Name
LESSON
Date
Class
Review for Mastery
3-1 Properties of Rational Numbers
You can use the Commutative Property, the Associative Property, and the Distributive
Property with mental math to simplify expressions.
1
1
20 ! 9 ! !4! " 20 ! !4! ! 9
Commutative Property of Multiplication
1
" (20 ! !4! ) ! 9
"5!9
Associative Property of Multiplication
" 45
Multiply.
Multiply.
7(22) " 7(20 # 2)
Rewrite 22 as a sum.
" 7 ! 20 # 7 ! 2
Distributive Property
" 140 # 14
Multiply.
" 154
Add.
Simplify each expression. Fill in the names of the properties you used.
1. 65 # 17 # 15 " 65 # 15 #
" (65 #
"
Property of
)#
Property of
#
"
1
1
2. 18 ! 7 ! !9! " 18 ! !9! !
"(
Property of
)!
!
Property of
!
"
"
5. 6(49) " 6(50 $
"6!
"
)
$6!
Property
$
"
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
8
Holt Mathematics
Practice B
3-1 Properties of Rational Numbers
Practice A
3-1 Properties of Rational Numbers
LESSON
LESSON
Name the property that is illustrated in each equation.
1
1
2. 4 ! (3 ! p) " (4 ! 3) ! p
1. 16 # !! " !! # 16
Tell which property is shown.
2. 7 # m " m # 7
1. (4.5 ! 2) ! 8 " 4.5 ! (2 ! 8)
2
3
2
Simplify each expression. Write a reason for each step.
Simplify each expression. Write a reason for each step.
5. 22 # 19 # 8
5. 38 # 19 # 2
22 # 19 # 8 " 22 # 8 # 19
Reason: Commutative Property of Addition
Reason:
30
49
Reason:
Add.
Reason:
Comm. Prop. of Mult.
Reason:
Assoc. Prop. of Mult.
"
# 19
Reason: Add.
(38 # 2) # 19
"
40 # 19
59
"
1
6. 8 ! 7 ! !4!
"
1
1
8
8 ! 7 ! !4! " 7
! !4!
7
14
"
"
1
8
"7!(
! !4!)
2
!
1
6. !3! ! 8 ! 18
1
!!
3
! 8 ! 18 "
Reason: Multiply.
"
Multiply.
Reason:
7. 7(13)
3
7(13) " 7(10 #
"
70
"
91
#
Reason:
"
120 $ 4
"
7 ! 30 # 7 ! 1
"
5 ! 30 $ 5 ! 2
"
116
"
210 # 7
"
150 $ 10
"
217
"
140
12 # 4
)#n
Holt Mathematics
6
You can use the Commutative Property, the Associative Property, and the Distributive
Property with mental math to simplify expressions.
2.7
1
5
1
20 ! 9 ! !4! " 20 ! !4! ! 9
Commutative Property of Multiplication
1
(3 # 6) " 5 ! 3 # 5 ! 6
Distrib. Prop.
Simplify each expression. Write a reason for each step.
" (20 ! !4! ) ! 9
"5!9
Associative Property of Multiplication
" 45
Multiply.
Multiply.
7(22) " 7(20 # 2)
2
Reason:
Comm. Prop. of Mult.
Reason:
Assoc. Prop. of Mult.
Reason:
Mult.
Mult.
2
(50 ! !5!) ! 6
20! 6
120
Reason:
Rewrite 22 as a sum.
" 7 ! 20 # 7 ! 2
Distributive Property
" 140 # 14
Multiply.
" 154
Add.
Simplify each expression. Fill in the names of the properties you used.
17
15 ) # 17
80 # 17
97
Commutative
Associative
1. 65 # 17 # 15 " 65 # 15 #
6. 3.7 # 9 # 1.3
" (65 #
3.7 # 1.3 # 9
Reason:
Comm. Prop. of Add.
(3.7 # 1.3) # 9
5#9
14
Reason:
Assoc. Prop. of Add.
Add.
Add.
3.7 # 9 # 1.3 "
"
"
"
Reason:
Reason:
"
"
2. 18 ! 7 !
"
8. 7(99)
"
3(100 # 4)
3 ! 100 # 3 ! 4
"
7(100 $ 1)
7 ! 100 $ 7 ! 1
"
300 # 12
"
700 $ 7
"
312
"
693
7(99)"
"
7
Copyright © by Holt, Rinehart and Winston.
Holt Mathematics
50
300 $
294
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
87
1
!!
9 )!
18 !
2 ! 7
14
"6!
"
7
1
! !9! !
5. 6(49) " 6(50 $
"
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
1
!! " 18
9
"(
Write each product using the Distributibe Property. Then simplify.
7. 3(104)
Holt Mathematics
Review for Mastery
3-1 Properties of Rational Numbers
4.
50 ! !5! ! 6
5(30 $ 2)
5(28)"
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Comm. Prop. of Mult.
7x
8. 5(28)
LESSON
2. 2.7 ! 8 " 8 !
Distrib. Prop.
"
Assoc. Prop. of Mult.
Multiply.
Multiply.
Reason:
21
Assoc. Prop. of Add.
"
Reason:
7(30 # 1)
7(31) "
Complete each equation. Then name the property that is illustrated.
2
Comm. Prop. of Mult.
7. 7(31)
Practice C
3-1 Properties of Rational Numbers
50 ! 6 ! !5! "
Reason:
1
)
4 ! 30 $ 4 ! 1
LESSON
2
5. 50 ! 6 ! !5!
Reason:
Assoc. Prop. of Add.
Add.
Add.
"
5
3. 7(5 # x ) " 7 ! 5 #
Reason:
Write each product using the Distributibe Property. Then simplify.
4(29)" 4(30 $
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
1. 12 # (4 # n) " (
Comm. Prop. of Add.
3
)
" 7 ! 10 # 7 !
6!8
48
"
8. 4(29)
Reason:
Reason:
1
!! ! 18 ! 8
3
1
!!3! ! 18" ! 8
"
Write each product using the Distributibe Property. Then simplify.
3(104) "
38 # 2 # 19
38 # 19 # 2 "
Assoc. Prop. of Add.
" (22 # 8) # 19
"
"
Comm. Prop. of Mult.
Assoc. Prop. of Add.
Assoc. Prop. of Add.
Comm. Prop. of Mult.
Assoc. Prop. of Mult.
4. 6 ! 1.5 " 1.5 ! 6
3. (11 # m) # 9 " 11 # (m # 9)
4. (4 # y ) # 12 " 4 # (y # 12)
3. 6 ! !3! " !3! ! 6
3
Comm. Prop. of Add.
Comm. Prop. of Add.
Assoc. Prop. of Mult.
1
7
Property of
Addition
Addition
Commutative
Property of
Multiplication
Associative
Property of
Multiplication
Distributive
Property
Property of
)
$6!
1
6
8
Holt Mathematics
Holt Mathematics