Question

if a and b are integers, then which property is shown in a+b=b+a​

Answer 1

Answer:

Integers

Integers are the set of whole numbers and their negatives. It is represented by Z. Z = {…-3, -2, -1, 1, 2, 3, …}. The direction of an integer is indicated by its sign (+ or –), that it is right of 0 or left of 0 on the number line.

Properties of addition and subtraction of integers: a) Integers are closed under addition and subtraction. If a and b are two integers, then (a + b) and (a – b) are also integers.

b) Integers are commutative under addition. {a + b = b + a} c) Integers are associative under addition. {(a + b) + c = a + (b + c)} d) The integer 0 is the additive identity. {a + 0 = a = 0 + a} e) For any integer ‘a’, its additive inverse is ‘–a’.

Multiplication of integers: The product of two positive integers is a positive integer. The product of a negative integer and a positive integer is a negative integer.

The product of two negative integers is a positive integer. The product of even number of negative integers is a positive integer. The product of odd number of negative integers is a negative integer.

Properties of multiplication of integers:

a) Integers are closed under multiplication. { a × b is an integer for any two integers a and b}

b) Multiplication is commutative for integers. { a × b = b × a}

c) The integer 1 is the identity under multiplication. {a × 1= a = 1 × a}

d) Integers are associative under multiplication. {(a × b) × c = a × (b × c)}

Distributive property of integers: a × (b + c) = a × b + a × c Division of a positive integer by a negative integer gives a negative integer as quotient and vice-versa. However, when a negative integer is divided by another negative integer, the quotient obtained is a positive integer. For any integer a, a ÷1 = a and a ÷ 0 is not defined. Keywords: ascending and descending order of integers, predecessor, successor

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Answer 2

Commutative property.

Step-by-step explanation:

• When a and b are two integers, that are joined by an operation, for example, addition or multiplication, that is + or .,

      the property of commutativity of integers is that,

a + b = b + a

Or

a.b = b.a

• This means the when we attempt to change the order of the operands, or to be precise, addends when it comes to the addition of integers, the remains exactly the same as it was when the operands or in case of addition, when the addends were not allowed to change their positions.
• Apart from addition, the commutative property for integers does not hold for the operations of subtraction and division as the entire result gets changed on the swapping of the operands.

Thus, this is the commutative property.

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