Download + (5 X 2)

Properties of Multiplication
6.C.1.a Multiply whole numbers
3.A.1.a.Use technology tools, including software
and hardware, from a range of teacher-selected
options to learn a new content or reinforce skills
Definitions
• Zero Property – The product of
any factor and 0 equals 0.
• 65 x 0 = 0
•8x0=0
Zero Property
•5x0=0
•ax0=0
•6x0=0
•yx0=0
• 18 x 0 = 0
4x0=0
bx0=0
3x0=0
zx0=0
19 x 0 = 0
Solve these equations using the zero
property
•
•
•
•
•
•
7xn=0
2xm=0
3xz=0
6xg=0
4xs=0
8xc=0
n=0
m=0
z=0
g=0
s=0
c=0
Definitions
• Commutative Property – The
order of the factors does not
change the product.
•6x8=8x6
• 14 x 3 = 3 x 14
Commutative Property
•
•
•
•
•
5 x 4 = 20
axb=c
6 x 3 = 18
axy=z
3 x 4 x 1 = 12
4 x 5 = 20
bxa=c
3 x 6 = 18
yxa=z
1 x 3 x 4 = 12
Solve these equations using the
commutative property
•n+7=7+4
•m+2=2+5
•z+3=3+9
• g + 6 = 6 + 11
• s + 4 = 4 + 20
• c + 8 = 8 + 32
n=4
m=5
z=9
g = 11
s = 20
c = 32
Definitions
• Associative Property – The way
factors are grouped does not
change a product.
• (11 x 3) x 4 = 11 x (3 x 4)
• 5 x (5 x 10) = (5 x 5) x 10
Associative Property
• 5 x (7 x 4) = (5 x 7) x 4
• a x (b x c) = (a x b) x c
• (6 x 3) x 2 = 6 x (3 x 2)
• 12 x (8 x 1) = (12 x 8) x 1
• (9 x 10) x 2 = 9 x (10 x 2)
Rewrite these equations using the
associative property
•
•
•
•
•
•
2 x (3 x 3) =
4 x (9 x 8) =
3 x (7 x 4) =
5 x (6 x 3) =
10 x (5 x 7) =
11 x (2 x 2) =
(2 x 3) x 3
(4 x 9) x 8
(3 x 7) x 4
(5 x 6) x 3
(10 x 5) x 7
(11 x 2) x 2
Definitions
• Identity Property – The product
of any factor and 1 equals the
factor.
• 56 x 1 = 56
• 38 x 1 = 38
Identity Property
•
•
•
•
•
5x1=5
ax1=a
6x1=6
yx1=y
18 x 1 = 18
4x1=4
bx1=b
3x1=3
zx1=z
19 x 1 = 19
Solve these equations using the
identity property
•
•
•
•
•
•
nx1=8
bx1=7
3x1=m
vx1=5
4x1=w
rx1=2
n=8
b=7
m=3
v=5
w=4
r=2
Definitions
• Distributive Property of Multiplication
over Addition – Multiplying a sum by
a number is the same as multiplying
each addend by the number and then
adding the products.
• 6 x (12 + 9) = (6 x 12) + (6 x 9)
• 4 x (15 + 6) = (4 x 15) + (4 x 6)
Distributive Property of
Multiplication over Addition
•
•
•
•
•
5 x (7 + 4) = (5 x 7) + (5 x 4)
a x (b + c) = (a x b) + (a x c)
6 x (3 + 2) = (6 x 3) + (6 x 2)
12 x (8 + 1) = (12 x 8) + (12 x 1)
9 x (10 + 2) = (9 x 10) + (9 x 2)
Solve these equations using the
distributive property of multiplication
over addition
•
•
•
•
•
•
10 x (5 + 2) =
3 x (3 + 4) =
8 x (9 + 2) =
12 x (4 + 8) =
15 x (10 + 11) =
13 x (6 + 3) =
(10 x 5) + (10 x 2) = 70
(3 x 3) + (3 x 4)
= 21
(8 x 9) + (8 x 2)
= 88
(12 x 4) + (12 x 8) = 144
(15 x 10) + (15 x 11) = 315
(13 x 6) + (13 x 3) = 117
Definitions
• Distributive Property of Multiplication over
Subtraction – To multiply a difference of
two numbers by a third number, you can
multiply the first two numbers by the third,
and then find the difference of the products.
• 7 x (23 – 9) = (7 x 23) – (7 x 9)
• 5 x (9 – 3) = (5 x 9) – (5 x 3)
Distributive Property of
Multiplication over Subtraction
• 5 x (7 - 4) = (5 x 7) - (5 x 4)
• a x (b - c) = (a x b) - (a x c)
• 6 x (3 - 2) = (6 x 3) - (6 x 2)
• 12 x (8 - 1) = (12 x 8) - (12 x 1)
• 9 x (10 - 2) = (9 x 10) - (9 x 2)
Solve these equations using the
distributive property of multiplication
over subtraction
•
•
•
•
•
•
(10 x 5) - (10 x 2)
10 x (5 - 2) =
3 x (4 - 3) =
(3 x 4) - (3 x 3)
(8 x 9) - (8 x 2)
8 x (9 - 2) =
(12 x 8) - (12 x 4)
12 x (8 - 4) =
15 x (11 - 10) = (15 x 11) - (15 x 10)
(13 x 6) - (13 x 3)
13 x (6 - 3) =
= 30
=3
= 56
= 48
= 15
= 39
Properties with Beans
• Now that you have learned
about the different properties
we are going to do a handson activity.
Name the property…
3 X 11 = 11 X 3
a.
b.
c.
d.
Identity
Commutative
Zero
associative
Name the property…
13 X 1 = 13
a.
b.
c.
d.
Identity
Commutative
Zero
associative
Name the property…
20 X 0
a.
b.
c.
d.
Identity
Commutative
Zero
associative
Name the property…
(12 X 4) X 3 = 12 X (4 X 3)
a.
b.
c.
d.
Identity
Commutative
Zero
associative
Name the property…
3 X (9 – 1) = (3 X 9) – (3 X 1)
a. Identity
b. Commutative
c.
d.
Distributive of
multiplication over
subtraction
Distributive of
multiplication over
addition
Name the property…
5 X (6 + 2) = (5 X 6) + (5 X 2)
a. Identity
b. Commutative
c.
d.
Distributive of
multiplication over
subtraction
Distributive of
multiplication over
addition
Now that you can identify the
properties…
Let’s use those properties to solve
some problems.
8 x 56
6
7
8
9
10
11
21
22
23
24
25
26
27
28
29
30
31
12
32
13
14
15
16
17
18
19
6
5
25%
45
4
25%
0
3
44
2
0
1
25%
50
25%
8
400
448
500
456
40
1.
2.
3.
4.
10
20
4 x (30 + 15)
6
7
8
9
10
11
21
22
23
24
25
26
27
28
29
30
31
12
32
13
14
15
16
17
18
19
0
5
25%
18
4
25%
0
3
14
2
0
1
25%
16
25%
0
120
140
160
180
12
1.
2.
3.
4.
10
20
(2000 x 0) x 16
5
6
7
8
9
10
11
21
22
23
24
25
26
27
28
29
30
31
12
32
13
14
00
4
32
3
00
2
32
1
15
25%
16
17
18
25%
16
25%
0
25%
00
32000
320000
0
16
0
1.
2.
3.
4.
10
19
20
(210 x 1) x 1
6
7
8
9
10
11
21
22
23
24
25
26
27
28
29
30
31
12
32
13
14
15
16
17
18
19
0
5
25%
22
4
25%
1
3
21
2
2
1
25%
21
25%
0
212
210
211
220
21
1.
2.
3.
4.
10
20
8 x (60 – 4)
6
7
8
9
10
11
21
22
23
24
25
26
27
28
29
30
31
12
32
13
14
15
16
17
18
19
8
5
25%
44
4
25%
6
3
42
2
6
1
25%
40
25%
0
416
420
406
448
41
1.
2.
3.
4.
10
20
4 x (80 – 5)
6
7
8
9
10
11
21
22
23
24
25
26
27
28
29
30
31
12
32
13
14
15
16
17
18
19
0
5
25%
22
4
25%
0
3
28
2
0
1
25%
32
25%
5
300
285
320
220
30
1.
2.
3.
4.
10
20