Best Answer

Usually, the identity of addition property is defined to be an axiom (which only specifies the existence of zero, not uniqueness), and the zero property of multiplication is a consequence of existence of zero, existence of an additive inverse, distributivity of multiplication over addition and associativity of addition.

Proof of 0 * a = 0:

0 * a = (0 + 0) * a [additive identity]

0 * a = 0 * a + 0 * a [distributivity of multiplication over addition]

0 * a + (-(0 * a)) = (0 * a + 0 * a) + (-(0 * a)) [existence of additive inverse]

0 = (0 * a + 0 * a) + (-(0 * a)) [property of additive inverses]

0 = 0 * a + (0 * a + (-(0 * a))) [associativity of addition]

0 = 0 * a + 0 [property of additive inverses]

0 = 0 * a [additive identity]

A similar proof works for a * 0 = 0 (with the other distributive law if commutativity of multiplication is not assumed).

Q: What is the difference between the zero property of multiplication and the identity property of addition?

Write your answer...

Submit

Still have questions?

Continue Learning about Algebra

The multiplication properties are: Commutative property. Associative property. Distributive property. Identity property. And the Zero property of Multiplication.

Because you can do the same with the Identity Property of Addition. Here's an example: 5 + 0 = 5 5 - 0 = 5 The same goes for multiplication/division.

Addition identity.

There are two forms of identity property. The first is in addition and states that anything plus zero will be itself while in multiplication the rule states that anything times one is its self.

There are many properties of multiplication. There is the associative property, identity property and the commutative property. There is also the zero product property.

Related questions

zero property of multiplication commutative property of multiplication identity property of addition identity prpertyof multiplication your welcome:-)

the distributed property,commmutative properties of addition and multiplication,Associative properties of addition and multiplication,additive identity, multiplicative identity.

meaning of identity property of multiplication

Identity property of multiplication

The, "Identity Property Of Multiplication," is a number multiplied by one, produces the original number. Example: 51x1=51 : Identity Property Of Multiplication

The concept of an identity property in arithmetic is of a process that does not alter the identity of a number, so with respect to addition, the number zero has the identity property; you can add zero to a number and that number does not change. With multiplication, the number one has the identity property; you can multiply anything by one, and it doesn't change.

Addition and subtraction property of equalityMultiplication and division property of equalityDistributive property of multiplication over additionAlso,Identity property of multiplicationZero property of addition and subtraction.

It is called Identity Property of Multiplication

The distributive property of multiplication over addition and the identity property of multiplication. RS + RS = 1*RS + 1*RS (using identity property) = (1 + 1)*RS (using distributive property) = 2*RS

Commutative Property of addition and multiplication...3+2=2+3 Associative Property of addition and multiplication...(5*13)*2=5*(13*2) Additive Identity Property...nn, hkvcytuyrxtezstdxfcgvh5+0=5 Multiplication Identity Property...10*1=10 Additive inverse property...72+(-72)=0 Add the opposite Property...6-8=6+(-8) Multiplication Property of Zero...0*3=0

The multiplication properties are: Commutative property. Associative property. Distributive property. Identity property. And the Zero property of Multiplication.

1 is the identity element of multiplication.