Match the following.

1 .

multiplicative identity

the number 0; when added to any number, the value of the number does not change

2 .

multiplicative inverse

the opposite or negative of a number; the sum of a number and its additive inverse is 0

3 .

commutative property

a property of the real numbers which states that how numbers are grouped in a sum or product does not change the value

4 .

additive identity

a property of the real numbers which states that the order in which numbers are added or multiplied does not change the value

5 .

additive inverse

a(b + c) = ab + ac, or a(b - c) = ab - ac

6 .

associative property

the number 1; when multiplied by any number, the value of the number does not change

7 .

distributive property

the reciprocal of a number; the product of a number and its multiplicative inverse is 1

1. Multiplicative identity:

The number 1; when multiplied by any number, the value of the number does not change.

2. Multiplicative inverse:

The reciprocal of a number; the product of a number and its multiplicative inverse is 1.

3. Commutative property:

a property of the real numbers which states that the order in which numbers are added or multiplied does not change the value

4. Additive identity:

The number 0; when added to any number, the value of the number does not change.

5. Additive inverse:

The opposite or negative of a number; the sum of a number and its additive inverse is 0

6. Associative property:

a property of the real numbers which states that how numbers are grouped in a sum or product does not change the value

7. Distributive property:

a(b + c) = ab + ac, or a(b - c) = ab - ac

Step-by-step explanation:

1. Multiplicative identity:

Ex: 3 × 1 = 3

2. Multiplicative inverse:

Ex: The multiplicative inverse of 2 is 1/2 ⇒ 2 × 1/2 = 1

3. Commutative property:

Ex: 2 + 3 + 5 = 10 ,  3 + 2 + 5 = 10 ,  5 + 3 + 2 = 10

     2 × 3 × 5 = 30 , 3 × 2 × 5 = 30 , 5 × 3 × 2 = 30

4. Additive identity:

Ex: 2 + 0 = 2

5. Additive inverse:

Ex: The additive inverse of 5 is -5 ⇒ 5 + -5 = 0

6. Associative property:

Ex: 2 + (3 + 5) = (2 + 3) + 5

     2× (3 × 5) = (2 × 3) × 5

7. Distributive property:

Ex: 2(3 + 5) = 2 × 3 + 2 × 5

     2(5 - 3) = 2 × 5 - 2 × 3