Properties

Question 0

Closure property of multiplication

Answer 0

a•b= a real #
5•2= 10

Question 1

Closure Property of addition

Answer 1

a+b= a real #

2+3=5

Question 2

Commutative property of addition

Answer 2

a+b= b+a
3+7= 7+3

Question 3

Commutative property of multiplication

Answer 3

a•b= b•a
9•4= 4•9

Question 4

Associative property of addition

Answer 4

(a+b)+c= a+(b+c)
(2+3)+4= 2+(3+4)

Question 5

Associative property of multiplication:

Answer 5

(ab)c= a(bc)
(2•3)4= 2(3•4)

Question 6

Reflexive property

Answer 6

x=x

2=2

Question 7

Symmetric property

Answer 7

a=b, b=a

7=b, b=7

Question 8

Transitive property

Answer 8

a=b and b=c, then a=c

2=b and b=c, then 2=c

Question 9

Additive identity

Answer 9

a+0=a, 0+a=0

2+0=2, 0+2=2

Question 10

Additive inverse

Answer 10

a+(-a)=0, -a+a=0

7+(-7)=0, -7+7=0

Question 11

Property of opposites of a sum

Answer 11

• (a+b)= -a+(-b)

- (2+3)= -2+(-3)

Question 12

Definition of subtraction

Answer 12

a-b= a+(-b)

3-2=3+(-2)

Question 13

Distributive property with respect to addition

Answer 13

a(b+c)= ab+ac
2(3+4)= 2•3+2•4

Question 14

Distributive property with respect to subtraction

Answer 14

a(b-c)= ab-ac
2(3-4)= 2•3-2•4

Question 15

Multiplicative identity

Answer 15

a(1)=a

7(1)=7

Question 16

Multiplicative property of zero

Answer 16

a(0)=0

7(0)=0

Question 17

Multiplicative property of -1

Answer 17

a(-1)=-a

7(-1)=-7

Question 18

Property of opposites

Answer 18

(-a)(b)= -ab, a(-b)= -ab, (-a)(-b)= ab
(-2)(3)= -6

Question 19

Multiplicative inverse

Answer 19

a•1/a= 1

2• 1/2= 1

Question 20

Property of reciprocal products

Answer 20

1/ab= 1/a • 1/b
1/2•3= 1/2 • 1/3

Question 21

Definition of division

Answer 21

a/b = a• 1/b
2/3 = 2• 1/3