Chapter 6
n
[kaesSGD l l
Multiplying by Skip Counting
Use skip counting to multiply.
1. Ken skip counted on a number line t o multiply.
+4
+4
8
0
f1
+4
You can skip count on a
number line t o solve
multiplication problems.
12
+5
+5
+5
+5
a) What 2 numbers did Ken multiply?
Write an equation.
•> x 7 =
b) Extend Ken's skip counting t o calculate 4 x 4 .
0
5
10 15 20
This number line shows t h a t
4 x 5 = 20.
x
2. Fill in the missing number in each equation.
Use the number line t o help you.
H
1
1
1
1
1
0
1
h
H
10
1
1
1
1
1
-I
h
1
1 (_
e) 5 < 7
b) 5 x 1
f) 8 x
d)
1.
X
2 - 4
7x2^
1
')
1
1
1
1
1
1
1
h
40
xi
'.
g) 4 x 6
h)
1
30
a) 3 x 3
c)
H
20
- 40
21
x 3 = 27
3. Calculate.
a)
3 X 7
d) 5 x 6 =
JO
b)
2 X 8
e) 9 x 4 -
56
c)
4x8
f) 2 x 9
Copyright © 2008 by Nelson Education Ltd.
Answers Chapter 6: Multiplication and Division Facts
45
Chapter 6
r
_
Building on Multiplication Facts
Skip count from facts y o u k n o w to calculate
other multiplication facts.
1. 5 x 5 = 25. Use this fact t o calculates x 5.
8 x 5 = 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5
5 x 5 = 25
so 8 x 5 equals 5 x 5 plus 3 more 5s
8X5=
25 + 5 + 5 + 5 = HO
You can use facts you k n o w t o
help you calculate other
multiplication facts. For
example:
I w a n t t o k n o w t h e answer t o
7X4=
.
I k n o w t h a t 5 X 4 = 20.
2. Use one fact t o help you complete the other fact. 7 x 4 = 4 + 4 + 4 + 4 + 4 + 4 + 4
Show your w o r k .
5 x 4 = 20
t
a) 2 X 7 = 14, so 3 X 7 =
H + 7 = 21
b) 5 X 5 = 25, so 6 x 5 =
25 + 5 = 30
c) 8 X 3 = 24, so 9 X 3 =
2^ + 3 = 27
d) 4 X 8 = 32, so 5 X 8 =
32 + S = HO
e) 8 X 5 = 40, so 9 x 5 =
HO + 5 = H5
f)
36 + 6 = H2
6 X 6 = 36, so 7 X 6 =
g) 7 X 4 = 28, so 9 X 4 =
28 + H + H = 36
h) 7 X 7 = 49, so 9 X 7 =
H3 + 7 + 7 = 63
So 7 x 4 equals 5 x 4 plus 2
more 4s.
7 X 4 = 20+ 4 + 4
7 X 4 = 28
3. Write a multiplication fact t h a t will help you calculate 5 x 7 .
Sample answer: 5 X 5 = 25
46
Nelson Math Focus 4 Workbook Answers
Copyright © 2008 by Nelson Education Ltd.
Chapter 6
*[k3e02OO§>
Doubling Multiplication Facts
Double facts you k n o w to calculate other
multiplication facts.
1. Use doubling t o complete the 8 x row of this
table.
You can double a number by
X
0
1
2
3
4
5
6
7
8
9
4
0
4
8
12
16
20
24
28
32
36
8
0
8
16
2H
32
HO
HS
.56
6<f
72
2. Use doubling t o complete the multiplication
facts.
adding the number t o itself.
For example, double 4 is
4 + 4-8.
You can double facts you k n o w
t o help you calculate other
multiplication facts. For
example:
I want to know 5 x 8 =
I k n o w t h a t 5 x 4 = 20.
a) 2 x 6 = 12, so 4 x 6 =
\ 2 + \ 2 = 2H
b) 3 x 5 = 15, so 6 x 5 =
15 + 15 = 30
c) 6 x 4 = 24, so 6 X 8 =
2H + 2H = HS
d) 7 x 3 = 21, so 7 X 6 =
21 + 21 = H2
e) 8 x 4 = 32, so 8 x 8 =
32 + 32 =
f)
9 X 2 = 18, so 9 X 4 =
18 + 18 = 36
g) 4 x 3 = 12, so 8 x 3 =
12 + 12 = 2H
h) 2 X 7 = 14, so 4 X 7 =
IH + IH = 28
I can double the product t o
calculate 5 x 8 .
5 x 8 = 20 + 20
5 x 8 = 40
3. Write a multiplication fact that will help you calculate 8 x 9 by doubling.
Sample answer: H X 9 = 36
Copyright © 2008 by Nelson Education Ltd.
Answers Chapter 6: Multiplication and Division Facts
47
Halving and Doubling
Multiplication Facts
Chapter 6
(ksesmi^
Halve and double facts you k n o w to calculate
other multiplication facts.
Use counters to help you multiply.
1. Calculate.
a) 3 X 7 =
21
c) 2 X 5 =
10
b) 4 X 4 =
16
d) 6 X 6 =
36
2. Calculate the first product. Use the answer t o
calculate the second product.
a) 2 X 9 =
. so 4 X 9 =
18
You can start f r o m facts you
k n o w t o help you calculate
other multiplication facts. For
example, I w a n t t o k n o w
9 X 7 = .J.
I can use an array of counters
t o show 9 x 7 .
18 + 13 = 36
4x7-
b) 3 x 3 = _
c) 4 x 6 =
9
. so 6 X 3 =
9 + 9 = 18
2H
. so 8 X 6 =
2H + 2H = H8
4X7'
ooooooo
ooooooo
ooooooo
ooooooo
ooooooo
ooooooo
ooooooo
ooooooo
•
d) 2 x 5 =
^8X7
• • • • • • > 1
X7
. so 5 X 5 = 10 + 10 + 5 = 25
10
My array shows t h a t 9 x 7
e) 5 X 4 =
20
. so 5 X 9 = 20 + 20 + 5 = H5
f) 3 x 6 =
18
. so 7 X 6 = 18 + 18 + 6 = H2
3. a) How many bottles are in 7 packages of
4 bottles?
7
x H = 28
bottles
b) How many bottles are in 7 packages of
8 bottles?
28 + 28 = 56
bottles
equals 8 x 7 plus 1 x 7.
I k n o w 4 x 7 = 28.
I can double 4 x 7 = 28 t o
figure o u t 8 x 7 .
9 x 7 = 8 x 7 + 1 x 7
9 x 7 = 4 x 7 + 4 x 7 + 1 x 7
9 X 7 = 28 + 28 + 7
9 X 7 = 63
c) How many bottles are in 8 packages of
8 bottles? Show how you can use your
answer t o (b) t o figure it out.
8 X 8 is 8 more than 7 X 8. 56 + 8 = 6f bottles.
48
Nelson Math Focus 4 Workbook Answers
Copyright © 2008 by Nelson Education Ltd.
Halving and Doubling
Multiplication Facts
Chapter 6
QfiSHDBqJi
Halve and double facts you k n o w to calculate
other multiplication facts.
Use counters to help you multiply.
1. Calculate.
a) 3 x 7 =
21
c)
b) 4 x 4 =
16
d) 6 X 6 =
2 X 5 =
10
36
2. Calculate the first product. Use the answer t o
calculate the second product.
You can start f r o m facts you
k n o w t o help you calculate
other multiplication facts. For
example, I w a n t t o k n o w
9X7= .3.
I can use an array of counters
t o show 9 x 7 .
("OOOOOOO
a) 2 X 9 =
18
. so4x9 =
18 + 18 = 36
4X7-
. so 6 X 3 =
b) 3 x 3 =
9
c) 4 x 6 =
2H
. SO
d) 2 x 5 =
10
. so 5 X 5 = 10 + 10 + 5 = 25
8 X 6 =
9 + 9 = 18
2^ + 2^ = ^/8
e) 5 X 4 =
20
. so 5 X 9 = 20 + 20 + 5 = f 5
f) 3 X 6 =
18
. so 7 X 6 = 18 + 18 + 6 = H2
3. a) How many bottles are in 7 packages of
4 bottles?
7 x h = 2S
bottles
b) How many bottles are in 7 packages of
8 bottles?
28 + 28 = 56
bottles
4X7-
ooooooo
ooooooo
ooooooo
o o o o o o o >8X7
ooooooo
ooooooo
ooooooo
My array shows t h a t 9 x 7
equals 8 x 7 plus 1 x 7.
I k n o w 4 x 7 = 28.
I can double 4 x 7 = 28 t o
figure o u t 8 x 7 .
9 x 7 = 8 x 7 + 1 x 7
9x7 = 4x7 + 4 x 7 + 1
x7
9 x 7 = 28 + 28 + 7
9 x 7 = 63
c) How many bottles are in 8 packages of
8 bottles? Show how you can use your
answer t o (b) t o figure it out.
8 X 8 is 8 more than 7 X 8, 56 + 8 = 6f bottles.
48
Nelson Math Focus 4 Workbook Answers
Copyright © 2008 by Nelson Education Ltd.
Chapter 6
—
^fk^ee^IDh)
Using 10s to Multiply
xx,;. X
Multiply by 10 to calculate other facts.
1. Calculate the first product. Use the answer t o
calculate the second product.
a) 3 x 1 0 =
m
, so 3 x 5 =
1.5
b) 5 x 10 =
so
, so 5 x 5 =
•) r
.j
c) 1 0 X 4 =
HO
, so 5 x 4 =
20
You can multiply by 10 t o
calculate other multiplication
facts. For example:
I want to know 5 x 7 =
I k n o w t h a t 10 x 7 = 70.
I can halve t h e answer t o
d) 6 x 10 =
60
, so 6 x 5 =
40
e) 9 X 1 0 =
70
, so 9 x 5 =
HS
f)
SO
, so 5 x 8 = ...HO.
10X8 =
calculate 5 x 7 .
Half of 70 is 35, so 5 x 7 = 35.
Calculate the first product. Use the answer t o
calculate the second product.
a) 3 X 1 0 =
20
, so 3 x 9 =
X) -
b) 9 x 10 =
90
, so 9 x 9 =
90 - 9 =
c) 1 0 x 4 =
50
, so 9 x 4 =
HO - H - 36
d) 6 x 1 0 =
60
, so 6 x 9 =
60 - 6 -
e) 7 X 1 0 =
70
, so 7 x 8 = 70 - 7 - 7 = 56
f)
20
, so 8 x 2 = 20 - 2 - 2 = 16
10X2 =
S = 21
S).
SH
QQGQQ
®®m®m
ooooo
3. There are 9 rows of 5 cookies on a cookie sheet. Michael
knows that 9 x 10 = 90. How can he use this fact t o
calculate the number of cookies?
9X5 =
9 x
copyright ©
1 0 = 90
.5 to half o f 10. so 9 X 5 is half o f 9 X 10.
2008 by Nelson Education Ltd.
0OOO0
I ©0 ©© Q
QOOQO
2 2 5 5 S
9 x 5 = 55 c o o k i e s
Answers Chapter 6: Multiplication and Division Facts
49
Chapter 6
j309SGQ(o)
Multiplying by 8 and 9
Multiply by 10 to multiply by 8 and 9.
Use counters to help you multiply.
1. Calculate the first product. Use the answer t o
help you calculate the second product.
a) 6 X 10
£0
, so 6 x 9
6 0 - 6 = 55
10
, so 7 x 9
7 0 - 7 = 63
i.
b) 7 X 10
c) 4 X 10
2f0
, so 4 x 9
5 0 - 5 = 36
d) 3 X 10
_2D
, so 3 X 9
30 - 3 = 27
e) 5 X 10
50
, so 5 X 9
5 0 - 5 = 55
2 X 10
20
, so 2 X 9
2 0 - 2 = 18
f)
9 ) 8 X 10
M
, so 8 X 9
8 0 - 8 = 72
h) 9 X 10
30
, so 9 X 9
9 0 - 9 = 81
2. Calculate the first product. Use the answer t o
help you calculate the second product.
a)
50
8X10
30
b) 5 x 10
50
,
c)
7X10
, so 8 x 8 =
80 - 8 - 8 = 65
so 5 X 8
5 0 - 5 - 5 = 50
10
, so 7 X 8
7 0 - 7 - 7 = 56
d) 9 x 10
JO
, so 9 X 8
9 0 - 9 - 9 = 72
e)
2x10
_20
, so 2 X 8
2 0 - 2 - 2 = 16
f)
6x10
j60
, so 6 X 8
6 0 - 6 - 6 = 58
Nelson Math Focus 4 Workbook Answers
You can multiply by 10 t o help
you multiply by 8 and 9. For
example:
I w a n t t o k n o w t h e answer t o
9X7.
I k n o w t h a t 10 x 7 = 70.
This is like 10 rows o f 7.
OOOOOOO
ooooooo
ooooooo
ooooooo
ooooooo
ooooooo
ooooooo
ooooooo
ooooooo
I will take away 1 row o f 7 t o
calculate 9 x 7 .
9 x 7 = 70 - 7
9 X 7 = 63
Copyright © 2008 by Nelson Education Ltd.
Chapter 6
H^asjm//
Sharing and Grouping
Use 2 meanings of division to solve problems.
1. Calculate.
^ ^ ^ w ^ ^ ^ ^ n ^ ^ c ^ d i v i s i o n:
a) 4)76
e) 5B5
b) 5)20
f) 9)27
c)
g) 6J36
2jl4
d) 8)32
Sharing: w h e n you have
something t o share in equal
groups; for example, you have
20 coins t o share among 4
friends.
h) 12)24
2. Calculate.
a)
30-3
b) 15 + 5
e) 24 + 8 = _
f)
40 + 2 = _
10 + 2
g) 25 + 5 = _
d) 12 + 4
h) 36 + 4 - _
c)
Grouping: w h e n you divide
something into groups of
equal size; f o r example, you
have 20 coins t o place in
groups of 4.
You can solve both types of
problems in t h e same way.
5
20 h- 4 --= 5 or 4)20
3. Ken placed 42 beads in 6 equal groups.
How many beads are in each group?
Use a drawing or a number line t o help
you solve the problem.
H'. + 6 = / [here a r e 7 bead:, in each qrotif i
1
4. Samia gave the same number of beads t o
each of 7 friends. She started w i t h 56 beads.
How many beads did she give t o each
friend?
55 + 7 = 6 ohecjave 6 beach to each I fiend.
Copyright © 2008 by Nelson Education Ltd.
CiCJ,-
^ ' iX
' ' -Co>
Answers Chapter 6: Multiplication and Division Facts
51
Division and Multiplication
by using related multiplication facts.
1. Use each multiplication fact t o calculate t h e
quotient.
a ) 4 x 5 = 20, so 20 + 5 =
The dividend is t h e starting
a m o u n t in a division
operation.
5
The divisor is t h e number you
divide by in division.
b) 3 x 6 = 18, so 18 + 3 =
c) 10 X 4 = 40, so 40 + 10
The quotient is the result you
get w h e n you divide.
d) 2 x 16 = 32, so 32 + 16
You can use multiplication
facts t o help you solve division
facts. For example,
2. Calculate.
a ) 15 + _
)
5
= 3
c)
+6 = 4
25
d) 49 + 7 =
b) 6 + 1 =
7
35 + 7 =
5 X 7 = 35, so 35 + 7 = 5.
• * \
3. Calculate.
a) 5)50
J
dividend
b) 9)63
c) 8)48
divisor
quotient
d) 8)72
4. A n airplane has 30 seats placed in rows of 5.
How many rows are there?
5 X
= 30
30 + 5 = 6
There are 6 rows.
5. Francois organizes 28 students into 7 groups.
How many students are in each group?
7x
=28
28 + 7 = 5
There are 5 students in each grocip.
6. Michael has $36. He gives $6 t o each friend.
How many friends get $6?
6x
52
= 36
36 + 6 = 6
Nelson Math Focus 4 Workbook Answers
6 friends get $6.
Copyright © 2008 by Nelson Education Ltd.
ml
•
mm mm fl ' fl •
flfl
Patterns in a Multiplication
Table
chapters
DfiagsxB'^)
r
^
Use number patterns in a table to multiply and
divide.
v
J
1 . Fill in the blanks in the multiplication table.
Look for patterns t o help you.
X
0
1
2
3
4
5
6
7
8
9
0
0
0
0
0
0
;o
0
0
0
0
j
2
3
4
r
6
7
8
9
6
8
10
12
14
16
18
1
:
0
2
0
2
3
0
3
6
9
12
'15
U
21
24
.27
4
0
4
8
12
16
20
24
28
32
36
5
0
5
10
15
20
25
'* 30
35
40
45
6
0
6
12
18
2H
30
36
42
48
54
7
0 ,
7
14
21
28
35
42
49
56
63
8
0
8
16
24
32
HQ
48
56
64
72
9
0
9
U
27
36
45
SH
63
72
81
2. Describe one pattern you noticed.
Each vertical row was the same as the horizontal row for that number
Copyright © 2008 by Nelson Education Ltd.
Answers Chapter 6: Multiplication and Division Facts
53
Solving Problems by Working
OSBaDflfi) Backwards
chapter 6
Work backwards to solve problems.
Work backwards to solve these problems.
Use the diagrams to help you.
1. Juliette cut a ribbon into 6 pieces. Each piece was
3 cm long. How long was the ribbon?
3 X 6 = 18, so the ribbon was 18 cm long.
How long was
the ribbon?
Divide by 6.
Each piece is
3 cm long.
How long was
the ribbon?
Multiply by 6.
Each piece is
3 cm long.
W h e n you w o r k backwards t o
solve a problem, remember t o
reverse each step:
•
•
•
•
subtraction
addition
addition
subtraction
multiplication -> division
division
multiplication
2. Cory cut a string into 5 pieces. Then he cut 1 cm f r o m each piece so
each piece was 4 cm long. How long was the string he started with?
How long was
the string?
How long was
the string?
W
Divide by 5.
Subtract
1 cm.
Each piece
is 4 cm long.
Multiply by 5.
Add 1 cm.
Each piece
is 4 cm long.
H + 1 = 5. and 5 X 5 = 25.
The string was 25 cm long.
3. Alec sorted stickers into 8 equal groups. Then he sorted each group
into 3 piles of 3 stickers. How many stickers did Alec start with?
Draw your o w n diagrams t o solve the problem.
How many
stickers?
Divide by 8.
Divide by 3.
Each pile has
3 stickers.
How many
stickers?
•Multiply by 8.
Multiply by 3.
Each pile has
3 stickers.
3 x 3 = 9 . a n d 9 x 8 = 72.
Alec started with 72 stickers.
54
Nelson Math Focus 4 Workbook Answers
Copyright O 2008 by Nelson Education Ltd.
^Chapter 6
Test Yourself
Circle the correct answer.
+4
1. Diane skip counted on a number line
t o multiply. What 2 numbers did she
multiply?
A . 4 and 4
B. 4 and 6
0
+4
4
+4
8
( £ ) 4 and 7
w
+4
12
+4
16
+4
20
+4
24
28
D. 4 and 8
2. Which multiplication fact helps you t o calculate 6 x 9 ?
( £ ) 6 x 8 = 48
B. 9 X 9 = 81
C 6 x 5 = 30
D. 6 x 2 = 1 2
3. If you double 3 x 6 = 18, w h a t new multiplication fact do you get?
A . 6 X 3 = 18
B. 9 x 6 = 54
C 3x3 = 9
@ 6 x 6 = 36
4. There are 60 cookies in 5 packages of 12 cookies.
How many cookies are in 5 packages of 6 cookies?
A . 15
B.)30
C 45
D. 60
5. Which 10x fact helps you t o calculate 9 x 5 ?
A . 10 X 8 = 80
B. 10 X 4 = 40
(£) 10 X 5 = 50
D. 10 x 10 = 100
6. What is the missing number in this division sentence?
32 + 8 =
A. 5
B. 3
C. 7
DJ4
7. Annie has $40. She wants t o buy T-shirts that cost $10 each.
How many T-shirts can she buy?
(K) 4
B. 3
C 5
D. 2
8. Cory cut a piece of string into 3 equal parts.
He cut each piece of string into 2 equal parts
so each piece was 2 cm long.
How long was Cory's string t o start with?
A . 6 cm
Copyright © 2008 by Nelson Education Ltd.
BJ12 cm
C. 15 cm
D. 9 cm
Answers Chapter 6: Multiplication and Division Facts
55