 loaves of
bannock.
2. Three brothers each read 5 books.
How many books do they read in total?
3 × 5 = 15
The brothers read 15 books in
total.
3. At the start of the Ivakkak there are 12
dog teams.
12 × 8 = 96
Each team has 8 dogs.
How many dogs are there in total?
There are 96 dogs in total.
4. There are two teams competing
in a volleyball tournament.
8 × 2 = 16
Each team has 8 members.
How many people are
There are 16 people in total.
there in total?
LES 1Numbers
| Application Situation 1
44 1.3 Multiplying and Dividing Whole
44
1.3 Multiplying
and Dividing
Whole
Application Situation
1  LES
1 Numbers
KNOWLEDGE KEY WHAT IS DIVISION?
To divide means to separate into equal groups.
Division is the opposite of multiplication.
EXAMPLE
There are
=
÷
6
2
6 ÷ 2 = 3 or 2 × 3 = 6
3
• The sign for division is ÷ or )
2 groups of 3 cans.
or
.
It is read as “divided by.”
Divisor
Dividend
• The total number of objects divided
Quotient
24 ÷ 3 = 8
is called the dividend.
• The number of groups created is
called the divisor.
Divisor
• The number of objects in each group
is called the quotient.
This is the result of a division.
8
3)24
Quotient
Dividend
EXAMPLES
Separate the eggs into equal groups.
1)
2)
There are 2 groups of 6 .
12 ÷ 2 =
6
or
2 × 6 = 12
1.3 Multiplying and Dividing Whole Numbers
1.3 Multiplying and Dividing Whole Numbers
There are 6 groups of 2 .
12 ÷ 6 =
2
or
6 × 2 = 12
Application Situation 1  LES 1
Application Situation 1 | LES 1
4545
KNOWLEDGE KEY PROPERTIES OF DIVISION
Division Table
÷
1
1
1
2
2
4
Commutative means the
3
3
6
9
order of terms is
4
4
8
12
16
important.
5
5
10
15
20
25
Example: 10 ÷ 5 ≠ 5 ÷ 10
6
6
12
18
24
30
36
7
7
14
21
28
35
42
49
8
8
16
24
32
40
48
56
64
9
9
18
27
36
45
54
63
72
81
10
10
20
30
40
50
60
70
80
90
100
11
11
22
33
44
55
66
77
88
99
110 121
12
12
24
36
48
60
72
84
96
108 120 132 144
• Division is
not commutative.
2
3
4
5
6
7
8
9
10 11 12
EXAMPLE
=
÷
10
5
=
÷
5
46
1.3 Multiplying and Dividing Whole Numbers
LES 1 | Application Situation 1
2
?
10
46
Application Situation 1  LES 1
1.3 Multiplying and Dividing Whole Numbers
KNOWLEDGE KEY SPECIAL RULES
Division by
Division by
Division by
0
1
10
Dividing by zero is
Dividing any number
Dividing any number
impossible.
by 1 doesn’t change
by 10 removes a zero from
the number.
the end of the number.
EXAMPLE
EXAMPLE
10 ÷ 1 = 10
10 ÷ 10 = 1
50 ÷ 1 = 50
50 ÷ 10 = 5
300 ÷ 1 = 300
300 ÷ 10 = 30
CHECK POINT
Divide.
a) 16 ÷ 4 = 4
g) 45 ÷ 8 = 5
m) 72 ÷ 9 = 8
b) 144 ÷ 12 = 12
h) 56 ÷ 7 = 8
n) 45 ÷ 5 = 9
c) 4 ÷ 2 = 2
i) 120 ÷ 10 = 12
o) 20 ÷ 4 = 5
d) 19 ÷ 0 = impossible
j) 56 ÷ 8 = 7
p) 12 ÷ 1 = 12
e) 18 ÷ 3 = 6
k) 48 ÷ 8 = 6
q) 32 ÷ 8 = 4
f) 121 ÷ 11 = 11
l) 81 ÷ 9 = 9
r) 63 ÷ 9 = 7
1.3 Multiplying and Dividing Whole Numbers
1.3 Multiplying and Dividing Whole Numbers
Application Situation 1  LES 1
Application Situation 1 | LES 1
4747
KNOWLEDGE KEY DIVISIBILITY RULES
We can use divisibility rules to test if one number
can be evenly divided by another number.
A number is
divisible by
2
3
5
The last digit is 0 or 5.
9
10
128 ÷ 2 = 64
621 ÷ 3 = 207
6+2+1=9
9÷3=3
The sum of the digits can be divided by 3.
The last two digits can be divided by 4.
8
EXAMPLE
The last digit of the number is even.
4
6
48
If
632 ÷ 4 = 158
32 ÷ 4 = 8
10 ÷ 5 = 2
The number can be divided by both 2 and 3.
The last three digits can be divided by 8.
The sum of the digits can be divided by 9.
The last digit is 0.
1.3 Multiplying and Dividing Whole Numbers
LES 1 | Application Situation 1
114 ÷ 6 = 19
114 ÷ 2 = 57
114 ÷ 3 = 38
36 288 ÷ 8 = 4 536
288 ÷ 8 = 36
8 991 ÷ 9 = 999
8 + 9 + 9 + 1 = 27
27 ÷ 9 = 3
40 ÷ 10 = 4
48
Application Situation 1  LES 1
1.3 Multiplying and Dividing Whole Numbers
CHECK POINT
1. Circle the numbers that are evenly divisible by 5.
a) 95
d) 37
g) 84
b) 19
e) 525
h) 8 014
2. Circle the numbers that are evenly divisible by 3.
a) 20 955
d) 156
g) 1 956
b) 3 847
e) 19 873
h) 520
3. Circle the numbers that are evenly divisible by 2.
a) 29 367
d) 364
g) 842 362
b) 84
e) 222 243
h) 14 365 202
4. Circle the numbers that are evenly divisible by 10.
a) 30
d) 63
g) 450
b) 984 357
e) 9 000
h) 840
5. Circle the numbers that are evenly divisible by 9.
a) 329 238
d) 36 904
g) 8 409
b) 3 974
e) 2 925
h) 82
6. Circle the numbers that are evenly divisible by 4.
a) 40
d) 260
g) 9 345
b) 639
e) 25 340
h) 26
Multiplyingand
andDividing
DividingWhole
WholeNumbers
Numbers
1.3 1.3
Multiplying
Application Situation 1 Application
| LES 1 Situation 1  LES 1
4949
KNOWLEDGE KEY DIVIDING WHOLE NUMBERS − LONG DIVISION
2 DIGITS BY 1 DIGIT
EXAMPLE
Divide 87 ÷ 3
Step 1 Write out the division.
3
87
There are :
•
10
10
10
8
tens
7
ones
10
10
10
10
10
•
2
3
87
– 6X
2
Step 2 How many times can we divide 8 tens by 3?
•
10
10
10
10
• Write the 2 in the
10
tens
10
10
10
=
2
times
column of the quotient.
• Multiply the 2 in the quotient by the divisor.
2×3=
6
• Write the 6 in the
tens
column under the 8.
• Subtract 8 − 6 = 2
• There are 2
50
tens left over.
1.3 Multiplying and Dividing Whole Numbers
LES 1 | Application Situation 1
50
Application Situation 1  LES 1
1.3 Multiplying and Dividing Whole Numbers
2
3
87
– 6X
27
Step 3
• Exchange 2 tens for 20 ones.
10
10
=
• 20 ones + 7 ones =
29
3
87
– 6X
27
–27
0
27 ones
Step 4 How many times can we divide 27 ones by 3?
•
=
• Write the 9 in the
ones
9
times
column of the quotient.
• Multiply the 9 in the quotient by the divisor.
9 x 3 = 27
• Write the 2 in the
tens
column under the 2.
• Write the 7 in the
ones
column under the 7.
• Subtract 27 − 27 = 0
• There are 0 ones left over.
1.3 Multiplying and Dividing Whole Numbers
1.3 Multiplying and Dividing Whole Numbers
Application Situation 1 | LES 1
Application Situation 1  LES 1
51
51
KNOWLEDGE KEY DIVIDING WHOLE NUMBERS − LONG DIVISION
3 DIGITS BY 2 DIGITS
EXAMPLE 1
848 ÷ 53
53
16
330 ÷ 15
15
22
6 985 ÷ 5
1 397
5
52
6
–5
1
–1
985
X
9
5X
48
– 42X
35
– 35
0
1.3 Multiplying and Dividing Whole Numbers
LES 1 | Application Situation 1
294 ÷ 7
7
42
294
– 28X
14
– 14
0
3 DIGITS BY 3 DIGITS
EXAMPLE 4
330
– 30X
30
– 30
0
4 DIGITS BY 1 DIGIT
EXAMPLE 5
EXAMPLE 2
848
– 53X
318
– 318
0
3 DIGITS BY 2 DIGITS
EXAMPLE 3
3 DIGITS BY 1 DIGIT
472 ÷ 236
236
2
472
– 472
0
4 DIGITS BY 2 DIGITS
EXAMPLE 6
1 625 ÷ 25
65
25
1 625
– 1 5 0X
125
– 125
0
52
Application Situation 1  LES 1
1.3 Multiplying and Dividing Whole Numbers
KNOWLEDGE KEY DIVISION WITH REMAINDER
Sometimes we have something left over when we divide.
We call this the remainder.
EXAMPLE 1 Divide 4 241 ÷ 57
57
3
74
11 1
4 241
–3 9 9X
251
– 228
2 3R
We have no more that we can exchange!
• We are left with 23.
• This is called the "remainder."
• 4 241 ÷ 57 = 74 with 23 R
EXAMPLE 2
Divide 5 276 ÷ 65
81
65
• 5 276 ÷ 65 = 81 with 11 R
5 276
–5 2 0X
76
–65
1 1R
1.3 Multiplying and Dividing Whole Numbers
1.3 Multiplying and Dividing Whole Numbers
Application Situation 1  LES 1
Application Situation 1 | LES 1
5353
CHECK POINT
Divide.
74
14
a)
36
536
– 3 6X
1 76
– 1 44
32R
d)
7
73
b)
7 1
25 1 825
– 1 7 5X
75
– 75
0
54
6 1 486
– 1 2X
28
– 2 4X
46
–42
4R
518
– 4 9X
28
– 28
0
83
g)
6 1
21 1 743
– 1 6 8X
63
– 63
0
16
e)
53
848
– 5 3X
3 18
– 3 18
0
26
h)
35
f)
16
1.3 Multiplying and Dividing Whole
LES 1Numbers
| Application Situation 1
64
–64
0
941
– 7 0X
2 41
– 2 10
31R
86
4
24 7
c)
4 1
i)
9
774
– 7 2X
54
– 54
0
54
Application Situation
1  LES
1 Numbers
1.3 Multiplying
and Dividing
Whole
KNOWLEDGE KEY WORD PROBLEMS – ANOTHER WAY OF SHOWING DIVISION
1. Your teacher has 25 pencils that need to be
divided evenly among students in the class.
÷
25
5
=
5
There are 5 students in your class.
How many pencils will each student get?
Each student will get
2. Today you caught 12 fish.
You want to divide them evenly between you
÷
12
3
=
5
pencils.
4
fish.
3
apples.
4
and your two friends.
How many fish will each person get?
Each person will get
3. Today you bought 6 apples at the Co-op.
You want to split them evenly
6
÷
2
=
3
between you and your sister.
How many apples will each person get?
Each person will get
4. Your mom picked 432 berries.
She wants to divide them into 12 containers.
How many berries will be in each container?
432
÷
12
There will be
=
36
36
berries in
each container.
1.3 Multiplying and Dividing Whole Numbers
1.3 Multiplying and Dividing Whole Numbers
Application Situation 1  LES 1
Application Situation 1 | LES 1
5555
Application Question
A. The Best Buy
RATING KEY
You want to buy toilet paper at the Co-op.
C2 USES MATHEMATICAL
EVALUATION CRITERIA
REASONING
OBSERVED LEVEL
3
5
4
3
2
1
You are deciding between
PuffPuff and Silkeez.
PuffPuff comes in packages of 6 rolls.
Each roll has 240 sheets.
The package costs $10.
3
2
4–5
$10
6
Silkeez comes in packages of 8 rolls.
Each roll has 160 sheets.
This package also costs $10.
Which one is the better buy?
Explain your answer.
I
ANALYSE THE SITUATION
rolls
What I Already Know
What I Need to Find Out
PuffPuff
Think about
• To multiply whole numbers, line up the numbers so that
all the
are in the
WORD BANK: same, ones.
160
z
Silkee
240
56
LES 1 | Application Situation 1
column.
Show Your Work
= 1 cm
Application Situation 1 | LES 1
57
Application Question
B. A Friendly Snack
RATING KEY
You are going to buy snacks for you
and two of your friends.
C2 USES MATHEMATICAL
EVALUATION CRITERIA
REASONING
OBSERVED LEVEL
3
5
4
3
2
You buy:
1
• a bag of 12 apples
3
2
• a package of 51 strawberries
4–5
• a box of cookies with 4 rows
of 6 cookies
4 rows
You want to split the snacks evenly.
How many of each snack do you get?
6
I
ANALYSE THE SITUATION
What I Already Know
What I Need to Find Out
Think about
12
•
Splitting evenly means
•
A number is divisible by 3 if the
can be divided by
WORD BANK: sum, 3, dividing.
apples
58
LES 1 | Application Situation 1
into equal groups.
.
of its digits
Show Your Work
= 1 cm
Application Situation 1 | LES 1
59
Application Situation 2
2.1 Prime and Composite Numbers
2.2 Factoring Composite Numbers
2.3 Powers of Whole Numbers
Counting Cases
APPLICATION QUESTION
Application Situation 2 | LES 1
61
2.1 Prime
and
Composite
Numbers Numbers
2.1 Prime
and Composite
KNOWLEDGE KEY WHAT
ARE PRIME
AND COMPOSITE
NUMBERS?
KNOWLEDGE
KEY WHAT
ARE PRIME AND
COMPOSITE NUMBERS?
All whole numbersAll
arewhole
eithernumbers
prime orare
composite
numbers
− except numbers
0 and 1. − except 0 and 1
either prime
or composite
• Prime numbers:
have
two factors:
and two
itself.
• Only
Prime
numbers:
Only 1have
factors: 1 and itself.
• Composite numbers:
Have more
than two
factors.
• Composite
numbers:
Have
more than two factors.
PRIME NUMBERS PRIME NUMBERS
COMPOSITE NUMBERS
COMPOSITE NUMBERS
(Two factors: 1 and(Two
itself)
(More
than
two
factors)
factors: 1 and itself)
(More than two factors)
EXAMPLES
EXAMPLES
EXAMPLES
EXAMPLES
13
1329
29 18
1812
12
1 × 13 = 13
1 1× × 1329 = =1329
× 18
= 29= 18
1 × 129
= 12
1 ×1 ×1812= 18
1 × 12 = 12
2×
9 = 18
= 12
2 ×2 × 9 6= 18
2×
6 = 12
3×
6 = 18
= 12
3 ×3 × 6 4= 18
3×
4 = 12
Factors:
Factors:1 ,1 , 2 2, , Factors: 1 ,
, 2 , Factors:
Factors: 1 , 13 Factors:
Factors: 1 1, , 1329 Factors:
1 , 129
3 , 6 , 9 , 18
CHECK POINT
3 3
, ,6 4, ,9 6, ,1812
3 , 4 , 6 ,
CHECK POINT
1. Circle the prime1.
numbers.
Circle the prime numbers.
a) 16
b) 9 a) 16
c) 11b) 9
d) 17c) 11
e) 36d) 17
f) 2 e) 36
f) 2
2. Write the factors2.ofWrite
eachthe
composite
numbers.
factors of
each composite numbers.
a) 24
b) 6
1 × 24 = 24
1 ×324
==
2424
×8
3 × 8 = 24
1×6=6
1×6=6
2 × 12 = 24
2 ×412
==
2424
×6
4 × 6 = 24
2×3=6
2×3=6
1, 2, 3,Factors:
6
1, 2, 3, 6
Factors:
62
b) 6
a) 24
1, 2,
3, 4, 6, 12, 24
Factors:
1, 2, 3, 4,Factors:
6, 12, 24
2.1 Prime and Composite Numbers2.1 Prime and Composite Numbers
LES 1 | Application Situation 2
Application Situation 2  LES 1
62
Application Situation 2  LES 1
2.1 Prime and Composite Numbers
2.2 Factoring
Composite Numbers
KNOWLEDGE KEY PRIME FACTORIZATION
Prime factorization shows all the prime factors of a composite number.
1.
Example: 60 = 2 × 2 × 2 × 3 × 3 × 3
The prime factors of a number can be found by using a factor tree.
EXAMPLE 1
Find the prime factors of 525.
Step 1
2
525
175
3
Divide 525 by the smallest
2
5
prime number possible.
2
2 ,
12
525 ÷ 3 = 175
35
5
7
Step 2
Divide 175 by the smallest prime number possible.
175 ÷ 5 = 35
Step 3
Divide 35 by the smallest prime number possible.
35 ÷ 5 = 7
Prime factorization: 3 × 5 × 5 × 7 = 525
2.2 Factoring Composite Numbers
Application Situation 2  LES 1
62
2.2 Factoring Composite Numbers
Application Situation 2 | LES 1
63
63
EXAMPLE 2
420
Find the prime factors of 420.
Step 1
210
2
Divide 420 by the smallest
2
105
prime number possible.
3
420 ÷ 2 = 210
35
5
Step 2
7
Divide 210 by the smallest prime number possible.
210 ÷ 2 = 105
Step 3
Step 4
Divide 105 by the smallest prime
Divide 35 by the smallest prime number
number possible.
possible.
105 ÷ 3 = 35
35 ÷ 5 = 7
Prime factorization: 2 × 2 × 3 × 5 × 7 = 420
CHECK POINT
627
Find the prime factors of 627.
209
3
Prime factorization: 3 × 11 × 13 = 627
64
LES 1 | Application Situation 2
2.2 Factoring Composite Numbers
11
13
2.2 Factoring Composite Numbers
Application Situation 2  LES 1
64
KNOWLEDGE KEY GREATEST COMMON FACTOR
Whole numbers often have factors in common.
The greatest common factor is the largest factor common to a set
of whole numbers.
EXAMPLE
Find the greatest common factor of 8, 12, 24.
Factors of 8
Factors of 12
Factors of 24
1×8=8
1 × 12 = 12
1 × 24 = 24
3×
8 = 24
2×4=8
2×
6 = 12
2 × 12 = 24
4×
6 = 24
3×
4 = 12
Factors:
Factors:
Factors:
1, 2, 4, 8
1, 2, 3, 4, 6, 12
1, 2, 3, 4, 6, 8, 12, 24
Factors common to 8, 12 and 24: 1, 2, 4
Greatest common factor: 4
CHECK POINT
Find the greatest common factor of 9, 16, 36.
Factors of 9
Factors of 16
Factors of 36
1×9=9
1 × 16 = 16
1 × 36 = 36
4 × 8 = 36
3×3=9
2 × 8 = 16
2 × 18 = 36
6 × 6 = 36
4 × 4 = 16
3 × 12 = 36
Factors:
Factors:
Factors:
1, 3, 9
1, 2, 4, 8, 16
1, 2, 3, 4, 6, 8, 12, 18, 36
Common factors to 9, 16, 36: 1
2.2 Factoring Composite Numbers
2.2 Factoring Composite Numbers
Greatest common factor: 1
Application Situation 2  LES 1
Application Situation 2 | LES 1
65
65
KNOWLEDGE KEY LEAST COMMON MULTIPLE
A multiple is the product of two whole numbers.
Whole numbers often have multiples in common.
The least common multiple is the smallest multiple common to a set
of whole numbers.
EXAMPLE
Find the least common multiple of 3, 4 and 12.
• Multiples of 3: 3, 6, 9, 12, 15 , 18 , 21 , 24 , 27 , 30
• Multiples of 4: 4, 8, 12, 16 , 20 , 24 , 28 , 32 , 36 , 40
• Multiples of 12: 12, 24 , 36 , 48 , 60 , 72 , 84 , 96 , 108 , 120
Common multiples of 3, 4 and 12: 12 , 24
Least common multiple: 12
CHECK POINT
Find the least common multiple of 2, 6 and 3.
• Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30
• Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90
• Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45
Common multiples: 6, 12, 18, 24, 30
Least common multiple: 6
2.2 Factoring Composite Numbers
66
LES 1 | Application Situation 2
Application Situation 2  LES 1
66
2.2 Factoring Composite Numbers
2.3 Powers
of Whole Numbers
KNOWLEDGE KEY EXPONENTIAL FORM
A shortcut can be used to multiply a number by itself.
EXAMPLE
2 × 2 × 2 × 2 × 2 = 32
•
2 ×2=
4
•
4 ×2=
8
•
8 × 2 = 16
•
16 × 2 = 32
The factor 2 is multiplied by itself 5 times.
This form shows repeated factors.
The operation 2 × 2 × 2 × 2 × 2
can also be shown in exponential form: 25.
Exponent
(power)
There are two parts of a number in exponential form:
• The base is the factor that is being multiplied.
• The exponent (power) tells us
Base
how many times to multiply the factor.
25 = 32
A number in exponential form can be read as:
two to the power of 5
OR
two to the fifth
OR
two to the exponent 5
BE CAREFUL!
63
6 × 6 × 6 = 216
2.3 Powers of Whole Numbers
2.3 Powers of Whole Numbers
6×3
is not the same as
6 × 3 =18
Application Situation 2  LES 1
Application Situation 2 | LES 1
67
67
KNOWLEDGE KEY THE ZERO EXPONENT
Any number to the power of 0 equals 1.
EXAMPLE 1
EXAMPLE 2
65 = 7 776
35 = 243
÷6
÷3
64 = 1 296
34 =
81
÷6
÷3
63 = 216
33 =
27
÷6
62 =
÷3
32 =
36
9
÷6
61 =
÷3
31 =
6
3
÷6
60 =
÷3
30 =
1
1
CHECK POINT
1. Fill in the table below.
Repeated Factors
Exponential Form
Standard Form
25
32
163
4 096
Ex.: 2 × 2 × 2 × 2 × 2
a) 16 × 16 × 16
b)
5×5
52
25
c)
3×3×3×3
34
81
d)
7×7×7×7×7×7
76
117 649
2.3 Powers of Whole Numbers
68
LES 1 | Application Situation 2
Application Situation 2  LES 1
68
2.3 Powers of Whole Numbers
2. Write these repeated factors in exponential form.
a) 2 × 2 × 2 = 23
f)
b) 6 × 6 × 6 × 6 × 6 = 65
g) 5 × 5 × 5 × 5 × 5 × 5 × 5 = 57
c) 9 × 9 = 92
h) 3 × 3 × 3 × 3 = 34
d) 7 × 7 × 7 × 7 = 74
i)
12 × 12 = 122
e) 10 = 101
j)
1 × 1 × 1 × 1 × 1 = 15
14 × 14 × 14 = 143
3. Write the exponential form as repeated factors.
a) 32 = 3 × 3
f)
15 = 1 × 1 × 1 × 1 × 1
b) 54 = 5 × 5 × 5 × 5
g) 122 = 12 × 12
c) 93 = 9 × 9 × 9
h) 84 = 8 × 8 × 8 × 8
d) 195 = 19 × 19 × 19 × 19 × 19
i)
46 = 4 × 4 × 4 × 4 × 4 × 4
e) 111 = 11
j)
105 = 10 × 10 × 10 × 10× 10
4. Write the exponential form and repeated factors in standard form.
a) 32 = 9
f)
b) 180 = 1
g) 136 = 4 826 809
c) 7 × 7 = 49
h) 5 × 5 × 5 × 5 = 625
d) 83 = 512
i)
6 × 6 × 6 × 6 × 6 = 7 776
e) 1 × 1 × 1 × 1 × 1 × 1 = 1
j)
102 = 100
2.3 Powers of Whole Numbers
2.3 Powers of Whole Numbers
114 = 14 641
Application Situation 2 | LES 1
Application Situation 2  LES 1
69
69
Application Question
Counting Cases
RATING KEY
Today the Co-op received
a pallet with 5 boxes on it.
C2 USES MATHEMATICAL
EVALUATION CRITERIA
REASONING
OBSERVED LEVEL
3
3
2
4–5
5
4
3
2
1
Inside each box are 5 cases.
Inside each case are
5 bags of potatoes.
How many bags of potatoes
are there in total?
I
ANALYSE THE SITUATION
What I Already Know
What I Need to Find Out
Think about
•39
= the factor
•The
multiplied by itself
is the factor that we are multiplying.
•The
multiply the factor.
WORD BANK: 9, base, exponent, 3.
70
LES 1 | Application Situation 2
times.
tells us how many times we
Show Your Work
Application Situation 2 | LES 1
71
Application Situation 3
3.1 Order
of Operations
A Raffle
Application Situation 3 | LES 1
APPLICATION QUESTION
73
3.1 Order
of3.1
Operations
Order of Operations
KNOWLEDGE KEY SOLVING
A SEQUENCE
OF OPERATIONS
KNOWLEDGE
KEY SOLVING
A SEQUENCE OF OPERATIONS
To solve a sequence
operations
we must
combine everything
we've learned
To of
solve
a sequence
of operations
we must combine
everything we've learn
about addition, subtraction,
multiplication,
division
and exponents.
about addition,
subtraction,
multiplication,
division and exponents.
EXAMPLE
EXAMPLE
(6 + 4)2 × 2 + 7
(6 + 4)2 × 2 + 7
There are specific There
rules toare
solve
a sequence
operations.
specific
rules to of
solve
a sequence of operations.
(6 + 4)2 × 2 + 7 = (6 + 4)2 × 2 + 7 =
Step 1 Brackets Step 1 Brackets
• Solve everything• inSolve
brackets
first. in brackets first.
everything
Step 2 ExponentsStep 2 Exponents
• Solve exponents• second.
Solve exponents second.
Step 3 Division/Multiplication
Step 3 Division/Multiplication
10
2
×2+7=
10
2
102 × 2 + 7 =
102 × 2 + 7 =
100 × 2 + 7 =
100 × 2 + 7 =
100 × 2 + 7 =
100 × 2 + 7 =
+ 7=
• Do these in the •order
to appear
right. from left200
Do they
theseappear
in the from
orderleft
they
to right.
Step 4 Addition/Subtraction
Step 4 Addition/Subtraction
×2+7=
200
200 + 7 = 207
+ 7=
200 + 7 =
• Do these in the •order
to appear
right. from left to right.
Do they
theseappear
in the from
orderleft
they
(6 + 4)2 × 2 +(6 7 + = 4)2 × 2 + 7 =
102
×
2 + 710=2
×
2 + 7 =
100
×
2 + 7100
=
×
2 + 7 =
200
74
3.1 Order of Operations
3.1 Order of Operations
LES 1 | Application Situation 3
+ 7 = 207
200
+ 7 = 207
74
Application Situation 3  LES 1 Application Situation 3  LES 1
3.1 Order of Operations
ned
1
There is a trick
1.
for remembering
2.
the steps when solving a
3.
sequence on operations:
“BEDMAS.”
4.
Brackets
Exponents
Division
Multiplication
Addition
Subtraction
Left to right
Left to right
CHECK POINT
Solve the following sequences of operations.
a)
3 + (2 + 4 × 2) − 32 =
d)
4 + 10 − (5 + 7) =
3 + (2 + 8) − 32 =
4 + 10 − (12) =
3 + 10 − 32 =
14 − 12 =
3 + 10 − 9 =
2
13 − 9 = 4
207
b)
c)
74
(10 ÷ 2 − 3)2 =
e)
1 × 2 ÷1 × 6 =
(5 − 3)2 =
2÷1×6=
(2)2 =
2×6=
4
12
32 + 4 ÷ 2 =
f)
8 ÷ 22 × 6 =
9+4÷2=
8÷4×6=
9+2=
2×6=
11
12
3.1 Order of Operations
3.1 Order of Operations
Application Situation 3 | LES 1
Application Situation 2  LES 1
75
75
Application Question
A Raffle
RATING KEY
The Co-op is having a raffle.
The top prize is a snowmobile.
C2 USES MATHEMATICAL
EVALUATION CRITERIA
REASONING
OBSERVED LEVEL
3
5
4
3
2
1
3
The raffle ticket
looks like this:
2
4–5
Name:
Skill testing question:
2
3
(20 ÷ 5) – 2 × 3 =
Solve the skill testing question.
Show your work.
I
ANALYSE THE SITUATION
What I Already Know
Think about
The order of operation is:
1.Brackets
2.Exponents
3. Division Multiplication (left to
)
4.Addition
Subtraction (
to right)
WORD BANK: S, D, left, A, E, right, B, M.
76
LES 1 | Application Situation 3
What I Need to Find Out
Show Your Work
= 1 cm
Application Situation 3 | LES 1
77
Application Situation 4
4.1 Decimal Numbers
4.2 Adding and Subtracting
Decimal Numbers
4.3 Multiplying and Dividing
Decimal Numbers
A. Paying the Bill
B. Too Expensive
Application Situation 4 | LES 1
APPLICATION QUESTIONS
79
4.1
Decimal Numbers
4.1 Decimal Numbers
KNOWLEDGE KEY WHAT IS A DECIMAL NUMBER?
ACTIVITY
KNOWLEDGE KEY WHAT IS A DECIMAL NUMBER?
Elisapi and three ofACTIVITY
her friends baked 26 cookies.
They want to divideElisapi
the cookies
evenly.
and three
of her friends baked 26 cookies.
They want to divide the cookies evenly.
Elisapi
Ruta
Lucy
Elisapi
Ruta
How can the girls divide the last two cookies evenly?
Paula
Lucy
Paula
How can the girls divide the last two cookies evenly?
Elisapi
Ruta
Each girl gets half (0.5)
Lucy
Elisapi
Ruta
of the two left over cookies.
Each girl has 6.5 Each
cookies
in total.
half (0.5)
girl gets
Each girl has 6.5
Lucy
4.1 Decimal Numbers
LES 1 | Application Situation 4
Paula
of the two left over cookies.
cookies in total.
Application Situation 4  LES 1
4.1 Decimal Numbers
80
Paula
80
Application Situation 4  LES 1
4.1 Decimal Numbers
A decimal number has 3 parts:
• Digits before the decimal point
The digits before the decimal
point are greater than or equal to
Greater than or
equal to a whole
a whole.
12 . 34
• The decimal point
The decimal point separates the
whole from the parts of a whole.
Decimal
point
• Digits after the decimal point
The digits after the decimal point
are parts of a whole.
Parts of
a whole
EXAMPLE
In 6.5 cookies:
a) The number before the decimal point tells us
there are 6
whole cookies.
b) The number after the decimal point tells us
there are 0.5 parts of a cookie.
80
4.1 Decimal Numbers
4.1 Decimal Numbers
Application Situation 4 | LES 1
Application Situation 4  LES 1
8181
KNOWLEDGE KEY PLACE VALUE OF DECIMAL NUMBERS
In a decimal number every digit has a place. Each place has a different value.
The place value table of decimal numbers has an extra period.
• This period shows the parts of a whole.
• This period is made up of tenths, hundredths and thousandths.
EXAMPLE
Show 14 352 726 954.261 in a place value table.
1 000 000
100 000
10 000
1 000
100
10
1
Ones
Hundreds
Tens
Ones
Hundreds
Tens
Ones
Hundreds
Tens
Ones
Hundred Ten
Hundred Ten
ThouHundred Ten
ThouBillions Billions Billions Millions Millions Millions sands sands
Thousands
(HB)
Hundreds
Tens
Ones
HunThouTenths dredths sandths
(B)
(HM)
(TM)
(M)
(HTH)
(TTH)
(TH)
(H)
(T)
(O)
1
4
3
5
2
7
2
6
9
5
4
.
.
(t)
(h)
(th)
2
6
1
column.
It has a value of 0.2.
• 6 is in the hundredths
column.
It has a value of 0.06.
• 1 is in the thousandths
14 352 726 954 . 261
Billions
column.
HunThoudredths sandths
Tenths
(TB)
• 2 is in the tenths
0.001
10 000 000
Tens
0.1
100 000 000
Hundreds
0.01
PARTS OF
A WHOLE
ONES
1 000 000 000
THOUSANDS
10 000 000 000
MILLIONS
100 000 000 000
BILLIONS
Millions
Thousands
Tenths
Hundredths
Thousandths
Ones
It has a value of 0.001.
Application Situation 4  LES 1
4.1 Decimal Numbers
82
LES 1 | Application Situation 4
82
4.1 Decimal Numbers
CHECK POINT
1. Put the number 46 482.937 in a place value table.
1 000 000
100 000
10 000
1 000
100
10
1
Ones
Hundreds
Tens
Ones
Hundreds
Tens
Ones
Hundreds
Tens
Ones
Hundreds
Tens
Ones
(TH)
(H)
(T)
(O)
.
HunThouTenths dredths sandths
(t)
(h)
(th)
6
4
8
2
. 9
3
7
Thousands
(TTH)
4
(TB)
(B)
(HM)
(TM)
(M)
(HTH)
HunThoudredths sandths
Tenths
Hundred Ten
Hundred Ten
ThouThouHundred Ten
Billions Billions Billions Millions Millions Millions sands sands
(HB)
0.001
10 000 000
Tens
0.1
100 000 000
Hundreds
0.01
PARTS OF
A WHOLE
ONES
1 000 000 000
THOUSANDS
10 000 000 000
MILLIONS
100 000 000 000
BILLIONS
b) 5 is in the
tenths
column.
c) 4 is in the
ones
column.
d) 7 is in the
tens
column.
e) 2 is in the
hundreds
column.
f) 3 is in the
thousands
column.
g) 1 is in the
ten thousands
column.
h) 9 is in the
hundred thousands
column.
i) 0 is in the
millions
column.
j) 8 is in the
ten millions
column.
4.1 Decimal Numbers
4.1 Decimal Numbers
Parts of a whole
Ones
Thousands
Millions
Application Situation 4  LES 1
Application Situation 4 | LES 1
PERIOD
column.
PERIOD
hundredths
PERIOD
a) 6 is in the
PERIOD
2. Write the location of each digit in the number 80 913 274.56.
83
83
To calculate the value of a digit in a decimal number, multiply the digit
by its place value.
EXAMPLE
Calculate the value of the digits 1, 0 and 7 in the number 39 482.107.
Hundred
Ten
Thousands Thousands Thousands
(HTH)
0.001
Tens
Ones
Tenths
Hundredths Thousandths
Hundreds
Tens
Ones
Tenths
Hundredths Thousandths
(t)
(h)
(th)
1
0
7
(TH)
(H)
(T)
(O)
3
9
4
8
2
tenths
0.01
Hundreds
(TTH)
• 1 is in the
0.1
1
Ones
PARTS OF A WHOLE
10
Tens
100
1 000
Hundreds
ONES
10 000
100 000
THOUSANDS
.
column.
The tenths column has a value of 0.1 .
1 × 0.1
=
0.1
• 0 is in the
hundredths
column.
The hundredths column has a value of 0.01 .
0 × 0.01
=
• 7 is in the
0
thousandths
column.
The thousandths column has a value of 0.001 .
7 × 0.001
844.1 Decimal Numbers
=
0.007
LES 1 | Application Situation 4
84
4.1 Decimal Numbers
Application Situation 4  LES 1
CHECK POINT
Put the number 10 394 852.576 in a place value table.
Calculate the value of each digit.
Ones
Hundreds
Tens
Ones
Tenths
Ten
Millions
Millions
Hundred
Thousands
Ten
Thousands
Thousands
Hundreds
Tens
Ones
(M)
(HTH)
(TTH)
(TH)
(H)
(T)
(O)
1
0
3
9
4
8
5
2
(TM)
a) 1 ×
10 000 000
=
10 000 000
b) 0 ×
1 000 000
=
0
c) 3 ×
100 000
=
300 000
d) 9 ×
10 000
=
90 000
e) 4 ×
1 000
=
4 000
8 ×
100
=
800
g) 5 ×
10
=
50
h) 2 ×
1
=
2
f)
i)
5 ×
0.1
=
0.5
j)
7 ×
0.01
=
0.07
k) 8 ×
0.001
=
0.006
4.1 Decimal Numbers
4.1 Decimal Numbers
0.001
Tens
0.01
1
Hundreds
0.1
10
Ones
100
Tens
100 000
1 000
(HM)
PARTS OF A WHOLE
10 000
Hundred
Millions
ONES
1 000 000
Hun-dreds
THOUSANDS
10 000 000
100 000 000
MILLIONS
Hundredths
Thousandths
Tenths
Hundredths
Thousandths
(t)
(h)
(th)
5
7
6
.
Application Situation 4  LES 1
Application Situation 4 | LES 1
85
85
KNOWLEDGE KEY INSIGNIFICANT ZERO — DECIMAL NUMBERS
A zero at the end of a decimal number doesn't count.
EXAMPLE 1
45.20
ONES
100
Hundreds
Hundreds
(H)
PARTS OF A WHOLE
10
1
0.1
Tens
Ones
Tenths
Tens
(T)
Ones
(O)
4
5
.
Hundreds
Hundreds
(H)
100
Tenths
(t)
Hundredths
Hundredths
(h)
Thousandths
Thousandths
(th)
Hundreds
Hundreds
(H)
2
0
45.20 = 45.2
PARTS OF A WHOLE
10
1
0.1
Tens
Ones
Tenths
Tens
(T)
Ones
(O)
.
and
10
1
0.1
Tens
Ones
Tenths
Tens
(T)
Ones
(O)
Tenths
(t)
4
5
.
0.01
0.001
Hundredths
Hundredths
(h)
Thousandths
Thousandths
(th)
2
•
5
ones
•
2
tenths
4.090
ONES
0.01
0.001
100
Tenths
(t)
Hundredths
Hundredths
(h)
Thousandths
Thousandths
(th)
Hundreds
Hundreds
(H)
9
0
PARTS OF A WHOLE
10
1
0.1
Tens
Ones
Tenths
Tens
(T)
Ones
(O)
4
There are:
• 4 ones
• 9 tenths
• 0 hundredths
.
0.01
0.001
Tenths
(t)
Hundredths
Hundredths
(h)
Thousandths
Thousandths
(th)
0
9
0
There are:
4 ones
•
4.90 ≠ 4.090
•
0
tenths
•
9
hundredths
•
0
thousandths
Application Situation 4  LES 1
4.1 Decimal Numbers
86
PARTS OF A WHOLE
There are:
4 tens
•
4.90
4
ONES
0.001
EXAMPLE 2
ONES
45.2
0.01
There are:
• 4 tens
• 5 ones
• 2 tenths
• 0 hundredths
100
and
LES 1 | Application Situation 4
86
4.1 Decimal Numbers
REMINDER!
A zero at the beginning of a whole number doesn’t count either.
We can combine these rules.
EXAMPLE 3
007.100
ONES
100
Hundreds
Hundreds
(H)
0
PARTS OF A WHOLE
10
1
0.1
7.1
0.01
0.001
100
Thousandths
Thousandths
(th)
Hundreds
Hundreds
(H)
0
Tens
Ones
Tenths
Tens
(T)
Ones
(O)
Tenths
(t)
Hundredths
Hundredths
(h)
0
7
1
0
.
and
There are:
• 0 hundreds
• 0 tens
• 7 ones
• 1 tenths
• 0 hundredths
• 0 thousandths
ONES
10
PARTS OF A WHOLE
1
0.1
Tens
Ones
Tenths
Tens
(T)
Ones
(O)
Tenths
(t)
7
.
0.01
0.001
Hundredths
Hundredths
(h)
Thousandths
Thousandths
(th)
1
There are:
7 ones
•
•
1
tenths
007.100 = 7.1
CHECK POINT
Match the equivalent numbers.
a)
16.4 •
• 01.89
b)
1.89 •
• 142.07
c)
007.480 •
d)
4.098 •
e)
00 142.070 •
4.1 Decimal Numbers
4.1 Decimal Numbers
• 016.400
• 000 000 004.098
• 7.48
Application Situation 4 | LES 1
Application Situation 4  LES 1
87
87
KNOWLEDGE KEY READING AND WRITING DECIMAL NUMBERS
There are two ways of reading decimal numbers.
EXAMPLES
OPTION A
 Three point two
1. The number before the decimal point. 3.2
2. The word point.
3. The digits after the decimal point.
56.409  Fifty-six point four zero
nine
817.34  Eight hundred seventeen
point three four
EXAMPLES
OPTION A
 Three and two tenths
1. The number before the decimal point. 3.2
2. The word and.
3. The place value of the number after
the decimal point.
56.409  Fifty-six and four hundred
nine thousandths
817.34  Eight hundred seventeen
and thirty-four hundredths
To write decimal numbers, follow the rules for writing whole numbers.
• Group the tenths, hundredths and
thousandths after the decimal point.
• Insert a space between the place
value periods.
EXAMPLES
• Forty-six point nine five  46.95
• One hundred sixty seven and
three tenths  167.3
• Twenty thousand four hundred
thirty-two point five  20 432.5
Application Situation 4  LES 1
4.1 Decimal Numbers
88
LES 1 | Application Situation 4
88
4.1 Decimal Numbers
CHECK POINT
1. Write the following numbers in words.
a) 642.94
six hundred forty-two point nine four
OR six hundred forty-two and ninety-four hundredths
b) 1.85
one point eight five
OR one and eighty-five hundredths
c) 10.52
ten point five two
OR ten and fifty-two hundredths
d) 185.365 one hundred eighty-five point three six five
OR one hundred eighty-five and three hundred sixty-five thousandths
e) 4 786.2
four thousand seven hundred eighty-six point two
OR four thousand seven hundred eighty-six and two tenths
2. Write the following numbers in digits.
a) Three hundred point four 300.4
b) Five point three zero nine 5.309
c) Four tenths 0.4
d) Sixty-five and four hundred thirty-two thousandths 65.432
e) Ninety-five and eight-four hundredths 95.84
f) Seven point nine zero six 7.906
g) Twelve thousand three hundred twenty-four and sixty-eight hundredths
12 324.68
4.1 Decimal Numbers
4.1 Decimal Numbers
Application Situation 4  LES 1
Application Situation 4 | LES 1
89
89
KNOWLEDGE KEY
STANDARD AND EXPANDED FORMS OF DECIMAL NUMBERS
We can show decimal numbers in standard and expanded forms.
EXAMPLE 1 Write 837.25 in expanded form.
837.25
Eight
hundreds
+
Three
Seven
+
tens
+
ones
Two
tenths
+
Five
hundredths
800
+
30
+
7
+
0.2
+
0.05
(8 × 100 )
+
(3 × 10 )
+
(7 × 1 )
+
(2 × 0.1 )
+
(5 × 0.01 )
EXAMPLE 2 Write this number in standard form.
(2 × 10)
+
(1 × 1)
+
(5 × 0.1)
+
(8 × 0.01)
+
(6 × 0.001)
20
+
1
+
0.5
+
0.08
+
0.006
Two
tens
+
One
Five
+
one
2
1
. 5
8
hundredths
+
Six
thousandths
6
Application Situation 4  LES 1
4.1 Decimal Numbers
90
+
tenths
Eight
LES 1 | Application Situation 4
90
4.1 Decimal Numbers
CHECK POINT
1. Write the following numbers in expanded form. Show your work.
a) 652.37
Six
Five
Two
Three
Seven
hundreds
+
tens
+
ones
+
tenths
+
hundredths
600
+
50
+
2
+
0.3
+
.07
(6 × 100)
+
(5 × 10)
+
(2 × 1)
+
(3 × 0.1)
+
(7 × 0.01)
b) 1.894
One
one
+
Eight
tenths
+
Nine
+
hundredths
Four
thousandths
1
+
0.8
+
.09
+
0.004
(1 × 1)
+
(8 × 0.1)
+
(9 × 0.1)
+
(4 × 0.001)
2. Write the following numbers in standard form. Show your work.
a) (2 × 1 000) +
2 000
Two
thousands
+
+
(6 × 100) +
600
Six
hundreds
+
+
(3 × 10)
+
(5 × 1)
+
(8 × 0.1)
30
+
5
+
0.8
Three
tens
Five
+
ones
+
Eight
tenths
= 2 635.8
b)
(6 × 1)
6
Six
ones
+
(4 × 0.1)
+
(3 × 0.01)
+
0.4
+
0.03
+
Four
tenths
+
Three
hundredths
+ (9 × 0.001)
+
+
0.009
Nine
thousandths
= 6.439
4.1 Decimal Numbers
4.1 Decimal Numbers
Application Situation 4  LES 1
Application Situation 4 | LES 1
91
91
COMPARING DECIMAL NUMBERS
KNOWLEDGE KEY
To compare decimal numbers:
• Compare the digits starting from the left.
• As soon as one digit is larger than the other, that decimal number is also larger
than the other.
• If all the digits in the two decimal numbers are the same, then the decimal
numbers are also equal.
EXAMPLE 1
Compare 24.987 and 24.382.
• The first two digits are
equal
• 9
equal
24.987
24.382
>
equal
.
3.
• This means that 24.987
>
24.382.
=
984.38.
9 is greater than 3
EXAMPLE 2
Compare 984.38 and 984.38.
equal
equal
equal
equal
equal
984.38
• All the digits are
equal
• This means that 984.38
.
984.38
CHECK POINT
Compare the following numbers.
a) 6.3 < 9.4
c) 10.84 < 11.763
e) 9.874 = 9.874
b) 0.17 < 0.5
d) 142.6 > 83.452
f) 3.65 > 3.45
Application Situation 4  LES 1
4.1 Decimal Numbers
92
LES 1 | Application Situation 4
92
4.1 Decimal Numbers
KNOWLEDGE KEY ORDERING DECIMAL NUMBERS
REMINDER!
To put decimal numbers in increasing order,
start with the smallest number and finish with
Increasing
order
the largest number.
Example: 0.46, 0.9, 13.842, 69.4, 187.1
To put decimal numbers in decreasing order,
Decreasing
order
start with the largest number and finish with
the smallest number.
Example: 187.1, 69.4, 13.842, 0.9, 0.46
To order decimal numbers, follow the rules for ordering whole numbers.
CHECK POINT
1. Put the following numbers in increasing order.
a) 0.97, 13.67, 5.638, 3.1
0.97
, 3.1
, 5.638
, 13.67
b) 19.47, 3.69, 10.47, 5.5
3.69
, 5.5
, 10.47
, 19.47
c) 13.856, 2.5, 9.7, 8.4
2.5
, 8.4
, 9.7
, 13.856
d) 0.7, 19.6, 0.302, 11.62
0.302
, 0.7
, 11.62
, 19.60
2. Put the following numbers in decreasing order.
a) 16.984, 27.402, 13.1, 3.6
27.402
, 16.984 , 13.1
, 3.6
b) 4.37, 15.89, 1.4, 0.39
15.89
, 4.37
, 1.4
, 0.39
c) 6.25, 11.37, 4.29, 1.1
11.37
, 6.25
, 4.29
, 1.1
d) 19.872, 0.26, 456.27, 52.1
456.27
, 52.1
, 19.872 , 0.26
4.1 Decimal Numbers
4.1 Decimal Numbers
Application Situation 4  LES 1
Application Situation 4 | LES 1
93
93
KNOWLEDGE KEY ROUNDING DECIMAL NUMBERS
REMINDER!
We can round decimal numbers to the nearest tenth, hundredth, thousandth,
or to the nearest whole.
• If the digit is greater than or equal to (≥) 5 we round up.
• If the digit is less than (<) 5 we round down.
EXAMPLES
1) Round 36.7 to the nearest whole.
36.7 
37
2) Round 9.43 to the nearest tenths.
9.43 
9.4
3) Round 8.763 to the nearest hundredth.
8.763 
8.76
CHECK POINT
1. Round the following numbers to the nearest thousandth.
a) 9.836 4
d) 11.040 3
11.040
g) 37.334 7
37.335
b) 13.402 7 13.403
e) 19.389 9
19.390
h) 58.000 2
58.000
c) 987.837 5 987.838
f) 86.989 5
86.990
i) 0.876 2
0.876
388
9.836
2. Round the following numbers to the nearest whole.
a) 16.4
16
d) 15.834
16
g) 387.963
b) 0.9
1
e) 119.04
119
h) 1 482.047 1 482
f) 45.672
46
i) 0.342
c) 99.999 100
Application Situation 4  LES 1
4.1 Decimal Numbers
94
0
LES 1 | Application Situation 4
94
4.1 Decimal Numbers
KNOWLEDGE KEY
ESTIMATING WITH DECIMAL NUMBERS
ACTIVITY
Today I am going shopping at the Co-op.
I want to know how much my groceries will cost before I get to the cash.
This is what I’m buying:
Item
Cost
• Bananas
$3.56
• Bread
$4.87
• Strawberries
$6.89
• Milk
$4.25
To estimate the cost of the groceries, round each price to the nearest dollar.
Item
Exact Cost
Rounded Cost
Bananas
$3.56
$4
Bread
$4.87
$5
Strawberries
$6.89
$7
Milk
$4.25
$4
• Approximate total:
$4
+ $5
+ $7
+ $4
= $20
The groceries will cost approximately $20 .
• Exact total:
$3.56 + $4.87 + $6.89 + $4.25 = $19.57
The groceries will cost exactly $19.57 .
4.1 Decimal Numbers
4.1 Decimal Numbers
Application Situation 4  LES 1
Application Situation 4 | LES 1
95
95
4.2 Adding
and Subtracting Decimal Number
Adding and
Subtracting
Decimal Numbers
and 4.2
Subtracting
Decimal
Numbers
KNOWLEDGE KEY ADDING DECIMAL NUMBERS
KEY ADDING DECIMAL NUMBERS
ADDINGKNOWLEDGE
DECIMAL NUMBERS
To add decimal numbers, line up the digits based on their place value.
All the on
decimal
points
must
be inonthe
same
column.
add
numbers,
line
up place
the
digits
based
their
place
value.
umbers,To
line
updecimal
the digits
based
their
value.
All be
theindecimal
points
must be in the same column.
nts must
the same
column.
EXAMPLE
Add 3.47 + 6.7 + 145.2
1
6.7 + 145.2
3.47 +EXAMPLE
6.7 + 145.2 Add 3.47 +
3. 4 7
1
3. 4 7
6. 7
1
6. 7
+ 1 4 5. 2
1
1 5 5. 3 7
+ 1 4 5. 2
1 5 5. 3 7
CHECK POINT
CHECK POINT
Add.
a) c)
+
Add.
a)
1 1
93. 7
42. 8
3.2
16. 40 2
+12 . 9 3. 76
3 62. 96 2
1 1
+
c)
e) 42.897 + 17.63
9.7
3 42. 8
1 1
3.2
16. 40 2
1 1 1
c) e) 342.897
e) 42.897 + 17.63 =
42. 8 + 17.63 =
+
3
.
7
6
4
2 . 897
12 . 9
16. 41012 1
1 1 1
+ 17 . 63
3 62. 96 2
+
3. 7462 . 8 9 7
42 . 897
60 . 527
+ 17 . 63
3+62. 91672. 6 3
60 . 527
60 . 527
b) 647.6 + 29.83 =
b) 647.6
d) 6.7++29.83
9.2 ==
1 1
6 47 . 6 6 . 7
+ +29 . 8 3
9.2
6 77 . 4
3
15 . 9
96
d) 6.7 + 9.2 =
1
d) 6.7 + 9.2
=
1 13 . 469
6 47 . 6 f)
+ 287 . 5
+ 29 . 8 3
63. 70 0 . 9 6 9
6 77 . 4 3
+
9.2
15 . 9
1 1
4.2 1
Adding
and Subtracting
Decimal
LES
| Application
Situation
4 Numbers
+
1
f)
1 13 . 469
6.7
+ 287 . 5
9.2
300 . 969
15 . 9
f)
1
1 13 . 469
+ 287 . 5
300 . 969
Application Situation 4  LES 1
4.2 Adding and Subtracting Decimal Numbers
KNOWLEDGE KEY SUBTRACTING DECIMAL NUMBERS
To subtract decimal numbers, line up the digits based on their place value.
All the decimal points must be in the same column.
EXAMPLE
3 14
Subtract 145.2 – 6.45
1
11
1 45 . 2 0
–
Add a zero.
6 . 45
1 38 . 7 5
CHECK POINT
Subtract.
a)
b)
–
0
–
c) 17.95 – 3.6 =
6 . 32
1 . 31
5 . 01
1
5
e) 395.2 – 148.3 =
1
–
1
12 . 360
4 . 205
8 . 155
4.2 Adding and Subtracting Decimal Numbers
17 . 9 5
3 . 60
14 . 3 5
d) 4.27 – 1.2 =
–
8 4
4 . 27
1 . 20
3 . 07
1
395 . 2
– 148 . 3
246 . 9
f)
3
–
Application Situation 4 | LES 1
1
45 . 9 8
36 . 5 4
9 . 44
97
ultiplying and Dividing
M
Numbers
4.3 MultiplyingDecimal
and Dividing
Decimal Numbers
4.3
KNOWLEDGE KEY MULTIPLYING DECIMAL NUMBERS BY FACTORS OF 10
There is a special rule for multiplying decimal numbers by factors of 10.
For every factor of 10 we move the decimal point one place to the right.
• × 10
 1 place to the right
• × 100
 2 places to the right
• × 1 000  3 places to the right
And so on.
EXAMPLES
1) Multiply 0.65 × 10
0.65 × 10 = 0.65 =
6.5
2) Multiply 15.278 × 100
15.278 × 100 = 15.278 = 1 527.8
3) Multiply 39.342 × 1 000
39.342 × 1 000 = 39.342 = 39 342.0
LESNumbers
1 | Application Situation 4
984.3 Multiplying and Dividing Decimal
98
4.3 Multiplying
Dividing
Applicationand
Situation
4  Decimal
LES 1 Numbers
KNOWLEDGE KEY MULTIPLYING DECIMAL NUMBERS
To multiply decimal numbers:
• Ignore the decimal points.
Line up the numbers based on the place value of their digits.
• Follow the rules for multiplying whole numbers.
• Count the total decimal places after the decimal point in the factors.
This is the number of decimal places there will be in the answer.
EXAMPLE
2756
×
32
1 1 1
2756
×
2 1 1
1
32
Multiply 27.56 × 3.2
Step 1
Ignore the decimal points.
• Line up the numbers based on the place value of their digits.
Step 2
Multiply.
• Follow the rules for multiplying whole numbers.
5512
+82680
88192
2756
×
32
88.1 9 2
Step 3
Count the total number of decimal places after the
decimal point in the factors.
• 27.5 6 × 3.2
• There are a total of 3 decimal places.
• This is the number of decimal places the product will have.
• Write the decimal point in your answer.
4.3 Multiplying and Dividing Decimal Numbers
88.192
Application Situation 4 | LES 1
99
CHECK POINT
Multiply.
a) 36.94 × 10
e) 9.83 × 2.5
36.94 = 369.4
4 1
983
1
×
+
b) 369.5 × 4.2
1
42
1
7390
+ 147800
1551.9 0
1
c) 15.6 × 13.9
5 5
156
×
+
f) 2.7 × 8.4
2
1
5
×
84
108
2160
22.6 8
+
g) 146.059 × 1 000
h) 9.83 × 2.5
57
3 99
2 8 50
32.49
1
1
12
270
1350
16.2 0
+
k) 16.84 × 10.5
3 4 2
1684
105
1 8420
00000
+ 168400
176.8 2 0
l) 15.84 × 3.9
4 1
57
1
×
×
1404
1 4680
15600
216.8 4
×
135
146.059 = 146 059.0
139
3
1
27
4
100
j) 13.5 × 1.2
1 1
d) 5.7 × 5.7
+
25
4915
19660
24.5 7 5
3695
×
19.357 = 1 935.7
1
1 1 1
2 3 2
i) 19.357 × 100
5 7 3
983
1
×
+
1
25
4915
19660
24.575
1
LES 1 | Application Situation 4
1584
×
+
1 2 1
1
39
14256
47520
61.776
4.3 Multiplying and Dividing Decimal Numbers
KNOWLEDGE KEY DIVIDING DECIMAL NUMBERS – REMAINDERS
We can show division in two ways:
with a remainder or as a decimal number quotient.
Remember when we looked at remainders?
EXAMPLE
Divide 6 693 ÷ 25
267
25 6693
– 50X
169
– 150X
8
• 6 693 ÷ 25 = 267 with 18R
1
193
–175
1 8R
We can turn the remainder into a decimal number quotient.
2 6 7 .7
2 5 6 6 9 3 .0
– 50X
169
– 150X
193
–175X
180
–175
5
Step 1
• We don’t have any more whole numbers left so we have to
borrow from the parts of a whole.
• Put a decimal point in the dividend and quotient.
• Add a zero to the dividend.
4.3 Multiplying and Dividing Decimal Numbers
Application Situation 4 | LES 1
101
2 6 7 .72
2 5 6 6 9 3 .00
– 50X
169
– 150X
193
–175X
180
–175X
50
–50
0
Step 2
• Add another zero to the dividend.
• 6 693 ÷ 25 =
267.72
KNOWLEDGE KEY DIVIDING A DECIMAL NUMBER BY A WHOLE NUMBER
EXAMPLE
5
3 6 .95
Divide 36.95 ÷ 5
• Follow the rules for whole number division.
• Line up the decimal points in the quotient and the dividend.
7 .3 9
5
102
3 6 .95
–35X
19
–15X
45
–45
0
• 36.95 ÷ 5 = 7.39
LES 1 | Application Situation 4
4.3 Multiplying and Dividing Decimal Numbers
KNOWLEDGE KEY DIVIDING DECIMAL NUMBERS BY FACTORS OF 10
There is a special rule for dividing decimal numbers by factors of 10.
For every factor of 10 we move the decimal point one place to the left.
• ÷ 10
 1 place to the left
• ÷ 100
 2 places to the left
• ÷ 1 000  3 places to the left
And so on.
EXAMPLES
1) Divide 346.984 ÷ 10
346.984 ÷ 10 = 346.984 =
34.698 4
887.52 ÷ 100 = 887.52 =
8.875 2
2) Divide 887.52 ÷ 100
3) Divide 15 632.9 ÷ 1 000
15 632.9 ÷ 1 000 = 15 632.9 =
4.3 Multiplying and Dividing Decimal Numbers
15.632 9
Application Situation 4 | LES 1
103
KNOWLEDGE KEY DIVIDING DECIMAL NUMBERS
To divide decimal numbers:
• Write out the division.
• Move the decimal point in the divisor to the right until it is a whole number.
• Move the decimal point in the dividend the same number of places you
moved it in the divisor.
• Follow the rules for whole number division.
EXAMPLE
Divide 10.5 ÷ 0.6
0. 6
Step 1
1 0 .5
Move the decimal point in the divisor to the right.
• Move it one place at a time until the divisor is a whole
number.
6
1 0 .5
Step 2
Move the decimal point in the dividend to the right.
• Move it the same number of places you moved the
decimal point in the divisor.
1 7 .5
6
104
1 0 5 .0
–6X
45
–42X
30
–30
0
Step 3
Follow the rules for whole number division.
• 10.5 ÷ 0.6 = 17.5
LES 1 | Application Situation 4
4.3 Multiplying and Dividing Decimal Numbers
CHECK POINT
Divide.
1 4 0 .2
2 6 .05
a) 3 5 4 9 0 7 .0
– 35X
140
– 140X
07
–0X
70
–70
0
d) 194.369 ÷ 10
b) 0 .4
e) 2 .5
4
0 .32
194.369 = 19.436 9
6 9 .5
g) 2 0 5 2 1 .00
–40X
121
–120X
10
–0X
100
–100
0
h) 0 .8
2 5 .6
0 .8
2 7 .8
32
3 .2
–0
32
–32
0
2 5 6 9 5 .0
–50X
195
–175X
200
–200
0
8 256
–24X
16
–16
0
c) 2 874.3 ÷ 10
2 874.3 = 287.43
4.3 Multiplying and Dividing Decimal Numbers
8
4 4 2 .5
1
f) 2 2 9 7 3 5 .0
– 88X
8
1
93
–88X
55
–44X
110
–110
0
i) 48.937 ÷ 100
48.937 = 0.489 37
Application Situation 4 | LES 1
105
Application Question
A. Paying the Bill
RATING KEY
C2 USES MATHEMATICAL
EVALUATION CRITERIA
REASONING
OBSERVED LEVEL
3
3
2
4–5
5
4
3
2
1
You go shopping
at the Co-op.
Here is your bill:
I
STORE
Groceries
Lettuce......
... $2.99
Apples.......
... $6.99
Orange juice.
... $6.75
Cereal.......
... $9.10
Total
$
What is the total amount of your bill?
ANALYSE THE SITUATION
What I Already Know
What I Need to Find Out
Think about
•
To add decimal numbers, line up
the
points in
the same
•
Finding the total means
WORD BANK: adding, column, decimal.
106
LES 1 | Application Situation 4
.
.
Show Your Work
= 1 cm
Application Situation 4 | LES 1
107
Application Question
B. Too Expensive
RATING KEY
You have $20.00 to buy
groceries at the Co-op.
C2 USES MATHEMATICAL
EVALUATION CRITERIA
REASONING
OBSERVED LEVEL
3
5
4
3
2
STORE
1
Groceries
3
2
4–5
Here is your bill:
You want to keep as many
items as you can.
Stay as close as possible
to $20.00.
Milk........
... $3.50
Butter.......
... $5.99
Flour........
... $7.75
Pop..........
... $2.18
Chips.......
... $3.82
Cookies......
... $5.64
Total
$28.88
Which items should you remove?
What will your new total be?
I
ANALYSE THE SITUATION
What I Already Know
What I Need to Find Out
Think about
•
To subtract decimal numbers,
line up the
in the
WORD BANK: same, decimal.
108
LES 1 | Application Situation 4
points
column.
Show Your Work
= 1 cm
Application Situation 4 | LES 1
109