Answer to Question #197338 in Algebra for Accordance

Question

• The identity property has two parts:

– 0 is the identity element for addition (or the additive

identity of number), meaning a number stays the

same if 0 is added to it.

– 1 is the identity element for multiplication (or

the multiplicative identity of number), meaning numbers stay the same if multiplied by 1.

It is also true that 0 subtracted from any number leaves the number unchanged; and that any number divided by 1 leaves the number unchanged.

• The zero product property. The product of numbers multiplied by each other is 0 only if at least one of them is 0.

• The density property. Between any two real numbers there is another real number.

  • Distributive property

Example:

4 (2 t + 5) = 8 t + 2 0 Do the following:

3 (3 t + 7) =

• Additive identity 7u + 0= 7u

• Multiplicative identity

5 v × 1 = 5v

• Zero product property

Example:

(2w-3)(3w+2)=0,meansthat either (2 w + 3) = 0 or (3w+2) = 0

Do the following:

3 x (4 x - 3) =0

Answer 1

Distributive property

3 (3 t + 7) = 9 t + 21

Additive identity

7 u + 0= 7 u, means that the expression 7 u stays the same

if 0 is added to it, 0 is the identity element for addition.

Multiplicative identity

5 v × 1 = 5 v, means that the expression 5 v stays the same

being multiplied by 1, 1 is the identity element for multiplication.

Zero product property

3 x (4 x - 3) = 0, mean sthat either 3x = 0 or (4 x - 3) = 0