EXAMPLE 3 Identifying Properties ell which property is being illustrated. Inverse property of multiplication Inverse property of addition Commutative property of addition Identity property of multiplication = 1 a. 5 4 4 5 – – b. –3.5 + 3.5 = 0 c. –4 + 8 = 8 + (–4) d. (–7.9)(1) = –7.9
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EXAMPLE 3 Identifying Properties
Tell which property is being illustrated.
Inverse property of multiplication
Inverse property of addition
Commutative property of addition
Identity property of multiplication
= 1a. 54
45– –
b. –3.5 + 3.5 = 0
c. –4 + 8 = 8 + (–4)
d. (–7.9)(1) = –7.9
EXAMPLE 4 Using Familiar Properties
Evaluate the expression. Justify each step.
= 3 + [( 10.6) + ( 4.4)]
= 3 + ( 10.6) + ( 4.4)
10.6 + 3 + ( 4.4)a.
Commutative property of addition
Associative property of addition
Add –10.6 and –4.4.
Add 3 and –15.
= 3 + ( 15)
= 12
EXAMPLE 4 Using Familiar Properties
= 7[( 25)( 4)]
= 7( 25)( 4)
= 7(100) = 700
–25(7)(–4)b.
Multiply –25 and –4, multiply 7 and 100.
Commutative property of multiplication
Associative property of multiplication
Evaluate the expression. Justify each step.
EXAMPLE 5 Using Properties
Commutative property of addition
Associative property of addition
Inverse property of addition
Identity property of addition
32a.
32+ 10
7 +
= 32
32+10
7 +
= 107 + 0
107=
32
32+10
7 +=
EXAMPLE 5
Associative property of multiplication
Inverse property of multiplication
Identity property of multiplication
35
74
47b.
74
35
47=
35 1=
35=
Using Properties
GUIDED PRACTICE for Examples 3, 4, and 5
3. 3 + 0 = 3
Tell which property is being illustrated.
4. 15 8 = 8 15
Identity property of additionANSWER
Commutative property of multiplicationANSWER
5. (5 + 4) + 6 = 5 + (4 + 6)
ANSWER Associative property of addition
GUIDED PRACTICE
Evaluate the expression. Justify each step.
6. 3.5 + [( 3) + 6.5]
= (3.5 + 6.5) + (–3)
= 10 + (– 3) = 7 Add 3.5 and 6.5, then 10 and – 3
Commutative property of addition
Associative property of addition
3.5 + [6.5 + (–3)]
for Examples 3, 4, and 5
GUIDED PRACTICE
7. 5( 9) ( 4)
= [5(–4)] (–9)
= –20 (–9) = 180
Associative property of multiplication
Multiply 5 and –4, then –20 and –9
Evaluate the expression. Justify each step.
= 5(–4) (–9) Commutative property of multiplication
for Examples 3, 4, and 5
GUIDED PRACTICE
8. 6(3) ( 5)
= –6(–5) (3)
= [–6(–5)] (3)
= 30(3) = 90 Multiply –6 and –5, then 30 and 3
Commutative property of multiplication
Associative property of multiplication
Evaluate the expression. Justify each step.
for Examples 3, 4, and 5
GUIDED PRACTICE
9. 2.8 + 7 + ( 1.8)
= 2.8 + (–1.8) + 7
= [2.8 + (–1.8)] + 7
= 1 + 7 = 8
Commutative property of addition
Add 2.8 and –1.8, then 1 and 7
Associative property of addition
Evaluate the expression. Justify each step.
for Examples 3, 4, and 5
GUIDED PRACTICE
0.5(7)(8)10.
Evaluate the expression. Justify each step.
= [0.5(8)](7)
= 4(7) = 28
Associative property of multiplication
Multiply 0.5 and 8, then 4 and 7
= 0.5(8)(7) Commutative property of multiplication
for Examples 3, 4, and 5
GUIDED PRACTICE
0.9 + [9.1 + ( 2)]11.
= (0.9 + 9.1) + (–2)
= 10 + (–2) = 8 Add 0.9 and 9.1, then 10 and –2
Associative property of addition
Evaluate the expression. Justify each step.
for Examples 3, 4, and 5
GUIDED PRACTICE
94 + 87 + ( 94)12.
= 94 + (–94) + 87
= [94 + (–94)] + 87
= 0 + 87
= 87
Associative property of addition
Identity property of addition
Commutative property of addition
Inverse property of addition
Evaluate the expression. Justify each step.
for Examples 3, 4, and 5
GUIDED PRACTICE
53 + ( 25) + 5313.
= –53 + 53 + (–25)
= (–53 + 53) + (–25)
= 0 + (–25)
= –25
Associative property of addition
Identity property of addition
Commutative property of addition
Inverse property of addition
Evaluate the expression. Justify each step.
for Examples 3, 4, and 5
GUIDED PRACTICE
Associative property of multiplication
Identity property of multiplication
Inverse property of multiplication
= 65
= 65
31 3
= 65
31 3
= 65 1
31
6514. 3
Commutative property of multiplication
Evaluate the expression. Justify each step.
for Examples 3, 4, and 5
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