1. Tell which property is being illustrated.
EXAMPLE 3
Identifying Properties
Tell which property is being illustrated.
= 1 a. 5 4 –
Inverse property of multiplication b. –
= 0
Inverse property of addition c.
–4 + 8
= 8 + (–4)
Commutative property of addition d.
(–7.9)(1)
= –7.9
Identity property of multiplication

2. Evaluate the expression. Justify each step.
EXAMPLE 4
Using Familiar Properties
Evaluate the expression. Justify each step.
( 4.4) a.
= 3 + ( 10.6) + ( 4.4)
Commutative property of addition
= 3 + [( 10.6) + ( 4.4)]
Associative property of addition
= 3 + ( 15)
Add –10.6 and –4.4.
= 12
Add 3 and –15.

3. Evaluate the expression. Justify each step.
EXAMPLE 4
Using Familiar Properties
Evaluate the expression. Justify each step.
–25(7)(–4) b.
= 7( 25)( 4)
Commutative property of multiplication
= 7[( 25)( 4)]
Associative property of multiplication
= 7(100)
= 700
Multiply –25 and –4, multiply 7 and 100.

4. EXAMPLE 5
Using Properties 3 2 a. + 10 7 = 3 2 + 10 7
Commutative property of addition 3 2 + 10 7 =
Associative property of addition = 10 7
+ 0
Inverse property of addition 10 7 =
Identity property of addition

5. EXAMPLE 5 3 5 7 4 b. 7 4 3 5 = 3 5 1 = 3 5 = Using Properties
Associative property of multiplication 3 5 1 =
Inverse property of multiplication 3 5 =
Identity property of multiplication

6. Tell which property is being illustrated.
GUIDED PRACTICE
for Examples 3, 4, and 5
Tell which property is being illustrated. 3.
3 + 0 = 3
Identity property of addition
ANSWER 4. =
Commutative property of multiplication
ANSWER 5.
(5 + 4) + 6 = 5 + (4 + 6)
ANSWER
Associative property of addition

7. Evaluate the expression. Justify each step.
GUIDED PRACTICE
for Examples 3, 4, and 5
Evaluate the expression. Justify each step. 6.
3.5 + [( 3) + 6.5]
3.5 + [6.5 + (–3)]
Commutative property of addition =
( ) + (–3)
Associative property of addition =
10 + (– 3) = 7
Add 3.5 and 6.5, then 10 and – 3

8. Evaluate the expression. Justify each step.
GUIDED PRACTICE
for Examples 3, 4, and 5
Evaluate the expression. Justify each step. 7.
5( 9) ( 4) =
5(–4) (–9)
Commutative property of multiplication =
[5(–4)] (–9)
Associative property of multiplication =
–20 (–9) = 180
Multiply 5 and –4, then –20 and –9

9. Evaluate the expression. Justify each step.
GUIDED PRACTICE
for Examples 3, 4, and 5
Evaluate the expression. Justify each step. 8.
6(3) ( 5) =
–6(–5) (3)
Commutative property of multiplication =
[–6(–5)] (3)
Associative property of multiplication =
30(3) = 90
Multiply –6 and –5, then 30 and 3

10. Evaluate the expression. Justify each step.
GUIDED PRACTICE
for Examples 3, 4, and 5
Evaluate the expression. Justify each step. 9.
( 1.8) =
2.8 + (–1.8) + 7
Commutative property of addition =
[2.8 + (–1.8)] + 7
Associative property of addition =
1 + 7 = 8
Add 2.8 and –1.8, then 1 and 7

11. Evaluate the expression. Justify each step.
GUIDED PRACTICE
for Examples 3, 4, and 5
Evaluate the expression. Justify each step.
0.5(7)(8)
10. =
0.5(8)(7)
Commutative property of multiplication =
[0.5(8)](7)
Associative property of multiplication =
4(7) = 28
Multiply 0.5 and 8, then 4 and 7

12. Evaluate the expression. Justify each step.
GUIDED PRACTICE
for Examples 3, 4, and 5
Evaluate the expression. Justify each step.
0.9 + [9.1 + ( 2)]
11. =
( ) + (–2)
Associative property of addition =
10 + (–2) = 8
Add 0.9 and 9.1, then 10 and –2

13. Evaluate the expression. Justify each step.
GUIDED PRACTICE
for Examples 3, 4, and 5
Evaluate the expression. Justify each step.
( 94)
12. =
94 + (–94) + 87
Commutative property of addition =
[94 + (–94)] + 87
Associative property of addition =
0 + 87
Inverse property of addition = 87
Identity property of addition

14. Evaluate the expression. Justify each step.
GUIDED PRACTICE
for Examples 3, 4, and 5
Evaluate the expression. Justify each step.
53 + ( 25) + 53
13. =
– (–25)
Commutative property of addition =
(– ) + (–25)
Associative property of addition =
0 + (–25)
Inverse property of addition =
–25
Identity property of addition

15. Evaluate the expression. Justify each step.
GUIDED PRACTICE
for Examples 3, 4, and 5
Evaluate the expression. Justify each step. 3 1 6 5
14. = 6 5 3 1
Commutative property of multiplication = 6 5 3 1
Associative property of multiplication = 6 5 1
Inverse property of multiplication = 6 5
Identity property of multiplication