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Multiplication Properties

In mathematics, multiplication is one of the important and basic arithmetic operations. Multiplying integer’s mean scaling a number by another. Integer is nothing but using notational symbol represents numbers.

Basic properties of multiplication, such as associative, commutative, distributive, zero and multiplicative identity.

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Properties of Multiplication

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To study multiplying integers, we have to know five basic properties such as associative, commutative, distributive, zero and multiplicative identity. These multiplication properties are described as below.

  • Commutative property
  • Associative property
  • Multiplicative identity property
  • Distributive property
  • Zero property


Commutative property:


Product of two numbers is same even we change their order.

That is, a x b = b x a.

Example: 5 x 4 = 4 x 5 = 20

Associative Property:

Product of three numbers is same even we change their order.

That is, (a x b) x c = a x (b x c).

Example: 5 x (4 x 3) = (5 x 4) x 3 = 60

Identity Property:

This property states that if we multiply any number with one the result is number itself.

That is, a x 1 = a. One is the multiplicative identity

Example: 9 x 1 = 9.

Distributive property:

Multiplication of a number with the addition of two numbers is same as addition of two products.

That is, a x (b + c) =ab + ac.

Example: 5 x (4 + 3) = (5 x 4) + (5 x 3).

= 20 + 15.
= 35


Zero property:

Any thing multiply with zero is zero. That is, a x 0 = 0.

Example: 7 x 0 = 0

Multiplication Rules

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Positive x Positive = Positive

Negative x Negative =Positive

Positive x Negative = Negative

Negative x Positive = Negative

The following examples are to study multiplying integers with multiplication rule

5 x 4 = 20

(-5) x (-4) = 20

5 x (-4) = (-20)

(-5) x 4 = (-20)


Multiplication Grid

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Multiplication Grid

Multiplication Methods

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Below are the multiplication methods:

Method 1:

Multiplying integers of 345 x 6

Solution:

Here, 5 is at unit place, so we do 5 x 1 = 5 x 6 = 30

4 is at 10's place, so we do 4 x 10 = 40 x 6 = 240

3 is at 100's place, so we do 3 x 100 = 300 x 6 = 1800

The product result = 2070


Method 2:

Multiplying integers of 345 x 6

Solution:

345

x 6
--------------
3 0
2 4 0
1 8 0 0
--------------
2 0 7 0
--------------

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