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Students
use variables in simple expressions, compute the
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UNDERLYING SKILLS AND CONCEPTS:
value of the expression for specific values of the variable, and
plot and interpret the results.
properties of additions;
properties of multiplication;
commutative property; associative
property
Review Properties of Addition
The Commutative Property of Addition
Changing the order of addends
does not change the sum.
So
x!y " y!x
75 ! 25 " 100 and 25 ! 75 " 100.
75 ! 25 " 25 ! 75
The Associative Property of Addition
Changing the grouping of addends
does not change the sum.
So,
2 ! (7 ! 9) "
(2 ! 7) ! 9 "
2 ! 16
" 18
9
! 9 " 18.
2 ! (7 ! 9)
" (2 ! 7) ! 9.
=
=
Al G. Braic
a ! (b ! c) " (a ! b) ! c
The Zero Property of Addition
The sum of any number and zero is the number.
n!0"n
Additive Inverse of Integers
The sum of a number and its opposite is 0.
#5 ! 5 " 0
7 ! (#7) " 0
=
=
Al G. Braic
#a ! a " 0
x ! (#x) " 0
E x am p l E
1
Complete the equation to make it true.
Tell which property it shows.
■
Commutative Property of Addition
125 ! 30 " 30 ! 125
E x am p l E
2
Tell what property each example shows.
117 ! 25 " 25 ! 117
Commutative Property of Addition
9!0"9
Zero Property of Addition
(2 ! 5) ! 8 " 2 ! (5 ! 8)
Associative Property of Addition
#3 ! 3 " 0
Additive Inverse
page 110
Chapter 10 – Lesson 1
E – © CSL Associates, Inc. All rights reserved.
45 ! 0 " 45
Name
P RAC T I C E
Complete the equation to make it true. Name the property you used.
1. x 29 29
x _______
0
zero property
2. (13 7) 50 13 (y 50)
y _______
7
associative property
3. 15 a 0
a _______
15
additive inverse
4. 69 13 b 69
b _______
13
commutative property
Complete the equation to make it true.
5. 21 21 7. 979 6. 93 (7 51) (93 7) 979
9. (144 12) 59 144 (
8. 43 59)
0
10. 0 1,239 Which expression is equivalent to the expression given?
E – © CSL Associates, Inc. All rights reserved.
11. 5 a 9
A
B
C
D
12. m 1
F
G
H
J
5a9
5a9
a59
a5a9
Math
Reasoning
m
mm
mm
mm
Properties
MR 2.3
13. Is there a commutative property for subtraction? Explain.
No. For example: 8 3 ≠ 3 8
Subtraction is not commutative.
If you subtract a smaller number from a larger number, you get
the same difference but it is negative.
Chapter 10 – Lesson 1
page 111
MCX94.HW.CL.G5.FM&Lesson.v211
8/2/04
18:02
Page 74
Name
…at home!
P RAC T I C E
Complete the equation to make it true. Name the property you used.
1. x 31 31
0
x _______
zero property
2. (13 5) 50 13 (y 50)
5
y _______
associative property
3. 18 a 0
18
a _______
additive inverse
4. 83 13 b 83
13
b _______
commutative property
Complete the equation to make it true.
0
5. 33 33 ______
62
6. 93 (7 62) (93 7) ______
0 856
7. 856 ______
29 0
8. 29 ______
16 59)
9. (144 16) 59 144 ( ______
1,654
10. 0 1,654 ______
Which expression is equivalent to the expression given?
A
B
C
D
12. m 3
5a7
F
m
5a7
G
mmm
a57
H
mmm
J
mmm
a5a7
Math
Reasoning
Properties
MR 2.3
13. Is there an associative property for subtraction? Use an example to explain.
?
No. For example: 7 ( 5 2 ) ( 7 5 ) 2
?
7 ( 3 )( 2 ) 2
4≠0
page 74
Home Resource and Homework
Chapter 10 Lesson 1
E – © CSL Associates, Inc. All rights reserved.
11. 5 a 7
MCX94TEG5CH01_32.v7.4.2 2/24/01 19:45 Page 205
Name
P RAC T I C E
Complete the equation to make it true. Name the property you used.
1. x 29 29
x _______
0
zero property
2. (13 7) 50 13 (y 50)
y _______
7
associative property
3. 15 a 0
a _______
15
additive inverse
4. 69 13 b 69
b _______
13
commutative property
Complete the equation to make it true.
5. 21 21 7. 979 0
6. 93 (7 51) (93 7) 0
8. 43 43
979
9. (144 12) 59 144 ( 12
59)
51
0
10. 0 1,239 1,239
Which expression is equivalent to the expression given?
E – © CSL Associates, Inc. All rights reserved.
11. 5 a 9
A
B
C
D
12. m 1
F
G
H
J
5a9
5a9
a59
a5a9
Math
Reasoning
m
mm
mm
mm
Properties
MR 2.3
13. Is there a commutative property for subtraction? Explain.
No. For example: 8 3 ≠ 3 8
Subtraction is not commutative.
If you subtract a smaller number from a larger number, you get
the same difference but it is negative.
Chapter 10 – Lesson 1
Student Book Page
page 111
Name
…at home!
P RAC T I C E
Complete the equation to make it true. Name the property you used.
1. x 31 31
0
x _______
zero property
2. (13 5) 50 13 (y 50)
5
y _______
associative property
3. 18 a 0
18
a _______
additive inverse
4. 83 13 b 83
13
b _______
commutative property
Complete the equation to make it true.
0
5. 33 33 ______
62
6. 93 (7 62) (93 7) ______
0 856
7. 856 ______
29 0
8. 29 ______
16 59)
9. (144 16) 59 144 ( ______
1,654
10. 0 1,654 ______
Which expression is equivalent to the expression given?
A
B
C
D
12. m 3
5a7
F
m
5a7
G
mmm
a57
H
mmm
J
mmm
a5a7
Math
Reasoning
Properties
MR 2.3
13. Is there an associative property for subtraction? Use an example to explain.
?
No. For example: 7 ( 5 2 ) ( 7 5 ) 2
?
7 ( 3 )( 2 ) 2
4≠0
page 74
Home Resource and Homework
Chapter 10 Lesson 1
E – © CSL Associates, Inc. All rights reserved.
11. 5 a 7