example 3 identifying properties tell which property is being illustrated. inverse property of...

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