Question

I need a brief discussion on properties of integers in the form of an essay or speech. Please answer, I will mark correct answer as brainliest.​

Answer 1

Answer:

There are a few properties of integers which determines its operations. These principles or properties help us to solve many equations. To recall, integers are any positive or negative numbers, including zero. Properties of these integers will help to simplify and answer a series of operations on integers quickly.

All properties and identities for addition, subtraction, multiplication and division of numbers are also applicable to all the integers. Integers include the set of positive numbers, zero and negative numbers which are denoted with the letter Z.

Properties of Integers

Integers have 5 main properties of operation which are:

Closure Property

Associative Property

Commutative Property

Distributive Property

Identity Property

Property 1: Closure Property

Among the various properties of integers, closure property under addition and subtraction states that the sum or difference of any two integers will always be an integer i.e. if x and y are any two integers, x + y and x − y will also be an integer.

Property 2: Commutative Property

The commutative property of addition and multiplication states that the order of terms doesn’t matter, the result will be the same. Whether it is addition or multiplication, swapping of terms will not change the sum or product.

Property 3: Associative Property

The associative property of addition and multiplication states that the way of grouping of numbers doesn’t matter; the result will be same. One can group numbers in any way but the answer will remain same. Parenthesis can be done irrespective of the order of terms.

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Answer 2

Answer:

Integer Property Addition    Multiplication Subtraction   Division

Commutative Property x + y = y+ x x × y = y × x x – y ≠ y – x x ÷ y ≠ y ÷ x

Associative Property x + (y + z) = (x + y) +z x × (y × z) = (x × y) × z (x – y) – z ≠ x – (y – z) (x ÷ y) ÷ z ≠ x ÷ (y ÷ z)

Identity Property x + 0 = x =0 + x x × 1 = x = 1 × x x – 0 = x ≠ 0 – x x ÷ 1 = x ≠ 1 ÷ x

Closure Property x + y ∈ Z x × y ∈ Z x – y ∈ Z x ÷ y ∉ Z

Distributive Property x × (y + z) = x × y + x × z

x × (y − z) = x × y − x × z