Question

Identify the property illustrated in each mathematical sentence.

1.)7 + 14 = 21

A. Closure Property
B. Commutative Property of Addition
C. Associative Property of Addition
D. Distributive Property
E. Identity Property of Addition
F. Inverse Property of Addition
G. Zero Property

2.) (4) (8) = (8) (4)

A. Closure Property
B.Commutative Property of Multiplication
C. Associative Property of Multiplication
D. Distributive Property
E. Identity Property of Multiplication
F. Inverse Property of Multiplication
G. Zero Property

4.) (6 + 14) + 23 = 6 + (14 + 23)

A. Closure Property
B. Commutative Property of Addition
C. Associative Property of Addition
D. Distributive Property
E. Identity Property of Addition
F. Inverse Property of Addition
G. Zero Property

4.) (5) ( 1/5) = 1

A. Closure Property
B. Commutative Property of Multiplication
C. Associative Property of Multiplication
D. Distributive Property
E. Identity Property of Multiplication
F. Inverse Property of Multiplication
G. Zero Property

5.) 0 + 15 = 15

A. Closure Property
B. Commutative Property of Addition
C. Associative Property of Addition
D. Distributive Property
E. Identity Property of Addition
F. Inverse Property of Addition
G. Zero Property

6) 3 (4 - 5) = 3(4) - 3(5) *

A. Closure Property
B. Commutative Property of Multiplication
C. Associative Property of Multiplication
D. Distributive Property
E. Identity Property of Multiplication
F. Inverse Property of Multiplication
G. Zero Property

7) 12 + 13 = 13 + 12 *

A. Closure Property
B. Commutative Property of Addition
C. Associative Property of Addition
D. Distributive Property
E. Identity Property of Addition
F. Inverse Property of Addition
G. Zero Property​

Answer 1

Step-by-step-Explanation:

Given:

Identify the property illustrated in each mathematical sentence.

1.)7 + 14 = 21

A. Closure Property

B. Commutative Property of Addition

C. Associative Property of Addition

D. Distributive Property

E. Identity Property of Addition

F. Inverse Property of Addition

G. Zero Property

Ans: Closure Property

Option A is correct.

Explanation: Closure property states that if two real numbers are added than result must be a unique real number.

Thus,

$7 + 14 = 21$, follows the closure property.

2.) (4) (8) = (8) (4)

A. Closure Property

B.Commutative Property of Multiplication

C. Associative Property of Multiplication

D. Distributive Property

E. Identity Property of Multiplication

F. Inverse Property of Multiplication

G. Zero Property

Ans: Commutative Property of Multiplication

Option B is correct.

Explanation: Commutative Property of Multiplication states that if two real numbers are multiplied than result must be same when numbers are reversed.

i.e. $a \times b = b \times a$

Thus,

$(4)(8) = (8)(4)$, follows the Commutative Property of Multiplication.

4.) (6 + 14) + 23 = 6 + (14 + 23)

A. Closure Property

B. Commutative Property of Addition

C. Associative Property of Addition

D. Distributive Property

E. Identity Property of Addition

F. Inverse Property of Addition

G. Zero Property

Ans: Associative Property of Addition

Option C is correct.

Explanation: Associative Property of Addition states that

$(a + b) + c = a + (b + c)$

Thus,

$(6 + 14) + 23 = 6 + (14 + 23)$, follows the Associative Property of Addition.

4.) (5) ( 1/5) = 1

A. Closure Property

B. Commutative Property of Multiplication

C. Associative Property of Multiplication

D. Distributive Property

E. Identity Property of Multiplication

F. Inverse Property of Multiplication

G. Zero Property

Ans: Inverse Property of Multiplication

Option F is correct.

Explanation: Inverse Property of Multiplication states that

$a \times \frac{1}{a} = 1$

Thus,

$5 \times \frac{1}{5} = 1$, follows the Inverse Property of Multiplication.

5.) 0 + 15 = 15

A. Closure Property

B. Commutative Property of Addition

C. Associative Property of Addition

D. Distributive Property

E. Identity Property of Addition

F. Inverse Property of Addition

G. Zero Property

Ans: Identity Property of Addition

Option E is correct.

Explanation: Identity Property of Addition states that

$a + 0 = a$

Thus,

$0 + 15 = 15$, follows Identity Property of Addition.

6) 3 (4 - 5) = 3(4) - 3(5) *

A. Closure Property

B. Commutative Property of Multiplication

C. Associative Property of Multiplication

D. Distributive Property

E. Identity Property of Multiplication

F. Inverse Property of Multiplication

G. Zero Property

Ans: Distributive Property

Option D is correct.

Explanation: Distributive Property states that

$a(b \pm \: c) = ab \: \pm \: bc$

Thus,

$3(4 - 5) = 3(4) - 3(5)$, follows the Distributive Property.

7) 12 + 13 = 13 + 12

A. Closure Property

B. Commutative Property of Addition

C. Associative Property of Addition

D. Distributive Property

E. Identity Property of Addition

F. Inverse Property of Addition

G. Zero Property

Ans: Commutative Property of Addition

Option B is correct.

Explanation: Commutative Property of Addition states that if two real numbers are added than result must be same when numbers are reversed.

i.e.

$a + b = b + a$

Thus,

$12 + 13 = 13 + 12$, follows the Commutative Property of Addition.

Hope it helps you.

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