Math, asked by addyamishra2009, 8 months ago

Commutative property is satisfied in integers w.r.t.
(A) -, +
(B) -, *
(C) +, -

Answers

Answered by rameshckp2588

plus and minus solve it

Answered by Bisman115119

There are a few properties of integers which determine 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.

Z = {……….−5, −4, −3, −2, −1, 0, 1, 2, 3, 4, 5,………}

Properties Of Integers

Properties of Integers

Integers have 5 main properties of operation which are:

Closure Property

Associative Property

Commutative Property

Distributive Property

Identity Property

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

The explanation of each of the integer properties is given below.

Example 5: 4 − (−6) = 10 ; (−6) – 4 = −10

⇒ 4 − (−6) ≠ (−6) – 4

Ex: 10 ÷ 2 = 5 ; 2 ÷ 10 = 1/5

⇒ 10 ÷ 2 ≠ 2 ÷ 10

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 the same. One can group numbers in any way but the answer will remain the same. Parenthesis can be done, irrespective of the order of terms. Let x, y and z be any three integers, then

⇒ x + (y + z) = (x + y) +z

⇒ x × (y × z) = (x × y) × z

Example 6: 1 + (2 + (-3)) = 0 = (1 + 2) + (−3);

1 × (2 × (−3)) =−6 = (1 × 2) × (−3)

Subtraction of integers is not associative in nature i.e. x − (y − z) ≠ (x − y) − z.

Example 7: 1 − (2 − (−3)) = −4; (1 – 2) – (−3) = −2

1 – (2 – (−3)) ≠ (1 − 2) − (−3)

Property 4: Distributive Property

The distributive property explains the distributing ability of operation over another mathematical operation within a bracket. It can be either distributive property of multiplication over addition or distributive property of multiplication over subtraction. Here, integers are added or subtracted first and then multiplied or multiply first with each number within the bracket and then added or subtracted. This can be represented for any integers x, y and z as:

⇒ x × (y + z) = x × y + x × z

⇒ x × (y − z) = x × y − x × z

Example 8: −5 (2 + 1) = −15 = (−5 × 2) + (−5 × 1)

Property 5: Identity Property

Among the various properties of integers, additive identity property states that when any integer is added to zero it will give the same number. Zero is called additive identity. For any integer x,

x + 0 = x = 0 + x

The multiplicative identity property for integers says that whenever a number is multiplied by 1 it will give the integer itself as the product. Therefore, 1 is called the multiplicative identity for a number. For any integer x,

x × 1 = x = 1 × x

If any integer multiplied by 0, the product will be zero:

x × 0 = 0 =0 × x

If any integer multiplied by -1, the product will be opposite of the number:

x × (−1) = −x = (−1) × x

Video Lesson Related to Integer Properties:

Commutative property is satisfied in integers w.r.t.(A) -, +(B) -, *(C) +, -​

Answers

Commutative property is satisfied in integers w.r.t.
(A) -, +
(B) -, *
(C) +, -