Question

What are the properties of the multiplication of integers?

Answer 1

The properties of the multiplication of integers:

Integers are a collection of all positive and negative numbers including zero.

• Closure Property of Multiplication:

If two integers $m$ and $n$ are multiplied then their resultant $m\times n$ is also an integer.

• Commutative Property of Multiplication:

Changing the order of the integers does not affect the result of the multiplication.

$m\times n=n\times m$

• Associative Property of Multiplication:

If $m,n\mathrm{and}p$ are three integers. Then, $m\times \left(n\times p\right)=\left(m\times n\right)\times p$

• Distributive Property of Multiplication:

If $m,n\mathrm{and}p$ are three integers. Then, $m\times \left(n+p\right)=\left(m\times n\right)+\left(m\times p\right)$

• Multiplication by zero:

$m\times 0=0\times m=0$

• Multiplicative Identity of Integers:

On multiplying any integer by $1$ the result obtained is the integer itself.

$m\times 1=1\times m=m$